Math Homework Answers - Recent questions and answers
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Powered by Question2Answer40316 P 12650 8471, find the P
https://www.mathhomeworkanswers.org/243462/40316-p-12650-8471-find-the-p
The cards arranged in descending orderOther Math Topicshttps://www.mathhomeworkanswers.org/243462/40316-p-12650-8471-find-the-pMon, 26 Jun 2017 01:44:11 +0000how do I write a math problem for my chart, that only gives the years and the amount of babies born for each year from 2006-2015 when each year is larger or smaller but never equal?
https://www.mathhomeworkanswers.org/243456/problem-chart-years-amount-babies-larger-smaller-never-equal
2006-275, 2007-280, 2008 320, 2009-366, 2010-358, 2011-336, 2012-375, 2013-390, 2014-455, and 2015-487, with a prediction for three years. How do I write this problem and show my prediction for the next three years. need answer immediatelyAlgebra 1 Answershttps://www.mathhomeworkanswers.org/243456/problem-chart-years-amount-babies-larger-smaller-never-equalSun, 25 Jun 2017 23:45:36 +0000explain why 19 -x is not a correct translation of "19 less thana number."
https://www.mathhomeworkanswers.org/243455/explain-why-not-correct-translation-of-19-less-thana-number
decide whether the following translates into an expression or an equation.Algebra 1 Answershttps://www.mathhomeworkanswers.org/243455/explain-why-not-correct-translation-of-19-less-thana-numberSun, 25 Jun 2017 22:35:34 +0000Answered: A is twice as good a workman as B andtogether they finish a piece of work in 18 days. In how many days will A alonefinish the work?
https://www.mathhomeworkanswers.org/243373/twice-workman-andtogether-finish-piece-days-will-alonefinish?show=243380#a243380
<p style="text-align:justify">Workman B counts as half of workman A, so the job is completed in 18 days by 1½ workmen. It will take one workman longer to do the work by himself, so workman A would take 18*1½=27 days.</p>
<p style="text-align:justify">If you find this problem difficult imagine this:</p>
<p style="text-align:justify">The two workmen are given the job of reshelving a warehouse that's divided into 3 sections. Between them, they decide that A will cover two sections while B covers the remaining section, because he's slower than A. It will take them 18 days each to do their work. Now workman B goes sick so A has to do all the work. He completes his two sections in 18 days, but he has one more section to go. It will only take him 9 days to complete it because he works twice as fast as B. So the total number of days is 18+9=27 days. (If workman A had gone sick it would have taken B 54 days, because each section would have taken 18 days to complete; and 54=2*27.)</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/243373/twice-workman-andtogether-finish-piece-days-will-alonefinish?show=243380#a243380Fri, 23 Jun 2017 13:22:11 +0000Answered: Given that OD=kOA find the value of k for which OD+OB is parallel to the x axis
https://www.mathhomeworkanswers.org/243337/given-that-od-koa-find-the-value-for-which-parallel-to-the-axis?show=243377#a243377
<p style="text-align: justify;">Let <strong>OA</strong>=a1<strong>i</strong>+a2<strong>j</strong>, then <strong>OD</strong>=ka1<strong>i</strong>+ka2<strong>j</strong>, and let <strong>OB</strong>=b1<strong>i</strong>+b2<strong>j</strong>. (<strong>i</strong> and <strong>j</strong> are the unit vectors in the orthogonal x and y directions respectively. a1, a2, b1, b2 are scalar quantities.)</p>
<p style="text-align: justify;"><strong>OD</strong>+<strong>OB</strong>=(ka1+b1)<strong>i</strong>+(ka2+b2)<strong>j</strong>. If this resultant vector is parallel to the x-axis then the y-component must be zero, so ka2+b2=0, k=-b2/a2. b2=<strong>OB.j</strong> and a2=<strong>OA.j</strong>, so k=-<strong>OB.j</strong>/<strong>OA.j</strong>. We have no more information about the vectors.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243337/given-that-od-koa-find-the-value-for-which-parallel-to-the-axis?show=243377#a243377Fri, 23 Jun 2017 12:57:46 +0000Answered: how to calculate pass mark if 60% of students pass
https://www.mathhomeworkanswers.org/243366/how-to-calculate-pass-mark-if-60%25-of-students-pass?show=243372#a243372
<p style="text-align:justify">If 60% of 100 students passed, then 60 students passed.</p>
<p style="text-align:justify">Let's say the pass mark was 45%, then it means that 60 students scored 45% or more.</p>
<p style="text-align:justify">If the pass mark was 67%, then 60 students scored 67% or more. </p>
<p style="text-align:justify">The number of students obtaining a pass is not directly related to the pass mark. The probability that a student selected randomly obtained a pass is 60%, but it doesn't determine the pass mark itself.</p>Statistics Answershttps://www.mathhomeworkanswers.org/243366/how-to-calculate-pass-mark-if-60%25-of-students-pass?show=243372#a243372Fri, 23 Jun 2017 09:53:16 +0000Answered: Find A one-one mapping from A to B
https://www.mathhomeworkanswers.org/243339/find-a-one-one-mapping-from-a-to-b?show=243357#a243357
<p>1</p>
<p style="text-align:justify">(i) b=a+3 maps {2,3,4} in A (all of A) to {5,6,7} in B. It doesn't matter that 2 in B is not mapped.</p>
<p style="text-align:justify">(ii) b=a+2 maps 3 and 4 in A to 5 and 6 in B, but 2 does not map to B,</p>
<p style="text-align:justify">(iii) a=b-3 maps 5, 6 and 7 in B to 2, 3 and 4 in A but fails to map 2.</p>
<p style="text-align:justify">2 This function implies that x=f(x,y), which implies x=f(f(x,y),y), which implies x=f(f(f(x,y),y),y) and so on. The "function" is mapping back into itself iteratively, recursively and indefinitely. It cannot be a function.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243339/find-a-one-one-mapping-from-a-to-b?show=243357#a243357Fri, 23 Jun 2017 00:29:08 +0000Answered: Prove that Principle for equality of fraction?
https://www.mathhomeworkanswers.org/243331/prove-that-principle-for-equality-of-fraction?show=243355#a243355
Multiply both sides by b: ab/b=bc/d, so a=bc/d; multiply both sides by d: ad=bcd/d=bc QED.Algebra 1 Answershttps://www.mathhomeworkanswers.org/243331/prove-that-principle-for-equality-of-fraction?show=243355#a243355Thu, 22 Jun 2017 23:28:16 +0000Answered: A 75-lb child is sitting on a teeter board at (-2.5, 3.5) and the fulcrum is at (4.5, -1.5), where units are in feet.
https://www.mathhomeworkanswers.org/243324/child-sitting-teeter-board-and-fulcrum-where-units-are-feet?show=243353#a243353
<p style="text-align:justify">The formulae for answering this question and similar questions are:
<br>
<br>
(x-x1)/(x2-x1)=(y-y1)/(y2-y1)=M2/(M1+M2)=a/R, and a^2=(x-x1)^2+(y-y1)^2 and R^2=(x2-x1)^2+(y2-y1)^2.
<br>
<br>
Where mass M1 is at point (x1,y1), mass M2 is at point (x2,y2), the fulcrum is at (x,y); a is M1's distance from the fulcrum; R is the distance between M1 and M2.</p>
<p style="text-align:justify">In this question M1=75lb, M2=37.5lb, x1=-2.5', y1=3.5', x=4.5', y=-1.5'.</p>
<p style="text-align:justify">(4.5+2.5)/(x2+2.5)=37.5/(75+37.5)=(-1.5-3.5)/(y2-3.5).</p>
<p style="text-align:justify">7*112.5=37.5x2+2.5*37.5, 787.5-93.75=37.5x2, x2=18.5'.</p>
<p style="text-align:justify">37.5y2-3.5*37.5=112.5(-5), 37.5y2=-431.25, y2=-11.5'. So the location of the second child is (18.5',-11.5').</p>
<p style="text-align:justify">The distance of the second child from the fulcrum is R-a=√(21^2+15^2)-√(7^2+5^2)=17.20' approx. Note that a/R=1/3, so R=3a and M1=2M2, so the results are as expected: the second child has to sit twice as far away from the fulcrum as the first child, because the first child is twice as heavy.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243324/child-sitting-teeter-board-and-fulcrum-where-units-are-feet?show=243353#a243353Thu, 22 Jun 2017 22:16:10 +0000Answered: Find the equation of a straight line
https://www.mathhomeworkanswers.org/243333/find-the-equation-of-a-straight-line?show=243351#a243351
<p style="text-align:justify">ysin30=-xcos30+2; y=-xtan60+2cosec30=-xtan60+4=-x√3+4. When x=0, y=4 (y-intercept), y=0, x=4√3/3.</p>
<p style="text-align:justify">(i) The slope of the line is -tan60=-√3 and this is also the slope of the parallel line which has the equation:</p>
<p style="text-align:justify">y-3=-tan60(x-4) in slope-intercept form.</p>
<p style="text-align:justify">Therefore y=3-xtan60+4tan60=3+4√3-x√3 or xcos30+ysin30=3sin30+4cos30.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=11387987010219004747" style="height:314px; width:450px"></p>
<p style="text-align:justify">For a general point P(x,y) on the line, OX=YP=x and OY=XP=y. OT=OS+ST=OS+QP.</p>
<p style="text-align:justify">OS=xcos30 and QP=ysin30, so OT=xcos30+ysin30=2. OT is the radius of the circle of which the line xcos30+ysin30=2 is a tangent.</p>
<p style="text-align:justify">(ii) ON is the length of the perpendicular on to the parallel line xcos30+ysin30=4cos30+3sin30. By analogy, ON=4cos30+3sin30=2√3+3/2 just as OT=2 for the other line.</p>
<p style="text-align:justify">(iii) The distance between the lines must therefore be the difference in the two radii, ON-OT=2√3+3/2-2=2√3-1/2.</p>
<p style="text-align:justify"> </p>Word Problem Answershttps://www.mathhomeworkanswers.org/243333/find-the-equation-of-a-straight-line?show=243351#a243351Thu, 22 Jun 2017 20:57:22 +0000Answered: A 65.75 lb child is sitting on a teeter board at(-1,-4) and the fulcrum is at (6.5, 3.5) where units are in feet.
https://www.mathhomeworkanswers.org/243329/child-sitting-teeter-board-and-the-fulcrum-where-units-feet?show=243347#a243347
<p style="text-align:justify">Use the formulae (x-x1)/(x2-x1)=M2/(M1+M2), (y-y1)/(y2-y1)=M2/(M1+M2) (see the question about the two children weighing 22 and 47.5 kilos, showing a representative diagram and derivation of the formulae). We have x=6.5, y=3.5, M1=65.75lb, M2=39.4lb, x1=-1, y1=-4. M1+M2=105.15lb.</p>
<p style="text-align:justify">(6.5+1)/(x2+1)=39.4/105.15=(3.5+4)/(y2+4).</p>
<p style="text-align:justify">Cross-multiplying:</p>
<p style="text-align:justify">105.15*7.5=39.4x2+39.4 and 105.15*7.5=39.4y2+39.4*4.</p>
<p style="text-align:justify">x2=19.016' and y2=16.016' approximately. So the coordinates are (19.016,16.016) feet.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243329/child-sitting-teeter-board-and-the-fulcrum-where-units-feet?show=243347#a243347Thu, 22 Jun 2017 17:01:25 +0000Answered: Differentiate the following functions w.r.t x.
https://www.mathhomeworkanswers.org/243336/differentiate-the-following-functions-w-r-t-x?show=243346#a243346
<ol>
<li style="text-align: justify;">Use d(uv)/dx=udv/dx+vdu/dx: (2x+3)(3x^2-1)+2(x^3-x+2)=6x^3-2x+9x^2-3+2x^3-2x+4=8x^3+9x^2-4x+1</li>
<li style="text-align: justify;">Use chain rule: 2sin(3x-2)cos(3x-2)*3=6sin(3x-2)cos(3x-2)=3sin(6x-4), because sin2A=2sinAcosA.</li>
</ol>Calculus Answershttps://www.mathhomeworkanswers.org/243336/differentiate-the-following-functions-w-r-t-x?show=243346#a243346Thu, 22 Jun 2017 16:41:34 +0000Answered: show that (1-x^2)dy/dx+y=0
https://www.mathhomeworkanswers.org/243338/show-that-1-x-2-dy-dx-y-0?show=243344#a243344
<p style="text-align:justify">y^2=(1-x)/(1+x); differentiating:</p>
<p style="text-align:justify">2yy'=(-(1+x)-(1-x))/(1+x)^2=(-1-x-1+x)/(1+x)^2=-2/(1+x)^2.</p>
<p style="text-align:justify">yy'+1/(1+x)^2=0; yy'(1+x)^2+1=0. </p>
<p style="text-align:justify">But y=√(1-x^2)/(1+x) when we multiply ((1-x)/(1+x))^(1/2) by ((1+x)/(1+x))^(1/2).</p>
<p style="text-align:justify">So we have yy'(1+x)^2+1=y'(1+x)√(1-x^2)+1=0. But 1+x=√(1-x^2)/y, so y'(1-x^2)/y+1=0 and (1-x^2)dy/dx+y=0 QED.</p>
<p style="text-align:justify"> </p>Calculus Answershttps://www.mathhomeworkanswers.org/243338/show-that-1-x-2-dy-dx-y-0?show=243344#a243344Thu, 22 Jun 2017 16:31:27 +0000Answered: For what values of m does the equation has reciprocal roots.
https://www.mathhomeworkanswers.org/243334/for-what-values-of-m-does-the-equation-has-reciprocal-roots?show=243343#a243343
<p><em>For what values of m will the equation x²-2mx+7m-12=0 has reciprocal roots?</em></p>
<p>Let there be reciprocal roots x1 = a and x2 = 1/a, where these two roots are reciprocal to each other.</p>
<p>Taking these roots as the solutions to a quadratic equation alows us to recreate the quadratic as,</p>
<p>(x - a)(x - 1/a) = 0</p>
<p>Multiplying out gives us,</p>
<p>x^2 - (a + 1/a)x + 1 = 0</p>
<p>Comparing this quadratic with the original x²-2mx+7m-12 = 0, and comparing the coefficient of x and the constant term,</p>
<p>-(a + 1/a) = -2m</p>
<p>1 = 7m - 12 ---> m<span style="text-decoration: underline;"> = 13/7</span></p>
<p><span style="text-decoration: underline;"><strong>The equation has reciprocal roots for m = 13/7</strong></span></p>
<p>Then,</p>
<p>(a + 1/a) = 26/7</p>
<p>7a^2 + 7 = 26a</p>
<p> 7a^2 - 26a + 7 = 0</p>
<p>Solution here gives the reciprocal roots as <span style="text-decoration: underline;">a1 = 13/7 + (2/7)sqrt(30)</span> and <span style="text-decoration: underline;">a2 = 13/7 - (2/7)sqrt(30)</span></p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/243334/for-what-values-of-m-does-the-equation-has-reciprocal-roots?show=243343#a243343Thu, 22 Jun 2017 16:27:38 +0000Answered: A 22 kilos child is sitting at A(-7, -3) and a 47.5 kilos child is at B(1,4), where units are in feet
https://www.mathhomeworkanswers.org/243326/kilos-child-sitting-and-kilos-child-is-where-units-are-in-feet?show=243335#a243335
<p style="text-align:justify">For a general solution to this problem let A be the point (x1,y1) and B be (x2,y2). Let AB=R and let a on AB be the distance between A and the fulcrum F(x,y).</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=18117121478703915139" style="height:313px; width:450px"></p>
<p style="text-align:justify">The masses are M1 at A and M2 at B. The moments about the fulcrum must be equal for equilibrium, so M1a=M2(R-a) and M1a+M2a=M2R, making a/R=M2/(M1+M2). By similar triangles (y-y1)/(y2-y1)=(x-x1)/(x2-x1)=a/R=M2/(M1+M2). Also, R=√(y2-y1)^2+(x2-x1)^2) and a=√(y-y1)^2+(x-x1)^2).</p>
<p style="text-align:justify">Therefore (x-x1)(M1+M2)=(x2-x1)M2; x(M1+M2)-x1M1-x1M2=x2M2-x1M2.</p>
<p style="text-align:justify">So x=(x1M1+x2M2)/(M1+M2) and y=(y1M1+y2M2)/(M1+M2).</p>
<p style="text-align:justify">Therefore the coordinates of F are ((x1M1+x2M2)/(M1+M2),(y1M1+y2M2)/(M1+M2)).</p>
<p style="text-align:justify">These formulae can be used in all problems of this nature.</p>
<p style="text-align:justify">We have M1=22kg and M2=47.5kg, so M1+M2=69.5kg.</p>
<p style="text-align:justify">x1=-7, y1=-3, x2=1, y2=4, so F is ((-7*22+47.5)/69.5,(-3*22+4*47.5)/69.5)=(-213/139,248/139)=(-1.53',1.78').</p>
<p style="text-align:justify">Note that the formula can be used to find any of the values M1, M2, x1, x2, x, y1, y2, y given the coordinates of A and B or F or M1 or M2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243326/kilos-child-sitting-and-kilos-child-is-where-units-are-in-feet?show=243335#a243335Thu, 22 Jun 2017 13:51:04 +0000A 35 kilos child is sitting on a teeter board at (4.-5, 3.7) and the fulcrum is at (-4.2, 5.6), where units are in feet.
https://www.mathhomeworkanswers.org/243330/kilos-child-sitting-teeter-board-fulcrum-where-units-are-feet
A 35 kilos child is sitting on a teeter board at (4.-5, 3.7) and the fulcrum is at (-4.2, 5.6), where units are in feet. At what point should a 26.5 kilos child sit to be in equilibrium? What is the distance of the second child from the fulcrum?Geometry Answershttps://www.mathhomeworkanswers.org/243330/kilos-child-sitting-teeter-board-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:49:13 +0000A 48.2 lb child is sitting on a teeter board at (-1.5,-4) and the fulcrum is at (6.7,-5) where units are in feet.
https://www.mathhomeworkanswers.org/243327/child-sitting-teeter-board-and-fulcrum-where-units-are-feet
A 48.2 lb child is sitting on a teeter board at (-1.5,-4) and the fulcrum is at (6.7,-5) where units are in feet. At what point should a 32lb child sit to be in equilibrium?Geometry Answershttps://www.mathhomeworkanswers.org/243327/child-sitting-teeter-board-and-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:38:22 +0000A 52-lb child is sitting on a teeter board at (-7.5, 1.7) and the fulcrum is at (-1.7, 4.1), where units are In feet.
https://www.mathhomeworkanswers.org/243325/child-sitting-teeter-board-and-fulcrum-where-units-are-feet
A 52-lb child is sitting on a teeter board at (-7.5, 1.7) and the fulcrum is at (-1.7, 4.1), where units are in feet. At what point should a 40 lb child sit to be in equilibrium? What is the distance of the second child from the fulcrum?Geometry Answershttps://www.mathhomeworkanswers.org/243325/child-sitting-teeter-board-and-fulcrum-where-units-are-feetThu, 22 Jun 2017 11:29:33 +0000Answered: Using determinant show that the points (1,0) (0,2) and (1,0) lie on a straight line.
https://www.mathhomeworkanswers.org/243308/using-determinant-show-that-the-points-and-lie-straight-line?show=243320#a243320
<p style="text-align:justify">The line joining (1,0) and (0,2) has a slope (2-0)/(0-1)=-2. The line joining (0,2) and (1,0) has a slope (0-2)/(1-0)=-2. So these points are colinear because (0,2) is a common point and the lines have the same slope.</p>
<p style="text-align:justify">The determinant is:</p>
<p style="text-align:justify">| 1 0 1 |</p>
<p style="text-align:justify">| 0 2 1 | = 1(2-0)-0+1(0-2)=2-2=0 which confirms collinearity.</p>
<p style="text-align:justify">| 1 0 1 |</p>
<p style="text-align:justify"> </p>
<p style="text-align:justify"> </p>Geometry Answershttps://www.mathhomeworkanswers.org/243308/using-determinant-show-that-the-points-and-lie-straight-line?show=243320#a243320Thu, 22 Jun 2017 10:08:52 +0000Answered: if x=2-√3 find x^4 - 3x^3+ 7x^2 +6x - 10
https://www.mathhomeworkanswers.org/243305/if-x-2-%E2%88%9A3-find-x-4-3x-3-7x-2-6x-10?show=243319#a243319
If x=2-√3, x^2=4+3-4√3=7-√3 and x^4=49+3-14√3=52-14√3=2(26-7√3).<br />
<br />
x^3=x * x^2=(2-√3)(7-√3)=14-9√3+3=17-9√3.<br />
<br />
The expression is: 52-14√3-3(17-9√3)+7(7-√3)+6(2-√3)-10=<br />
<br />
52-51+49+12-10+√3(-14+27-7-6)=52.Algebra 1 Answershttps://www.mathhomeworkanswers.org/243305/if-x-2-%E2%88%9A3-find-x-4-3x-3-7x-2-6x-10?show=243319#a243319Thu, 22 Jun 2017 09:50:49 +0000Answered: A circle in quadrant II is tangent to both axes. It touches the y-axis at (0,3). a.At what point does it meet the x-axis? b. Find the coordinates of the center of the circle.
https://www.mathhomeworkanswers.org/243304/circle-quadrant-tangent-touches-coordinates-center-circle?show=243317#a243317
<p style="text-align: justify;">If an axis is at a tangent, it is right angles to the radius, so the y axis (x=0) is a distance of 3 units to the right of the centre, making the centre 3 units to the left at x=-3. Because the axis is also a tangent it must be above the x-axis by 3 units (y=3), so the centre is at (-3,3).</p>Geometry Answershttps://www.mathhomeworkanswers.org/243304/circle-quadrant-tangent-touches-coordinates-center-circle?show=243317#a243317Thu, 22 Jun 2017 09:40:50 +0000Answered: A rectangle with sides parallel to the axes has vertices at (3,-2) and (-1,-7). a. Find the coordinates of the other two vertices. b. Find the area of the rectangle
https://www.mathhomeworkanswers.org/243303/rectangle-parallel-vertices-coordinates-vertices-rectangle?show=243316#a243316
<p style="text-align:justify">(a) The other two vertices are at (-1,-2) and (3,-7) so combining the given coordinates.
<br>
<br>
(b) The area is (3-(-1)) * (-2-(-7))=4*5=20 sq units.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=13886319500752037138" style="height:551px; width:375px"></p>Geometry Answershttps://www.mathhomeworkanswers.org/243303/rectangle-parallel-vertices-coordinates-vertices-rectangle?show=243316#a243316Thu, 22 Jun 2017 09:34:49 +0000Answered: A person 6 ft tall is standing near a street light so that the ration of his height to the pole is 2/3.
https://www.mathhomeworkanswers.org/243307/person-tall-standing-near-street-light-that-ration-height-pole?show=243315#a243315
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=1551357372730325276" style="height:265px; width:375px"></p>
<p style="text-align:justify">The picture shows the details. (a) DE=(2/3)AC, so AC=(3/2)DE=3*6/2=9'.</p>
<p style="text-align:justify">(b) DE=FC=6'; AF=AC-FC=9-6=3'; DF^2=AB^2-AF^2 (Pythagoras)=25-9=16, so DF=4'.</p>
<p style="text-align:justify">(c) BE/(BE+4)=2/3 (similar triangles BDE and BAC); 3BE=2BE+8; BE=8' (shadow length).</p>
<p style="text-align:justify">(d) all points shown on the picture with coordinates.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243307/person-tall-standing-near-street-light-that-ration-height-pole?show=243315#a243315Thu, 22 Jun 2017 09:23:25 +0000Answered: A person 6 ft tall is standing near a street light so that the ration of his height to the pole is 2/3.
https://www.mathhomeworkanswers.org/243309/person-tall-standing-near-street-light-that-ration-height-pole?show=243314#a243314
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=1551357372730325276" style="height:265px; width:375px"></p>
<p style="text-align:justify">The picture shows the details. (a) DE=(2/3)AC, so AC=(3/2)DE=3*6/2=9'.</p>
<p style="text-align:justify">(b) DE=FC=6'; AF=AC-FC=9-6=3'; DF^2=AB^2-AF^2 (Pythagoras)=25-9=16, so DF=4'.</p>
<p style="text-align:justify">(c) BE/(BE+4)=2/3 (similar triangles BDE and BAC); 3BE=2BE+8; BE=8' (shadow length).</p>
<p style="text-align:justify">(d) all points shown on the picture with coordinates.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243309/person-tall-standing-near-street-light-that-ration-height-pole?show=243314#a243314Thu, 22 Jun 2017 09:18:00 +0000Answered: calculate integration of x log(x+1)dx
https://www.mathhomeworkanswers.org/9007/calculate-integration-of-x-log-x-1-dx?show=243312#a243312
Problem: ∫ x ln ( x + 1 ) d x ∫xln(x+1)dx Integrate by parts: ∫ f g ′ = f g − ∫ f ′ g ∫fg′=fg−∫f′g f f = ln ( x + 1 ) =ln(x+1), g ′ g′ = x =x ↓ ↓ Steps ↓ ↓ Steps f ′ f′ = 1 x + 1 =1x+1, g g = x 2 2 =x22: = x 2 ln ( x + 1 ) 2 − ∫ x 2 2 ( x + 1 ) d x =x2ln(x+1)2−∫x22(x+1)dx Now solving: ∫ x 2 2 ( x + 1 ) d x ∫x22(x+1)dx Apply linearity: = 1 2 ∫ x 2 x + 1 d x =12∫x2x+1dx Now solving: ∫ x 2 x + 1 d x ∫x2x+1dx Substitute u = x + 1 u=x+1 ⟶ ⟶ d u d x = 1 dudx=1 (Steps), use x 2 = ( u − 1 ) 2 x2=(u−1)2: = ∫ ( u − 1 ) 2 u d u =∫(u−1)2udu … or choose an alternative: Substitute 1 x + 1 1x+1 Don't substitute Expand: = ∫ ( u + 1 u − 2 ) d u =∫(u+1u−2)du Apply linearity: = ∫ u d u + ∫ 1 u d u − 2 ∫ 1 d u =∫udu+∫1udu−2∫1du Now solving: ∫ u d u ∫udu Apply power rule: ∫ u n d u = u n + 1 n + 1 ∫undu=un+1n+1 with n = 1 n=1: = u 2 2 =u22 Now solving: ∫ 1 u d u ∫1udu This is a standard integral: = ln ( u ) =ln(u) Now solving: ∫ 1 d u ∫1du Apply constant rule: = u =u Plug in solved integrals: ∫ u d u + ∫ 1 u d u − 2 ∫ 1 d u ∫udu+∫1udu−2∫1du = ln ( u ) + u 2 2 − 2 u =ln(u)+u22−2u Undo substitution u = x + 1 u=x+1: = ln ( x + 1 ) + ( x + 1 ) 2 2 − 2 ( x + 1 ) =ln(x+1)+(x+1)22−2(x+1) Plug in solved integrals: 1 2 ∫ x 2 x + 1 d x 12∫x2x+1dx = ln ( x + 1 ) 2 + ( x + 1 ) 2 4 − x − 1 =ln(x+1)2+(x+1)24−x−1 Plug in solved integrals: x 2 ln ( x + 1 ) 2 − ∫ x 2 2 ( x + 1 ) d x x2ln(x+1)2−∫x22(x+1)dx = x 2 ln ( x + 1 ) 2 − ln ( x + 1 ) 2 − ( x + 1 ) 2 4 + x + 1 =x2ln(x+1)2−ln(x+1)2−(x+1)24+x+1 The problem is solved: ∫ x ln ( x + 1 ) d x ∫xln(x+1)dx = x 2 ln ( x + 1 ) 2 − ln ( x + 1 ) 2 − ( x + 1 ) 2 4 + x + 1 + C =x2ln(x+1)2−ln(x+1)2−(x+1)24+x+1+C Rewrite/simplify: = ( x + 1 ) ( 2 ( x − 1 ) ln ( x + 1 ) − x + 3 ) 4Calculus Answershttps://www.mathhomeworkanswers.org/9007/calculate-integration-of-x-log-x-1-dx?show=243312#a243312Thu, 22 Jun 2017 08:22:07 +0000Answered: Question about Proof of Real Number..?
https://www.mathhomeworkanswers.org/243294/question-about-proof-of-real-number?show=243298#a243298
<p style="text-align: justify;">Let c be a real number, then the associative rule says that (a*b)*c=a*(b*c); the commutative rule says that a*b=b*a, a*c=c*a and b*c=c*b. a*c=a*-1=c*a=-1*a=-a and b*c=c*b=-1*b=-b, when c=-1.</p>
<p style="text-align: justify;">(-a)(b)=(ca)b=(ac)b=a(cb)=a(-b).</p>
<p style="text-align: justify;">Let x=c*c=c^2=(-1)^2=1. (ca)(cb)=(ac)(cb)=a(c*c)b by the associative rule=a(x)b=(xa)b=x(ab)=1(ab)=ab.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/243294/question-about-proof-of-real-number?show=243298#a243298Wed, 21 Jun 2017 20:26:49 +0000Answered: if a = 0 ; b = 0 ; then prove it a\b =2
https://www.mathhomeworkanswers.org/243292/if-a-0-b-0-then-prove-it-a-b-2?show=243296#a243296
<p style="text-align: justify;">Let a=2b then a/b=2b/b=2. If a=2b=0 then a/b still equals 2 even though both a and b are zero and 0/0 would otherwise be undefined.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/243292/if-a-0-b-0-then-prove-it-a-b-2?show=243296#a243296Wed, 21 Jun 2017 19:36:05 +0000Answered: find all the zeroes of the polynomial 2x^4+5x^3-11x^2-20x+12 if two of its zeroes are 2 and -2
https://www.mathhomeworkanswers.org/243293/find-the-zeroes-the-polynomial-11x-20x-two-its-zeroes-are-and?show=243295#a243295
<p style="text-align:justify">Since two zeroes are 2 and -2, (x-2)(x+2)=x^2-4 must be a factor. Algebraic long division gives us:</p>
<p style="text-align:justify"> <span style="text-decoration: underline;">2x^2+5x-3 </span>= (2x-1)(x+3) so the other zeroes are 1/2 and -3.</p>
<p style="text-align:justify">x^2-4 ) 2x^4+5x^3-11x^2-20x+12</p>
<p style="text-align:justify"> <span style="text-decoration: underline;">2x^4 -8x^2</span></p>
<p style="text-align:justify"> 5x^3 -3x^2-20x</p>
<p style="text-align:justify"> <span style="text-decoration: underline;">5x^3 -20x</span></p>
<p style="text-align:justify"> -3x^2 +12</p>
<p style="text-align:justify"> <span style="text-decoration: underline;">-3x^2 +12</span></p>
<p style="text-align:justify"> 0</p>
<p style="text-align:justify"> </p>
<p style="text-align:justify"> </p>Other Math Topicshttps://www.mathhomeworkanswers.org/243293/find-the-zeroes-the-polynomial-11x-20x-two-its-zeroes-are-and?show=243295#a243295Wed, 21 Jun 2017 19:30:52 +0000Which expression is equivalent to mc018-1.jpg? Assume x mc018-2.jpg 0 and y > 0.
https://www.mathhomeworkanswers.org/243289/which-expression-equivalent-mc018-jpg-assume-mc018-jpg-and
jimmy johns subsAlgebra 1 Answershttps://www.mathhomeworkanswers.org/243289/which-expression-equivalent-mc018-jpg-assume-mc018-jpg-andWed, 21 Jun 2017 15:34:11 +0000Answered: Question about Proof of Real Number..?
https://www.mathhomeworkanswers.org/243285/question-about-proof-of-real-number?show=243288#a243288
<p style="text-align: justify;">If ab=x, then a=x/b and b=x/a. When x=0, a=0 or b=0, or a=b=0.
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When a and b are real their reciprocals 1/a and 1/b are also real. The product of any number and zero is always zero. x/b is the same as x * 1/b and similarly x/a. When x=0 the product of x and any other number must be zero.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243285/question-about-proof-of-real-number?show=243288#a243288Wed, 21 Jun 2017 14:39:44 +0000Answered: A man earns 2500 a year and if a raise of 500 is given each year, calculate the amount he will earn in 20 years and 18 years
https://www.mathhomeworkanswers.org/243274/earns-2500-raise-given-calculate-amount-will-earn-years-years?show=243287#a243287
<p style="text-align: justify;">After n years the man earns 2500+500n. When n=20, this is 2500+500*20=12500.
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After 18 years it's 2500+500*18=11500.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243274/earns-2500-raise-given-calculate-amount-will-earn-years-years?show=243287#a243287Wed, 21 Jun 2017 14:35:00 +0000Answered: can someone simplify, sinx(1+ctn^2x) & ctn^2x/1+ctn^2x.
https://www.mathhomeworkanswers.org/243281/can-someone-simplify-sinx-1-ctn-2x-%26-ctn-2x-1-ctn-2x?show=243286#a243286
<p style="text-align:justify">(sinx)^2+(cosx)^2=1 is the fundamental identity. Divide through by (sinx)^2: 1+(ctnx)^2=1/(sinx)^2 so sinx(1+ctn^2x)=sinx/(sinx)^2=1/sinx=cscx.</p>
<p style="text-align:justify">ctn^2x/(1+ctn^2x): multiply top and bottom by tan^2x: 1/(tan^2x+1)=1/sec^2x=cos^2x.</p>
<p style="text-align:justify">sinA/tanA-tanA/secA: sinAcosA/sinA-sinA/1=cosA-sinA.</p>
<p style="text-align:justify">secYcosY-cos^2Y=1-cos^2Y=sin^2Y</p>Trigonometry Answershttps://www.mathhomeworkanswers.org/243281/can-someone-simplify-sinx-1-ctn-2x-%26-ctn-2x-1-ctn-2x?show=243286#a243286Wed, 21 Jun 2017 14:30:04 +0000Answered: can someone simplify the following: sinx(1+ctn^2x) and ctn^2x/1+ctn^2x and sinA/tanA - tanA/secA and secY cosY - cos^2Y
https://www.mathhomeworkanswers.org/243272/someone-simplify-following-sinx-sina-tana-tana-seca-secy-cosy?show=243284#a243284
<p style="text-align:justify">(sinx)^2+(cosx)^2=1 is the fundamental identity. Divide through by (sinx)^2: 1+(ctnx)^2=1/(sinx)^2 so sinx(1+ctn^2x)=sinx/(sinx)^2=1/sinx=cscx.</p>
<p style="text-align:justify">ctn^2x/(1+ctn^2x): multiply top and bottom by tan^2x: 1/(tan^2x+1)=1/sec^2x=cos^2x.</p>
<p style="text-align:justify">sinA/tanA-tanA/secA: sinAcosA/sinA-sinA/1=cosA-sinA.</p>
<p style="text-align:justify">secYcosY-cos^2Y=1-cos^2Y=sin^2Y.</p>
<p> </p>Trigonometry Answershttps://www.mathhomeworkanswers.org/243272/someone-simplify-following-sinx-sina-tana-tana-seca-secy-cosy?show=243284#a243284Wed, 21 Jun 2017 13:44:48 +0000Answered: question about integration.please, show the working steps.
https://www.mathhomeworkanswers.org/30383/question-about-integration-please-show-the-working-steps?show=243283#a243283
<p style="text-align: justify;">The right-hand side is not integrable because there's no dx or dy to show what variable is being integrated. Also if x and y are variables we don't know their relationship (y=f(x)). With two variables we would expect a double integration, which is not expressed here.</p>Calculus Answershttps://www.mathhomeworkanswers.org/30383/question-about-integration-please-show-the-working-steps?show=243283#a243283Wed, 21 Jun 2017 13:40:44 +0000Answered: Simplify 2/4x-5 - 5/10x+1 show working
https://www.mathhomeworkanswers.org/243278/simplify-2-4x-5-5-10x-1-show-working?show=243282#a243282
<p style="text-align: justify;">2/(4x-5)-5/(10x+1)=</p>
<p style="text-align: justify;">(2(10x+1)-5(4x-5))/((4x-5)(10x+1))=</p>
<p style="text-align: justify;">(20x+2-20x+25)/((4x-5)(10x+1))=</p>
<p style="text-align: justify;">27/((4x-5)(10x+1)=27/(40x^2-46x-5).</p>Calculus Answershttps://www.mathhomeworkanswers.org/243278/simplify-2-4x-5-5-10x-1-show-working?show=243282#a243282Wed, 21 Jun 2017 13:35:53 +0000Answered: simplify secΘ ctnΘ
https://www.mathhomeworkanswers.org/243265/simplify-sec%CE%B8-ctn%CE%B8?show=243270#a243270
secA*ctnA=1/cosA * cosA/sinA = 1/sinA = cscA<br />
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sexA = 1/cosA an ctnA = cosA/sinATrigonometry Answershttps://www.mathhomeworkanswers.org/243265/simplify-sec%CE%B8-ctn%CE%B8?show=243270#a243270Wed, 21 Jun 2017 00:47:17 +0000Answered: what is the number
https://www.mathhomeworkanswers.org/243257/what-is-the-number?show=243263#a243263
<p style="text-align: justify;">If the number is n, then 2n+5=3(n-2); 2n+5=3n-6; 11=n, so the number is 11.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/243257/what-is-the-number?show=243263#a243263Tue, 20 Jun 2017 22:18:47 +0000Answered: how old am I now
https://www.mathhomeworkanswers.org/243258/how-old-am-i-now?show=243262#a243262
Age=x.<br />
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x-5=½(x+8); 2x-10=x+8; x=18 years old.Algebra 2 Answershttps://www.mathhomeworkanswers.org/243258/how-old-am-i-now?show=243262#a243262Tue, 20 Jun 2017 21:31:06 +0000Answered: Calculate 50+50+40+40+b+d=360
https://www.mathhomeworkanswers.org/243246/calculate-50-50-40-40-b-d-360?show=243249#a243249
b+d=360-(50+50+40+40)=180. If the figure is symmetrical b=d=90.Other Math Topicshttps://www.mathhomeworkanswers.org/243246/calculate-50-50-40-40-b-d-360?show=243249#a243249Tue, 20 Jun 2017 16:42:51 +0000Answered: If f(x)=2(x+1) (x+1) + 3 for x greater than equal to k has inverse , what is minimum value of k?
https://www.mathhomeworkanswers.org/243243/for-greater-than-equal-to-has-inverse-what-is-minimum-value-of?show=243248#a243248
<p style="text-align: justify;">To find the inverse let y=f(x)=(x+1)^2+3. Therefore (x+1)^2=y-3 and x+1=√(y-3). Let g(x)=√(x-3)-1 then g(x) is the inverse of f(x). The inverse can only exist if x≥3. f(g(x))=x by definition of inverse so f(g(x))≥k.</p>
<p style="text-align: justify;">g(x) is minimum when x=3 and g(3)=-1 and f(-1)=3 so for g(x) to exist, x≥-1; therefore k=-1.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243243/for-greater-than-equal-to-has-inverse-what-is-minimum-value-of?show=243248#a243248Tue, 20 Jun 2017 16:39:37 +0000convert 2.712
https://www.mathhomeworkanswers.org/243210/convert-2-712
i dont get the real answerAlgebra 1 Answershttps://www.mathhomeworkanswers.org/243210/convert-2-712Tue, 20 Jun 2017 15:55:33 +0000Answered: What is the general term if the 1st term is 1, the 2nd term is 1/2 and the third term is 1/4
https://www.mathhomeworkanswers.org/243240/what-the-general-term-1st-term-the-2nd-term-and-the-third-term?show=243242#a243242
<p style="text-align: justify;">If this an arithmetic sequence, then the first term a=1, second term a+d=1/2 and third term a+2d=1/4. So d from the second and third terms is 1/4-1/2=-1/4. However, d from the first and second terms is -1/2. Therefore the numbers are not in an arithmetic series.</p>
<p style="text-align: justify;">If the series is geometric then r=1/2 and a=1, so the general term is (1/2)^n or 1/2^n and n starts from 0. If n starts from 1 the general term is (1/2)^(n-1).</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243240/what-the-general-term-1st-term-the-2nd-term-and-the-third-term?show=243242#a243242Tue, 20 Jun 2017 12:58:46 +0000Answered: 3m + 8 = 15
https://www.mathhomeworkanswers.org/243239/3m-8-15?show=243241#a243241
<p style="text-align: justify;">This isn't a quadratic equation, it's a linear equation: subtract 8 from each side: 3m=7, and divide through by 3: m=7/3 or 2 1/3.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243239/3m-8-15?show=243241#a243241Tue, 20 Jun 2017 12:51:54 +0000Answered: A bag has 5 white & 3 red balls. 2 players, A&B, take turns @drawing 1 ball frm the bag @ random, & balls aren't replacd. 'A' draws 1st,Find P(A is the winner /the winning player wins on his 2nd draw)
https://www.mathhomeworkanswers.org/243182/players-%40drawing-random-balls-replacd-winner-winning-player?show=243237#a243237
<p style="text-align:justify">If the winner wins on his second draw then 3 balls have been drawn, 2 by player A and one by player B.</p>
<p style="text-align:justify">A draws. P(RED) on first draw is 3/8, P(WHITE)=5/8. After A has drawn a red, there are 7 balls left, 5W+2R. B draws: P(RED)=2/7, P(WHITE)=5/7. Now A draws again. There are only 6 balls left, and if B has drawn red, then there is only one red left, so P(RED)=1/6; if B drew white, there are still two reds left, so P(RED)=2/6. So the results of drawing resulting in A as the winner are RWR (3/8*5/7*2/6=5/56) or RRR (3/8*2/7*1/6=1/56). Either possibility makes A the winner so P=5/56+1/56=6/56=3/28.</p>
<p> </p>Other Math Topicshttps://www.mathhomeworkanswers.org/243182/players-%40drawing-random-balls-replacd-winner-winning-player?show=243237#a243237Tue, 20 Jun 2017 12:41:21 +0000Answered: seven digit numbers when rounded to the nearest hundred thousands gives 6,800,000
https://www.mathhomeworkanswers.org/243202/seven-digit-numbers-rounded-nearest-hundred-thousands-gives?show=243235#a243235
It means the number before rounding is between 6,750,000 and 6,850,000 approximately.Other Math Topicshttps://www.mathhomeworkanswers.org/243202/seven-digit-numbers-rounded-nearest-hundred-thousands-gives?show=243235#a243235Tue, 20 Jun 2017 12:24:26 +0000Answered: Ruth took 11 minutes and 20 seconds to solve 5 problems. On the average, how long did she take to solve 1 problem?
https://www.mathhomeworkanswers.org/243197/took-minutes-seconds-solve-problems-average-solve-problem?show=243234#a243234
<p style="text-align: justify;">To find out how long she takes to solve 5 problems, we need to divide the time by 5.</p>
<p style="text-align: justify;">5 into 11 goes 2 and 1 minute over. A minute is 60 seconds, so we add 60 to 20 to get 80, then we divide by 5, so that's 16 seconds. Therefore the time taken to solve one problem (on average) is 2 minutes 16 seconds.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/243197/took-minutes-seconds-solve-problems-average-solve-problem?show=243234#a243234Tue, 20 Jun 2017 12:11:33 +0000Answered: What is the product of (2x+2)(2x+2) in two binomial
https://www.mathhomeworkanswers.org/243213/what-is-the-product-of-2x-2-2x-2-in-two-binomial?show=243233#a243233
The general way of solving (a+b)(a+b) or (a+b)^2 is sum the squares: a^2+b^2 then add twice their product: a^2+b^2+2ab. If we put a=2x and b=2 we get 4x^2+4+8x or in descending order of powers of x: 4x^2+8x+4.Other Math Topicshttps://www.mathhomeworkanswers.org/243213/what-is-the-product-of-2x-2-2x-2-in-two-binomial?show=243233#a243233Tue, 20 Jun 2017 12:08:00 +0000Answered: The line through the points (1, 1) and (2, 0) cuts the y- axis at the point (0, b). Find b by using similar triangles.
https://www.mathhomeworkanswers.org/243224/through-points-cuts-axis-point-find-using-similar-triangles?show=243232#a243232
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=16182601298244544606" style="height:351px; width:400px"></p>
<p style="text-align: justify;">The axes have been removed in the picture, but the coordinates of the points are shown.</p>
<p style="text-align: justify;">In the similar triangles CNB and COA, CN/CO=NB/OA; that is, 1/2=1/b or 2/1=b/1, so b=2.</p>Geometry Answershttps://www.mathhomeworkanswers.org/243224/through-points-cuts-axis-point-find-using-similar-triangles?show=243232#a243232Tue, 20 Jun 2017 12:04:02 +0000Answered: (x-2/5)2=2/3
https://www.mathhomeworkanswers.org/243199/x-2-5-2-2-3?show=243231#a243231
<p style="text-align: justify;">Is this (x-(2/5))^2=2/3? If so then x-(2/5)=±√(2/3) and x=(2/5)±√(2/3), so x=1.2165 or -0.4165 approx.
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If the question is (x-(2/5))2=2/3, then x-(2/5)=1/3 and x=2/5+1/3=(6+5)/15=11/15.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/243199/x-2-5-2-2-3?show=243231#a243231Tue, 20 Jun 2017 11:52:14 +0000Answered: Let f(x) = 2x-3 and g(x) = 4x, find (fog)(x
https://www.mathhomeworkanswers.org/243228/let-f-x-2x-3-and-g-x-4x-find-fog-x?show=243229#a243229
(fog)(x)=f(g(x))=2g(x)-3=2(4x)-3=8x-3.Calculus Answershttps://www.mathhomeworkanswers.org/243228/let-f-x-2x-3-and-g-x-4x-find-fog-x?show=243229#a243229Tue, 20 Jun 2017 11:45:12 +0000