Math Homework Answers - Recent questions and answers
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Powered by Question2AnswerAnswered: (a) What is the rate of change in sales volume when the price is $23? (Round your answer to three decimal places.)
https://www.mathhomeworkanswers.org/252704/change-sales-volume-price-round-answer-three-decimal-places?show=252705#a252705
<p style="text-align:justify">I suspect the given equation is incorrect because, as written, it is linear and that means the rate of change of volume is constant independent of price. Also there would be an increase in volume when the price increased, not a decrease because dy/dp would be positive. Please check.</p>
<p style="text-align:justify">a) If y=31(3p+1)^(-2/5)=31(3p+1)⁻⁰⋅⁴ then:</p>
<p style="text-align:justify">dy/dp=-12.4(3p+1)⁻¹⋅⁴×3=-37.2(3p+1)⁻¹⋅⁴.</p>
<p style="text-align:justify">When p=23, dy/dp=-0.097 (thousands of units per dollar).</p>
<p style="text-align:justify">b) This means that when p=$23, the volume is decreasing by 97 units per dollar increase of the price.</p>
<p style="text-align:justify">We can write dy=-0.097dp, as long as dp, the increase in price, is quite small, which means that if dp=$1 then dy=-0.097, a decrease of 97 units approximately.</p>
<p style="text-align:justify">Another approach is to avoid calculus and simple calculate y for p=$23 and p=$24. The difference in the y values gives the decrease in units. When we do this, the decrease is nearer to 94 units.</p>Calculus Answershttps://www.mathhomeworkanswers.org/252704/change-sales-volume-price-round-answer-three-decimal-places?show=252705#a252705Wed, 20 Jun 2018 06:25:25 +0000Answered: if you are given a figure and rotation image of the figure,
https://www.mathhomeworkanswers.org/105422/if-you-are-given-a-figure-and-rotation-image-of-the-figure?show=252703#a252703
<p style="text-align:justify"><span style="font-size:14px">Let O(h,k) be a point in an x-y Cartesian frame of reference. O is the origin of another Cartesian frame of reference parallel to the x-y plane. Now let P'(x',y') be a point in the second frame of reference. O'(0,0) is the origin in this plane and is equivalent to O(h,k) in the first frame of reference. So we can write x=x'+h and y=y'+k. That’s translation. </span></p>
<p style="text-align:justify"><span style="font-size:14px">Let O'P'=r and the angle between O'P' and the x' axis be θ. We can write x'=rcosθ and y'=rsinθ. Now we rotate P' anti-clockwise ɸ degrees about O'.</span></p>
<p style="text-align:justify"><span style="font-size:14px">The new position of P' after rotation is given by polar coordinates r and θ+ɸ.</span></p>
<p style="text-align:justify"><span style="font-size:14px">So the new values for x' and y' are:</span></p>
<p style="text-align:justify"><span style="font-size:14px">x''=rcos(θ+ɸ)=rcosθcosɸ-rsinθsinɸ=x'cosɸ-y'sinɸ,</span></p>
<p style="text-align:justify"><span style="font-size:14px">y''=rcos(θ+ɸ)=rsinθcosɸ+rcosθsinɸ=y'cosɸ+x'sinɸ.</span></p>
<p style="text-align:justify"><span style="font-size:14px">But x'=x-h and y'=y-k so the point (x'',y'') becomes ((x-h)cosɸ-(y-k)sinɸ,(y-k)cosɸ+(x-h)sinɸ). In the first frame of reference these become </span><span style="font-size:14px">(h+</span><span style="font-size:14px">(x-h)cosɸ-(y-k)sinɸ,k+</span><span style="font-size:14px">(y-k)cosɸ+(x-h)sinɸ).</span></p>
<p style="text-align:justify"><span style="font-size:14px">The point P' becomes P((x-h),(y-k)).</span></p>
<p style="text-align:justify"><span style="font-size:14px">If we are given a point A(a₁,a₂) before translation and rotation, we can relate it to the corresponding point A'(a₁',a₂') on the image with respect to the first frame of reference.</span></p>
<p style="text-align:justify"><span style="font-size:14px">a₁'-h=(a₁-h)cosɸ-(a₂-k)sinɸ,</span></p>
<p style="text-align:justify"><span style="font-size:14px">a₂'-k=(a₂-k)cosɸ+(a₁-h)sinɸ.</span></p>
<p style="text-align:justify"><span style="font-size:14px">From these we get (a₁'-h)²+(a₂'-k)²=(a₁-h)²+(a₂-k)².</span></p>
<p style="text-align:justify"><span style="font-size:14px">We are trying to find h, k and ɸ, but we only have two equations. So we need another point on the original figure and the corresponding point on the rotated image to give us another pair of equations.</span></p>
<p style="text-align:justify"><span style="font-size:14px">Similarly, for a point B:</span></p>
<p style="text-align:justify"><span style="font-size:14px">b₁'-h=(b₁-h)cosɸ-(b₂-k)sinɸ,</span></p>
<p style="text-align:justify"><span style="font-size:14px">b₂'-k=(b₂-k)cosɸ+(b₁-h)sinɸ.</span></p>
<p style="text-align:justify"><span style="font-size:14px">From these we get (b₁'-h)²+(b₂'-k)²=(b₁-h)²+(b₂-k)².</span></p>
<p style="text-align:justify"><span style="font-size:14px">We now have two equations, so we can use them to find the unknown h and k.</span></p>
<p style="text-align:justify"><span style="font-size:14px">(h=)a₁-√((a₁'-h)²+(a₂'-k)²-(a₂-k)²)=b₁-√((b₁'-h)²+(b₂'-k)²-(b₂-k)²).</span></p>
<p style="text-align:justify"><span style="font-size:14px">Similarly, (k=)a₂-√((a₁'-h)²+(a₂'-k)²-(a₁-h)²)=b₂-√((b₁'-h)²+(b₂'-k)²-(b₁-h)²).</span></p>
<p style="text-align:justify"><span style="font-size:14px">Because of size limits on this website, there is insufficient space here to show the solutions for h and k.</span></p>
<p style="text-align:justify"><span style="font-size:14px">Knowing h and k we can move to the second frame of reference and we can calculate for one point (let’s use A) the angle θ that point makes with the x' axis before rotation: tanθ=(a₂-k)/(a₁-h), so θ=arctan((a₂-k)/(a₁-h)). We can write tan(θ+ɸ)=(a₂'-k)/(a₁'-h).</span></p>
<p style="text-align:justify"><span style="font-size:14px">So θ+ɸ=arctan((a₂'-k)/(a₁'-h)). Therefore ɸ=arctan((a₂'-k)/(a₁'-h))-arctan((a₂-k)/(a₁-h)).</span></p>Geometry Answershttps://www.mathhomeworkanswers.org/105422/if-you-are-given-a-figure-and-rotation-image-of-the-figure?show=252703#a252703Tue, 19 Jun 2018 14:46:57 +0000Answered: there is a 3m wide path on the inside running aroud a rectangular park of length 48m and breadth 36m.find the area of the path?
https://www.mathhomeworkanswers.org/213285/there-inside-running-aroud-rectangular-length-breadth-path?show=252690#a252690
area of the rectangle ABCD = L×b = 48×36 =1728msq area of rectangle EFGH = L×b =54×42 =2268 there four area of path = 1728 -2268 = 540msqOther Math Topicshttps://www.mathhomeworkanswers.org/213285/there-inside-running-aroud-rectangular-length-breadth-path?show=252690#a252690Mon, 18 Jun 2018 12:34:55 +0000Answered: For each of the statements opposite, decide whether it is true or false.
https://www.mathhomeworkanswers.org/252679/for-each-the-statements-opposite-decide-whether-true-false?show=252688#a252688
<p style="text-align:justify">(i) True.</p>
<p style="text-align:justify">Let a+b=9n where n is an integer and a and b are integers. So b=9n-a.</p>
<p style="text-align:justify">10a+b=10a+9n-a=9(a+n). Therefore a+n=(10a+b)/9, and, since a, n and b are integers, 10a+b must be divisible by 9 when the sum of the digits is a multiple of 9. The argument can be extended to cases where a and b are positive and less than 10. In cases where a>10, the argument can be extended to consider a=10a₁+a₂ where a₁ and a₂ are less than 10. So in any integer of n digits, their sum is divisible by 9 if the entire integer is divisible by 9.</p>
<p style="text-align:justify">(ii)(a) True. (The sum of the digits is divisible by 3)</p>
<p style="text-align:justify">Let a+b=3n, then 10a+b=10a+3n-a=3(3a+n). 3a+n=(10a+b)/3 so 10a+b is exactly divisible by 3 when a, b and n are integers. See (i) for extension of the argument. </p>
<p style="text-align:justify">(ii)(b) False, ABC must have C=0 or 5, because even multiples of 5 can be represented by 10x and odd multiples by 10x+5 where x is an integer (2x is an even multiple, 2x+1 is an odd multiple).</p>
<p style="text-align:justify">(iii) False. A n-sided polygon has n internal angles.</p>
<p style="text-align:justify">Two non-parallel lines form one internal angle between them. Three open lines form an additional internal angle. (As many external angles are also formed such that the sum of any internal and associated external angle is 360 degrees.) In general, n open lines create n-1 internal angles, because one angle is created between each pair of adjacent lines. When the end lines are connected by another line, two angles are formed, one at each end of the line. The figure created is a polygon, n-gon. If the original number of lines was n, the number of sides of the polygon increases by 1 to n+1 and the number of angles increases by 2 to n-1+2=n+1, the number of sides.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/252679/for-each-the-statements-opposite-decide-whether-true-false?show=252688#a252688Mon, 18 Jun 2018 10:10:14 +0000Answered: Call the prime numbers, in order, p1, p2, p3 and so on.
https://www.mathhomeworkanswers.org/252680/call-the-prime-numbers-in-order-p1-p2-p3-and-so-on?show=252687#a252687
<p style="text-align: justify;">(i) Let the product of the first n prime numbers be N, then the remainder when N+1 is divided by any of the prime factors of N must be 1. p₁=2 and p₂=3, so p₂>2, its subscript. Similarly p₃=5 and p₃>3 its subscript. p₄=7>4 and p₄=p₁×p₂+1. If N+1 is prime, its index must be greater than the index of the largest prime factor of N. If N+1=pᵪ then N+1>χ. If N+1 is a composite, none of its factors can be included in the set of the first n prime numbers, because each of these gives a remainder of 1 when divided into N+1.</p>
<p style="text-align: justify;">(ii) Let the product of the first χ prime numbers be N', where pᵪ is as defined in (i), then we know from (i) that N'+1 must be either a prime itself, or be a composite with a factor greater than pᵪ. That means there is another prime pᵧ>pᵪ. This implies that we can never find an ultimate prime number, because we can either generate a larger prime directly through prime products, or indirectly, because a generated composite has a prime factor greater than the largest we have generated so far. The implication is that the number of primes is infinite.</p>
<p style="text-align: justify;"> </p>Other Math Topicshttps://www.mathhomeworkanswers.org/252680/call-the-prime-numbers-in-order-p1-p2-p3-and-so-on?show=252687#a252687Mon, 18 Jun 2018 09:59:19 +0000Answered: At a supermarket till you have the choice of joining a queue
https://www.mathhomeworkanswers.org/252676/at-a-supermarket-till-you-have-the-choice-of-joining-a-queue?show=252677#a252677
<p style="text-align:justify">Let t=c+an where t=time for one shopper to pass through checkout, c=transaction time (to pay), n=items to be checked out.</p>
<p style="text-align:justify">T=xc+aN where T is total waiting time, x the total number of shoppers in the checkout lines, N=total number of items to be checked out. Assume a and c are constants for all checkouts</p>
<p style="text-align:justify">While waiting you can estimate N for each line and count x.</p>
<p style="text-align:justify">To compare lines use the formula for each line and compare the results. The line with the smallest T is the one to pick.</p>
<p style="text-align:justify">For example, c=30seconds and a=20 seconds (includes presenting, cashing up, and bagging).</p>Other Math Topicshttps://www.mathhomeworkanswers.org/252676/at-a-supermarket-till-you-have-the-choice-of-joining-a-queue?show=252677#a252677Sat, 16 Jun 2018 13:46:40 +0000Answered: what number does 3,5,4 and 7 all go into
https://www.mathhomeworkanswers.org/252667/what-number-does-3-5-4-and-7-all-go-into?show=252672#a252672
<p style="text-align: justify;">The LCM is 3×4×5×7=20×21=420.</p>
<p style="text-align: justify;">2/5=168/420, 2/3=280/420, 3/7=180/420, 3/4=315/420.</p>
<p style="text-align: justify;">So the order is 168/420, 180/420, 280/420, 315/420 that is, 2/5, 3/7, 2/3, 3/4.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252667/what-number-does-3-5-4-and-7-all-go-into?show=252672#a252672Sat, 16 Jun 2018 08:46:30 +0000Answered: how to graph (x^2/5)-(y^2/2)=1
https://www.mathhomeworkanswers.org/24255/how-to-graph-x-2-5-y-2-2-1?show=252666#a252666
<p style="text-align:justify">Draw the asymptotes first. To find them solve x²/5-y²/2=0, (x√0.4+y)(x√0.4-y)=0.</p>
<p style="text-align:justify">The two asymptote lines are y=-x√0.4 and y=x√0.4. </p>
<p style="text-align:justify">Then put y=0 to find the x intercepts, which are x=-√5 and x=√5.</p>
<p style="text-align:justify">The hyperbola can now be drawn so that it passes through (-√5,0) and (√5,0) and is trapped between the asymptote lines on either side of the origin.</p>
<p style="text-align:justify">Before rotation:</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9238400513358784211" style="height:229px; width:400px"></p>Calculus Answershttps://www.mathhomeworkanswers.org/24255/how-to-graph-x-2-5-y-2-2-1?show=252666#a252666Fri, 15 Jun 2018 18:03:38 +0000Answered: how do you find a 180 degree rotation of f(x)=3x^(4)-2x^(3)+x^(2)-4x-5 ?
https://www.mathhomeworkanswers.org/69080/how-do-you-find-a-180-degree-rotation-of-f-x-3x-4-2x-3-x-2-4x-5?show=252665#a252665
<p style="text-align:justify">Replace x with -x: 3x⁴+2x³+x²+4x-5 then negating the whole expression: -3x⁴-2x³-x²-4x+5.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/69080/how-do-you-find-a-180-degree-rotation-of-f-x-3x-4-2x-3-x-2-4x-5?show=252665#a252665Fri, 15 Jun 2018 17:31:20 +0000Answered: a clockwise rotation by an angle of 710 degrees is equivalent what counterclock wise degree
https://www.mathhomeworkanswers.org/68234/clockwise-rotation-degrees-equivalent-counterclock-degree?show=252664#a252664
710=720-10=2 complete clockwise rotations less 10°. Anti-clockwise rotation is 10°.Trigonometry Answershttps://www.mathhomeworkanswers.org/68234/clockwise-rotation-degrees-equivalent-counterclock-degree?show=252664#a252664Fri, 15 Jun 2018 17:27:09 +0000Answered: The coordinates of vertex A′ of ∆A′B′C′ are . The coordinates of vertex B′ of ∆A′B′C′ are . The coordinates of vertex C′ of ∆A′B′C′ are .
https://www.mathhomeworkanswers.org/252661/coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2-coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2-coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2?show=252663#a252663
<p style="text-align:justify">No coords given in question. Let the following apply: A(a(x),a(y)), B(b(x),b(y)), C(c(x),c(y)).</p>
<p style="text-align:justify">A(a(x),a(y))➝A(a(x)-1,a(y)-2)➝A'(a(y)-2,1-a(x))</p>
<p style="text-align:justify">B(b(x),b(y))➝B(b(x)-1,b(y)-2)➝B'(b(y)-2,1-b(x))</p>
<p style="text-align:justify">C(c(x),c(y))➝C(c(x)-1,c(y)-2)➝C'(c(y)-2,1-c(x))</p>
<p style="text-align:justify">EXAMPLE</p>
<p style="text-align:justify">A(-4,5), B(5,2), C(-3,-3)➝A'(3,5), B'(0,-4), C'(-5,4)</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=10248337250289573055" style="height:377px; width:400px"></p>
<p style="text-align:justify">The diagram uses the coords in the example. Track the translation and rotation of each vertex. The blue points show the results of translation and the 90° arcs show the rotation to the final position.</p>Geometry Answershttps://www.mathhomeworkanswers.org/252661/coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2-coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2-coordinates-%E2%88%86a%E2%80%B2b%E2%80%B2c%E2%80%B2?show=252663#a252663Fri, 15 Jun 2018 15:50:55 +0000Answered: Solve the inequality. 4x-1> -9
https://www.mathhomeworkanswers.org/252650/solve-the-inequality-4x-1-9?show=252653#a252653
<p style="text-align: justify;">4x-1>-9, 4x>-8, x>-2.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252650/solve-the-inequality-4x-1-9?show=252653#a252653Thu, 14 Jun 2018 20:12:59 +0000Answered: Solve the following inequality. 4x- 1> -9.
https://www.mathhomeworkanswers.org/252649/solve-the-following-inequality-4x-1-9?show=252652#a252652
<p style="text-align: justify;">4x-1>-9, 4x>-8, x>-2.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252649/solve-the-following-inequality-4x-1-9?show=252652#a252652Thu, 14 Jun 2018 20:10:34 +0000Answered: Paul wants to buy exactly 14 sweets for 10 pounds.
https://www.mathhomeworkanswers.org/103577/paul-wants-to-buy-exactly-14-sweets-for-10-pounds?show=252651#a252651
<p>You could have 5,2,3,4 <strong>or 3,5,4,2 </strong>:)</p>Word Problem Answershttps://www.mathhomeworkanswers.org/103577/paul-wants-to-buy-exactly-14-sweets-for-10-pounds?show=252651#a252651Thu, 14 Jun 2018 18:53:20 +0000Answered: Can a pair of events have a number of outcomes that is prime? Explain
https://www.mathhomeworkanswers.org/252632/can-pair-of-events-have-number-outcomes-that-is-prime-explain?show=252643#a252643
<p style="text-align:justify">If the two events are independent and neither event has only one outcome, the answer is no, because the number of outcomes is the product of the outcomes of each event taken separately. And the product of two numbers, each greater than 1, is a composite number, not a prime. For example, tossing a coin twice. This is a pair of binary events, one event taking place before the other. The outcomes are not related so there are four outcomes: HH, HT, TH, TT (heads and tails) including the order in which they occur (permutation, not merely combination) and this is illustrated by a tree diagram. There are 4 “leaves”.</p>
<p style="text-align:justify">Two events are separated by time and/or space. If the events can be linked by cause and effect (temporal events), so that they are not independent, one of the outcomes of the first event may preclude all but one outcome of the second event. In such a case, the total outcomes for the pair of events could be prime. For example, an astronaut can choose one of two spaceships, one bound for the Moon, the other to Mars. Each spaceship may malfunction at launch time. Or it may not. If it doesn’t malfunction, we can assume that it reaches its destination. The two events are:</p>
<ol>
<li style="text-align:justify">the choice that the astronaut makes; and</li>
<li style="text-align:justify">whether the spaceship malfunctions.</li>
</ol>
<p style="text-align:justify">So there are three (prime number) outcomes.</p>
<ol>
<li style="text-align:justify">The astronaut picks a spaceship that malfunctions, so he’s not going anywhere!</li>
<li style="text-align:justify">The astronaut goes to the Moon.</li>
<li style="text-align:justify">The astronaut goes to Mars.</li>
</ol>
<p style="text-align:justify">So the answer in this case is yes, the number of outcomes can be prime.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252632/can-pair-of-events-have-number-outcomes-that-is-prime-explain?show=252643#a252643Thu, 14 Jun 2018 08:46:07 +0000Answered: the population of 5000 fish is expected to increase by 12% each year. How many fish will there be in 15 years?algebra
https://www.mathhomeworkanswers.org/252631/population-expected-increase-many-fish-there-years-algebra?show=252639#a252639
<p style="text-align: justify;">Each year the growth factor will be (p+0.12p)/p=1.12 where p is the population at the beginning of a particular year. Therefore, after n years the growth is 1.12ⁿ. So the population will increase to 1.12ⁿp where p is the initial population.</p>
<p style="text-align: justify;">If p=5000 and n=15 the increased population will be 1.12¹⁵×5000=27368 approximately.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252631/population-expected-increase-many-fish-there-years-algebra?show=252639#a252639Thu, 14 Jun 2018 08:24:08 +0000Answered: A skid average is measured at 30 feet from a vehicle that has a breaking efficiency of 100% on a road surface of. 56 what is the MIS of the vehicle
https://www.mathhomeworkanswers.org/250093/average-measured-vehicle-breaking-efficiency-surface-vehicle?show=252630#a252630
<p style="text-align:justify">Kinetic energy of vehicle where m=mass and v=velocity is ½mv².</p>
<p style="text-align:justify">If 0.56 is µ, the coefficient of friction, the frictional force is µmg=17.92m where g=32ft/s².</p>
<p style="text-align:justify">The work done by friction=537.6m acting over 30 feet.</p>
<p style="text-align:justify">This counterbalances the KE of the vehicle so 537.6m=½mv². So v²=1075.2 and v=32.79fps=22.36mph approx. (36kph).</p>Word Problem Answershttps://www.mathhomeworkanswers.org/250093/average-measured-vehicle-breaking-efficiency-surface-vehicle?show=252630#a252630Wed, 13 Jun 2018 21:30:30 +0000Answered: Complex Number
https://www.mathhomeworkanswers.org/252592/complex-number?show=252629#a252629
<p style="text-align:justify">We can write 2=e^(ln(2)) and we can write z=a+ib.</p>
<p style="text-align:justify">So 2^z=</p>
<p style="text-align:justify">(e^(ln(2)))^z=</p>
<p style="text-align:justify">e^(zln(2))=</p>
<p style="text-align:justify">e^(ln(2)(a+ib))=</p>
<p style="text-align:justify">e^(aln(2))×e^(ibln(2)). Let r=e^(aln(2)).</p>
<p style="text-align:justify">But e^(ibln(2)) can be expressed as cosθ+isinθ where θ=bln(2).</p>
<p style="text-align:justify">So we have re^iθ to replace the original 2^z, where r is the modulus |2^z|.</p>
<p style="text-align:justify">So r=1=e^(aln(2)) making a=0. Since a is the real part of z, Re(z)=0, answer A.</p>
<p style="text-align:justify"> </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252592/complex-number?show=252629#a252629Wed, 13 Jun 2018 17:10:16 +0000Answered: James can jog twice as fast as he can walk. He jog the first 9 miles to his house and walked the remaining 1.5 miles. If the total trip took 2 hours, then what was his average jogging speed?
https://www.mathhomeworkanswers.org/252607/first-miles-walked-remaining-total-hours-average-jogging-speed?show=252627#a252627
<p style="text-align: justify;">distance=speed times time, so time=distance/speed.</p>
<p style="text-align: justify;">His jogging speed is 2w where w is the walking speed.</p>
<p style="text-align: justify;">So 9/(2w)+1.5/w=2.</p>
<p style="text-align: justify;">Multiply through by 2w: 9+3=4w, 4w=12, w=3mph, his walking speed. So his jogging speed is 6mph.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252607/first-miles-walked-remaining-total-hours-average-jogging-speed?show=252627#a252627Wed, 13 Jun 2018 13:33:48 +0000Answered: Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. How long can a side of his patio be?
https://www.mathhomeworkanswers.org/252608/vince-wants-square-patio-enough-concrete-area-square-patio?show=252626#a252626
<p style="text-align:justify">If the side is length a, then a²=130, a=11.4 feet approx.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252608/vince-wants-square-patio-enough-concrete-area-square-patio?show=252626#a252626Wed, 13 Jun 2018 13:28:41 +0000Answered: The length of the skid marks was 175 feet. What was the speed of the vehicle before the brakes were applied?
https://www.mathhomeworkanswers.org/252610/length-marks-what-speed-vehicle-before-brakes-were-applied?show=252625#a252625
<p style="text-align:justify">The usual formula is d=v²/(2µg) where µ is the coefficient of friction of the road surface. We have to assume a value of µ, so let’s take 0.5. The formula then becomes d=v²/32 for g=32ft/s². So v²=32×175=5600 and v=74.8fps=51mph. For µ=0.4, v=66.9fps=45.6 mph, and for µ=0.6, v=82.0fps=55.9mph. When µ is small the skid is longer for the same speed. If µ=1, v=105.8fps=72.2mph, the maximum speed for maximum friction when the skid length is 175 feet. (When there is no friction, µ=0. This is more or less icy conditions and the skid length is effectively infinite.)</p>
<p style="text-align:justify">The kinetic energy of the vehicle is mv²/2. This energy is dissipated through the work done by friction. The normal force on a flat surface is mg. The frictional force is µmg and the work done is the frictional force acting over the distance d, the skid length. This work is µmgd=mv²/2, and d=v²/(2µg).</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252610/length-marks-what-speed-vehicle-before-brakes-were-applied?show=252625#a252625Wed, 13 Jun 2018 13:22:24 +0000Answered: A hang glider dropped his cell phone from a height of 350 feet. How many seconds did it take for the cell phone to reach the ground?
https://www.mathhomeworkanswers.org/252609/glider-dropped-phone-height-many-seconds-phone-reach-ground?show=252623#a252623
<p style="text-align: justify;">The only force acting on the phone is gravity, which causes all objects to fall at the same rate (neglecting air resistance). The magnitude of this is 32 feet per second per second approx. That means, that for every second of fall the speed increases by 32 ft/sec. the phone starts from rest, zero velocity. After t seconds its speed increases to 32t ft per second. Its average speed is (0+32t)/2=16t. The distance it falls in time t is speed times time = 16t×t=16t² so if t is the time it takes to reach the ground 350=16t². And t=√(350/16)=4.7 seconds approx.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252609/glider-dropped-phone-height-many-seconds-phone-reach-ground?show=252623#a252623Wed, 13 Jun 2018 12:51:05 +0000Answered: How far from the base of the house do you need to place a 15-foot ladder so that it exactly reaches the top of a 12- foot tall wall?
https://www.mathhomeworkanswers.org/252611/from-house-need-place-foot-ladder-that-exactly-reaches-foot?show=252622#a252622
<p style="text-align: justify;">A right triangle is formed between the ladder, the ground and the wall.</p>
<p style="text-align: justify;">The ladder is the hypotenuse so we use Pythagoras: 15²=12²+x² where x is the distance between the foot of the ladder and the wall, so x²=15²-12²=(15-12)(15+12)=3×27=81 sq ft. Therefore x=9 feet, the answer to the question.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252611/from-house-need-place-foot-ladder-that-exactly-reaches-foot?show=252622#a252622Wed, 13 Jun 2018 12:41:07 +0000Answered: A baseball diamond is a square that is 90 feet on each side. What is the distance a catcher has to throw the ball from home to second base?
https://www.mathhomeworkanswers.org/252612/baseball-diamond-square-side-distance-catcher-throw-second?show=252621#a252621
<p style="text-align:justify">I guess that the distance from home to 2nd base is a diagonal of the square.</p>
<p style="text-align:justify">The diagonal is the hypotenuse of the right triangle with legs of length 90 feet.</p>
<p style="text-align:justify">Using Pythagoras, the length of the diagonal is √(90²+90²)=√16200=127.3 feet to the nearest 10th of a foot.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252612/baseball-diamond-square-side-distance-catcher-throw-second?show=252621#a252621Wed, 13 Jun 2018 12:35:07 +0000Answered: A line that passes midway between and is parallel to both x - y = 6 and x - y = -6.
https://www.mathhomeworkanswers.org/252593/line-that-passes-midway-between-and-is-parallel-to-both-and-x?show=252606#a252606
<p style="text-align: justify;">The line passes midway between the x and y intercepts. These are x=-6 and +6 and y=-6 and +6.</p>
<p style="text-align: justify;">Therefore the line passes through the origin (0,0) and has the same slope so y=x is the equation.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252593/line-that-passes-midway-between-and-is-parallel-to-both-and-x?show=252606#a252606Tue, 12 Jun 2018 23:29:38 +0000Answered: Determine the amount of money you will have accrued if you deposited $6000 compounded quarterly for 3 years at 2% interest
https://www.mathhomeworkanswers.org/252599/determine-accrued-deposited-compounded-quarterly-interest?show=252605#a252605
<p style="text-align: justify;">2% annually is 0.5% (0.005) quarterly. So the growth rate is 1.005¹²=1.06168 approx.</p>
<p style="text-align: justify;">Apply this to $6000 and we get $6370.07.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252599/determine-accrued-deposited-compounded-quarterly-interest?show=252605#a252605Tue, 12 Jun 2018 23:17:12 +0000Answered: Limit of a function
https://www.mathhomeworkanswers.org/252591/limit-of-a-function?show=252604#a252604
<p style="text-align: justify;">sin(1/x) becomes indeterminate (between +1 and -1) as x➝0. However sinx➝0 as x➝0 and any value multiplied by 0 is also 0. So the limit appears to be 0, answer A.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/252591/limit-of-a-function?show=252604#a252604Tue, 12 Jun 2018 23:02:36 +0000Answered: A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/10. Find the two integers.
https://www.mathhomeworkanswers.org/252594/positive-another-reciprocals-positive-integers-integers?show=252602#a252602
<p style="text-align: justify;">If one integer is x the other is 2x, so 1/x+1/(2x)=3/10.</p>
<p style="text-align: justify;">Multiply through by 10x: 10+5=3x and 3x=15 making x=5, so the two integers are 5 and 10.</p>
<p style="text-align: justify;">Another way to solve this is to add 1/x and 1/(2x)=3/(2x)=3/10. The 3s cancel: 1/2x=1/10 so 2x=10 and x=5. The other integer is 10.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252594/positive-another-reciprocals-positive-integers-integers?show=252602#a252602Tue, 12 Jun 2018 22:52:52 +0000Answered: A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/8. Find the two integers.
https://www.mathhomeworkanswers.org/252595/positive-difference-reciprocals-positive-integers-integers?show=252601#a252601
<p style="text-align: justify;">If one integer is x the other is 2x. 1/x-1/2x=1/8. Multiply through by 8x: 8-4=x so x=4. The two integers are 4 and 8.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252595/positive-difference-reciprocals-positive-integers-integers?show=252601#a252601Tue, 12 Jun 2018 22:47:02 +0000Answered: Allison can complete a sales route by herself in 6 hours. Working with an associate, she completes the route in 4 hours. How long would it take her associate to complete the route by herself?
https://www.mathhomeworkanswers.org/252597/complete-herself-associate-completes-associate-complete?show=252600#a252600
<p style="text-align: justify;">Allison completes a route in 6 hours. So she can do 1/6 route in 1 hour.</p>
<p style="text-align: justify;">Her associate completes a route in a hours, so she does 1/a route in 1 hour.</p>
<p style="text-align: justify;">Together their working speed is 1/6+1/a. But together it takes 4 hours to do a route so in an hour they can only do 1/4 of a route. Therefore 1/6+1/a=1/4.</p>
<p style="text-align: justify;">Multiply through by 12a: 2a+12=3a, so a=12 hours, the time it takes the associate to complete a route alone.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252597/complete-herself-associate-completes-associate-complete?show=252600#a252600Tue, 12 Jun 2018 22:43:34 +0000Answered: A bus averages 6 miles per hour faster than a trolley. If the bus travels 90 miles in the same time it takes the trolley to travel 75 miles, then what is the speed of each?
https://www.mathhomeworkanswers.org/252596/averages-faster-trolley-travels-takes-trolley-travel-miles?show=252598#a252598
<p style="text-align: justify;">If the trolley’s speed is T then the bus’s speed is T+6.</p>
<p style="text-align: justify;">Time=distance/speed so 90/(T+6)=75/T.</p>
<p style="text-align: justify;">Cross multiply: 90T=75(T+6)=75T+450, 15T=450, T=30mph and the bus’s speed is T+6=36mph.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/252596/averages-faster-trolley-travels-takes-trolley-travel-miles?show=252598#a252598Tue, 12 Jun 2018 22:09:00 +0000Answered: The sum of the digits of a two-digit number is 16. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
https://www.mathhomeworkanswers.org/252589/digits-number-reversed-number-original-number-original-number?show=252590#a252590
<p>Assume, the unit place digit will be y & the ten's place digit will be x</p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">∴ The number will be 10x+y [Think it as, if the number is 13, then 10*1+3 = 13]</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">& the sum of the digits of the number will be x+y which is equal to 16 (already given)</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">x+y = 16 ----------- 1)</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">If the digits are reversed, the new number will be 10y+x</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">According to the question or the data given,</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">(10x+y) - (10y+x) = 18</span></p>
<p><span style="font-family: arial, sans-serif; color: #222222;"><span style="font-size:16px">10x + y - 10y -x = 18</span></span></p>
<p><span style="font-family: arial, sans-serif; color: #222222;"><span style="font-size:16px">Or, 9x - 9y = 18</span></span></p>
<p><span style="font-family: arial, sans-serif; color: #222222;"><span style="font-size:16px">Or, 9(x - y) = 18</span></span></p>
<p><span style="font-family: arial, sans-serif; color: #222222;"><span style="font-size:16px">Or, x - y = 18/9 = 2 </span></span></p>
<p><span style="font-family: arial, sans-serif; color: #222222;"><span style="font-size:16px">Or, x - y = 2 </span></span><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">----------- 2)</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Now, add 1) + 2)</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">x + y + x - y = 16 +2</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Or, 2x = 18</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Or, x = 9</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Putting the value of x = 9 in equation 1)</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">x + y = 16</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Or, 9 + y = 16</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">Or, y = 16 - 9 = 7</span></p>
<p><span style="color:rgb(34, 34, 34); font-family:arial,sans-serif; font-size:16px">∴ </span>The original number will be 97 & the reversed number is 79</p>Word Problem Answershttps://www.mathhomeworkanswers.org/252589/digits-number-reversed-number-original-number-original-number?show=252590#a252590Tue, 12 Jun 2018 18:25:40 +0000Answered: How many people lived in the city 5 years ago?
https://www.mathhomeworkanswers.org/252584/how-many-people-lived-in-the-city-5-years-ago?show=252588#a252588
<p style="text-align: justify;">120% is 1.2. 5 years ago the population was 205200/1.2=171000.</p>Statistics Answershttps://www.mathhomeworkanswers.org/252584/how-many-people-lived-in-the-city-5-years-ago?show=252588#a252588Tue, 12 Jun 2018 15:40:03 +0000Answered: 12+ 12 ^ 2 =
https://www.mathhomeworkanswers.org/252583/12-12-2?show=252587#a252587
<p style="text-align:justify">Yes, the median is 12 as you observed. The mode (the most popular size) is also 12. See other answers re the black skirts.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252583/12-12-2?show=252587#a252587Tue, 12 Jun 2018 15:33:59 +0000Answered: 10 12 10 8 16 16 8 12 6 16 12 12 12 10 22 8 20 16 12 14 6 12 18 16 10 8 12 10
https://www.mathhomeworkanswers.org/252582/10-12-10-8-16-16-8-12-6-16-12-12-12-10-22-8-20-16-12-14-6-12-18-16-10-8-12-10?show=252585#a252585
<p style="text-align:justify">Order the dataset:</p>
<p style="text-align:justify">6 6 8 8 8 <a href="denied:tel:8 10 10 10 10 10 12 12" rel="nofollow">8 10 10 10 10 10 12 12</a> <a href="denied:tel:12 12 12 12 12 12 14" rel="nofollow">12 12 12 12 12 12 14</a> <a href="denied:tel:16 16 16 16 16 18 20" rel="nofollow">16 16 16 16 16 18 20</a> 22.</p>
<p style="text-align:justify">The mean is (2(6)+4(8)+5(10)+8(12)+14+5(16)+18+20+22)/28=12.29.</p>
<p style="text-align:justify">The mode is 12.</p>
<p style="text-align:justify">The median, mode and mean all give an idea of the central value of the data.</p>
<p style="text-align:justify">But in this case the mode is best because it gives an actual skirt size, whereas the mean gives a number which doesn’t correspond to an actual skirt size. The store would then most likely reorder size 12.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252582/10-12-10-8-16-16-8-12-6-16-12-12-12-10-22-8-20-16-12-14-6-12-18-16-10-8-12-10?show=252585#a252585Tue, 12 Jun 2018 15:30:41 +0000Answered: (2,2) (0,-4)
https://www.mathhomeworkanswers.org/252570/2-2-0-4?show=252581#a252581
<p style="text-align:justify">The slope of the line connecting the points is (-4-2)/(0-2)=(-6)/(-2)=3.</p>
<p style="text-align:justify">So the standard form of the line is y=3x+b where we need to find the constant b by plugging in one of the coords: 2=3×2+b, b=2-6=-4, so y=3x-4 is the line.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252570/2-2-0-4?show=252581#a252581Tue, 12 Jun 2018 13:29:15 +0000Answered: f(x)=e^x; a=0; f(0.05)
https://www.mathhomeworkanswers.org/252577/f-x-e-x-a-0-f-0-05?show=252580#a252580
<p style="text-align:justify">1. f(a)=f(0)=e⁰=1. So the slope of the linear approximation is 1 at x=a=0.</p>
<p style="text-align:justify">L(x)=x+b is the general form of the equation, where we need to find the constant b.</p>
<p style="text-align:justify">The line must pass through the point (0,1) which is (x, f(x))=(0,1).</p>
<p style="text-align:justify">Plug the coords in: 1=0+b so b=1 and L(x)=x+1.</p>
<p style="text-align:justify">2. So, when x=0.05, L(0.05)=1.05.</p>
<p style="text-align:justify">3. f(0.05)=e⁰⋅⁰⁵=1.05127 approx.</p>
<p style="text-align:justify">The error is 100(1.05-e⁰⋅⁰⁵)/e⁰⋅⁰⁵=-0.12% which means the approximation was 0.12% too low.</p>Calculus Answershttps://www.mathhomeworkanswers.org/252577/f-x-e-x-a-0-f-0-05?show=252580#a252580Tue, 12 Jun 2018 13:22:09 +0000Answered: Find the linear approximation.
https://www.mathhomeworkanswers.org/252578/find-the-linear-approximation?show=252579#a252579
<p style="text-align:justify">h'(t)=4t³-18t²+3. This equation will provide the slope of the line. So h'(-3)=-4×27-18×9+3=-108-162+3=-267. The slope (coefficient of t) is therefore -267.</p>
<p style="text-align:justify">The line will have the general form L(t)=-267t+b where we find b by plugging in the coords of the tangent point. When t=-3, h(-3)=81-6×(-27)-9-7=81+162-16=227. So the coords are (-3,227). The line passes through this point.</p>
<p style="text-align:justify">Therefore 227=-267×(-3)+b, 227=801+b, b=227-801=-574. So L(t)=-267t-574.</p>
<p style="text-align:justify">Another way to work out the equation is to plug in the point differently (slope-intercept format).</p>
<p style="text-align:justify">This format is y-y₀=m(x-x₀) where m is the slope, x the independent variable and y the dependent variable. (x₀,y₀) is the tangent point. We have m=-267, and we are using t instead of x and L(t) instead of y.</p>
<p style="text-align:justify">So we write:</p>
<p style="text-align:justify">L(t)-227=-267(t-(-3)), L(t)=227-267(t+3)=-267t-574.</p>Calculus Answershttps://www.mathhomeworkanswers.org/252578/find-the-linear-approximation?show=252579#a252579Tue, 12 Jun 2018 12:38:27 +0000Answered: How many bags of fertilizer will you need to complete the job?
https://www.mathhomeworkanswers.org/252565/how-many-bags-of-fertilizer-will-you-need-to-complete-the-job?show=252569#a252569
<p style="text-align: justify;">Area of field is 360×160=57600 sq ft.</p>
<p style="text-align: justify;">The field needs 57600/1000×8=460.8 lbs of fertiliser.</p>
<p style="text-align: justify;">The number of bags of fertiliser=460.8/50=9.216 so 10 bags are needed (500lb). 39.2lbs of fertiliser are unused.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/252565/how-many-bags-of-fertilizer-will-you-need-to-complete-the-job?show=252569#a252569Mon, 11 Jun 2018 21:41:41 +0000Answered: simplified expression for volume of a cube with an edge length of 3s with an exponent of 4
https://www.mathhomeworkanswers.org/72052/simplified-expression-volume-cube-with-edge-length-exponent?show=252568#a252568
<p style="text-align:justify">If 3s⁴ is the edge length, the volume is (3s⁴)³=27s¹².</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/72052/simplified-expression-volume-cube-with-edge-length-exponent?show=252568#a252568Mon, 11 Jun 2018 21:35:00 +0000Answered: The volume of a cube is 1000 cubic inches. What is the edge length of the cube?
https://www.mathhomeworkanswers.org/252566/the-volume-cube-1000-cubic-inches-what-the-edge-length-the-cube?show=252567#a252567
<p style="text-align: justify;">Cube root of 1000 is 10 so the side length is 10 inches.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/252566/the-volume-cube-1000-cubic-inches-what-the-edge-length-the-cube?show=252567#a252567Mon, 11 Jun 2018 21:33:05 +0000Answered: rolle's theorem how do you solve f(x)= x^1/2 - 1/3x , [0,9]
https://www.mathhomeworkanswers.org/49870/rolles-theorem-how-do-you-solve-f-x-x-1-2-1-3x-0-9?show=252564#a252564
<p style="text-align:justify">At the extremes of the range f(x)=0. So by Rolle’s Theorem there must be at least one value where f(x)≠0 in the interval. If we put x=1 f(1)=⅔ and midrange f(4)=2-4/3=⅔. Both values are positive so the curve does not cross the x axis because there is no change of sign. f(8.41)=2.9-8.41/3>0 and 8.41 is close to the end of the interval. Rolle’s Theorem maintains that only if there is a change of sign does the curve cross the x axis. Therefore we conclude that the solutions are x=0 and x=9, other values in the range being positive.</p>Calculus Answershttps://www.mathhomeworkanswers.org/49870/rolles-theorem-how-do-you-solve-f-x-x-1-2-1-3x-0-9?show=252564#a252564Mon, 11 Jun 2018 18:31:25 +0000Answered: Graph function y=ln(lnx)
https://www.mathhomeworkanswers.org/14912/graph-function-y-ln-lnx?show=252563#a252563
<p style="text-align:justify">The graph is shown below. The vertical line is an asymptote and is not part of the curve.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=7380310382004153307" style="height:397px; width:400px"></p>
<p style="text-align:justify">The zero is at x=e, the base of natural logarithms.</p>Calculus Answershttps://www.mathhomeworkanswers.org/14912/graph-function-y-ln-lnx?show=252563#a252563Mon, 11 Jun 2018 17:39:01 +0000Answered: i need help with the questio under thnks
https://www.mathhomeworkanswers.org/51588/i-need-help-with-the-questio-under-thnks?show=252562#a252562
<p style="text-align: justify;">52 hours is 48+4 hours which is 2 days + 4 hours. That would mean the process ends on Monday at 5am.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/51588/i-need-help-with-the-questio-under-thnks?show=252562#a252562Mon, 11 Jun 2018 17:21:23 +0000Answered: find the x-intercepts of the graph of f(x)= ln(x+1) - sin^2 x
https://www.mathhomeworkanswers.org/12758/find-the-x-intercepts-of-the-graph-of-f-x-ln-x-1-sin-2-x?show=252561#a252561
<p style="text-align:justify">The x intercepts are when ln(1+x)=sin²x. One obvious solution is x=0. There are two other zeroes in the given range. The graph of the function shows that x=1 and x=1.7 are close to the zeroes. Newton’s Method can be used to find these. First we need to differentiate the function: f'(x)=1/(1+x)-2sin(x)cos(x)=1/(1+x)-sin(2x). The iterative equation is x=x-(ln(x)-sin²x)/(1/(1+x)-sin(2x)). If we put x=1 into the right-hand side we get x=1-(0-sin²(1))/(1/2-sin(2))=0.9635.... We then resubmit x with this value and repeat the process until we get a consistent result. We get 0.9643632012 to 10 decimal places.</p>
<p style="text-align:justify">Now we start with x=1.7. We get x=1.683885012 to 9 decimal places.</p>Calculus Answershttps://www.mathhomeworkanswers.org/12758/find-the-x-intercepts-of-the-graph-of-f-x-ln-x-1-sin-2-x?show=252561#a252561Mon, 11 Jun 2018 17:17:23 +0000Answered: If log4096 is converted to log(base4) A, find the value of A.
https://www.mathhomeworkanswers.org/78847/if-log4096-is-converted-to-log-base4-a-find-the-value-of-a?show=252560#a252560
<p style="text-align: justify;">4⁶=4096, so log₄4006=6. Therefore A=6.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/78847/if-log4096-is-converted-to-log-base4-a-find-the-value-of-a?show=252560#a252560Mon, 11 Jun 2018 16:48:16 +0000Answered: 10 12 10 8 16 16 8 12 6 16 12 12 12 10 22 8 20 16 12 14 6 12 18 16 10 8 12 10
https://www.mathhomeworkanswers.org/252557/10-12-10-8-16-16-8-12-6-16-12-12-12-10-22-8-20-16-12-14-6-12-18-16-10-8-12-10?show=252558#a252558
<p style="text-align:justify">Order the dataset:</p>
<p style="text-align:justify">6 6 8 8 8 <a rel="nofollow" href="denied:tel:8 10 10 10 10 10 12 12">8 10 10 10 10 10 12 12</a> <a rel="nofollow" href="denied:tel:12 12 12 12 12 12 14">12 12 12 12 12 12 14</a> <a rel="nofollow" href="denied:tel:16 16 16 16 16 18 20">16 16 16 16 16 18 20</a> 22.</p>
<p style="text-align:justify">The median is 12.</p>
<p style="text-align:justify">The mean is (2(6)+4(8)+5(10)+8(12)+14+5(16)+18+20+22)/28=12.29.</p>
<p style="text-align:justify">The mode is 12.</p>
<p style="text-align:justify">The median, the mode and the mean indicate that, on average, women chose size 12 in the black skirt.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/252557/10-12-10-8-16-16-8-12-6-16-12-12-12-10-22-8-20-16-12-14-6-12-18-16-10-8-12-10?show=252558#a252558Mon, 11 Jun 2018 14:55:10 +0000Answered: if cos(x-y)+cos(y-z)+cos(z-x)=-3/2 then prove that sinx+siny+sinz=0=cosx+cosy+cosz
https://www.mathhomeworkanswers.org/106828/if-cos-cos-cos-3-then-prove-that-sinx-siny-sinz-0-cosx-cosy-cosz?show=252545#a252545
We will take RHS and prove LHS, so it is given that, cosx+cosy+cosz=0......(1)sinx+siny+sinz=0.......(2)Now multiplying equation 1 by cosy , cos z, cosx one by one we will get threeequation as, cosycosx+ cos 2 y+coszcosy=0......(3) cosxcosz+cosycosz+ cos 2 z=0......(4) cos 2 x+cosycosx+coszcosx=0......(5) ANd now multiply equation 2 by sinx, siny , sinz then we will get three equation as, sin 2 x+sinysinx+sinzsinx=0.......(6) sinxsiny+ sin 2 y+sinzsiny=0.......(7) sinxsinz+sinysinz+ sin 2 z=0.......(8) Add all the six equation we get,2cosxcosy+2sinxsiny+2cosycosz+2sinysinz+2coszcosx+2sinzsinx+ + sin 2 x+ cos 2 x+ cos 2 y+ sin 2 y+ sin 2 z + cos 2 z=0 2cos(x−y)+2cos(y−z)+2cos(z−x)+3=02cos(x−y)+2cos(y−z)+2cos(z−x)=−3cos(x−y)+cos(y−z)+cos(z−x)=− 3 2 =LHSTrigonometry Answershttps://www.mathhomeworkanswers.org/106828/if-cos-cos-cos-3-then-prove-that-sinx-siny-sinz-0-cosx-cosy-cosz?show=252545#a252545Mon, 11 Jun 2018 14:22:40 +0000Answered: f(x) = ln(1 + x); a = 0; f(0.9)
https://www.mathhomeworkanswers.org/252554/f-x-ln-1-x-a-0-f-0-9?show=252556#a252556
<p style="text-align:justify">1. Differentiate f(x); so f'(x)=1/(1+x). f'(0)=1 which is the gradient of the line of the tangent.</p>
<p style="text-align:justify">y=L(x)=x+b where b is found by substituting x and y values. We need f(0)=ln(1)=0, so the (x,y) values will be (0,0). That makes b=0. So y=L(x)=x. Nice and simple!</p>
<p style="text-align:justify">2. 0.9 is close to 0 so L(0.9)=0.9.</p>
<p style="text-align:justify">3. f(0.9)=ln(1.9)=0.6419, so the approximation is quite poor. The %ge error is 100(0.9-ln(1.9))/ln(1.9)=40.22% too high.</p>Calculus Answershttps://www.mathhomeworkanswers.org/252554/f-x-ln-1-x-a-0-f-0-9?show=252556#a252556Mon, 11 Jun 2018 13:24:19 +0000f(x) = 12 - x^2 ; a = 2 ; f(2.1)
https://www.mathhomeworkanswers.org/252553/f-x-12-x-2-a-2-f-2-1
<p>Please help ASAP sirs thanks alot<img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=4170872781036823107" style="height:410px; width:557px"></p>Calculus Answershttps://www.mathhomeworkanswers.org/252553/f-x-12-x-2-a-2-f-2-1Mon, 11 Jun 2018 12:25:54 +0000