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Powered by Question2AnswerAnswered: I need help with these problems
https://www.mathhomeworkanswers.org/274060/i-need-help-with-these-problems?show=274094#a274094
<p style="text-align:justify">(1) The denominator can be factorised:</p>
<p style="text-align:justify">x³-ax²-x+a=x³-x-(ax²-a)=x(x²-1)-a(x²-1)=(x-a)(x²-1)=(x-a)(x-1)(x+1).</p>
<p style="text-align:justify">The numerator can be factorised:</p>
<p style="text-align:justify">(x+2)(x+1).</p>
<p style="text-align:justify">The common factor x+1 can be cancelled (for x≠-1) so the expression is (x+2)/((x-1)(x-a).</p>
<p style="text-align:justify">We can use partial fractions:</p>
<p style="text-align:justify">(x+2)/((x-1)(x-a))≡A/(x-1)+B/(x-a) where A and B are constants:</p>
<p style="text-align:justify">x+2≡A(x-a)+B(x-1)=Ax-Aa+Bx-B.</p>
<p style="text-align:justify">Matching coefficients:</p>
<p style="text-align:justify">A+B=1, -Aa-B=2, add these equations: A-Aa=3, A(1-a)=3, A=3/(1-a).</p>
<p style="text-align:justify">B=1-A=1-3/(1-a)=(1-a-3)/(1-a)=-(2+a)/(1-a)</p>
<p style="text-align:justify">So the expression becomes 3/((x-1)(1-a))-(2+a)/((x-a)(1-a)).</p>
<p style="text-align:justify">(2) I read this as y=log₂(tan(√x)).</p>
<p style="text-align:justify">The argument of square root must be positive, and the argument of log must be strictly positive. The argument of tangent must be less than π/2. Therefore 0<x<π²/4, and the range is (-∞,∞). However, √x can be in the third quadrant where tangent is positive. π<√x<3π/2, meaning π²<x<9π²/4. This pattern repeats every cycle, without altering the range, but the domain is discontinuous. There is no valid value of x between π²/4 and π². Each domain region gets progressively wider.</p>https://www.mathhomeworkanswers.org/274060/i-need-help-with-these-problems?show=274094#a274094Wed, 27 May 2020 21:08:55 +0000Answered: 2x^5 y−2x^2 y
https://www.mathhomeworkanswers.org/274061/2x-5-y%E2%88%922x-2-y?show=274093#a274093
<p style="text-align: justify;">Factorise? 2x²y(x³-1)=2x²y(x-1)(x²+x+1)</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/274061/2x-5-y%E2%88%922x-2-y?show=274093#a274093Wed, 27 May 2020 20:42:03 +0000Answered: Prove that Ris an equivalence relation on D.
https://www.mathhomeworkanswers.org/274070/prove-that-ris-an-equivalence-relation-on-d?show=274092#a274092
<p style="text-align: justify;">The symbol is “≡”, so A≡B shows equivalence, meaning that the sets have equal numbers of elements.</p>https://www.mathhomeworkanswers.org/274070/prove-that-ris-an-equivalence-relation-on-d?show=274092#a274092Wed, 27 May 2020 20:39:11 +0000Answered: how many lettuces out of every 20 does he grow unsuccessfully?
https://www.mathhomeworkanswers.org/274074/how-many-lettuces-out-of-every-20-does-he-grow-unsuccessfully?show=274091#a274091
<p style="text-align: justify;">Out of 15000 lettuces n lettuces are unsuccessful and can’t be sold. Let c=cost of producing one lettuce (successful or unsuccessful). Total cost of producing all lettuces=15000c. No fixed costs are mentioned. If s=sale price of 1 lettuce, income is (15000-n)s.</p>
<p style="text-align: justify;">Total profit = (15000-n)s-15000c=15000s-ns-15000c=15000(s-c)-ns.</p>
<p style="text-align: justify;">s-c=R1.72 for a successful lettuce, so total profit=25800-ns=15380. Therefore ns=R10420. This is the total of lost sales because of unsuccessful lettuces. We don’t know the sale price of a lettuce. If s=R5, then n=2084, if s=R4, n=2605, if s=R10, n=1042, if s=R20, n=521. If we assume n=521, then 521/15000 are unsuccessful, and this means that in 20 lettuces, less than 1 would be unsuccessful.</p>
<p style="text-align: justify;">Now assume n=1042, then about 1.39 in 20 are unsuccessful; n=2605, 3.47 unsuccessful in 20; n=2084, 2.78 unsuccessful in 20.</p>
<p style="text-align: justify;"> </p>Word Problem Answershttps://www.mathhomeworkanswers.org/274074/how-many-lettuces-out-of-every-20-does-he-grow-unsuccessfully?show=274091#a274091Wed, 27 May 2020 20:32:46 +0000Answered: How many tomatoes will be in each of the fifth and seventh piles?
https://www.mathhomeworkanswers.org/274075/how-many-tomatoes-will-be-in-each-the-fifth-and-seventh-piles?show=274089#a274089
<p style="text-align: justify;">The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, ... each of which is the sum of natural numbers: e.g., 15=5+4+3+2+1. The sums of the triangular numbers are, 1, 4, 10, 20, 35, 56, 84, ... Therefore the sum of the first 3 is 10, the sum of the first 5 is 35, the sum of the first 7 is 84, first 9 165, first 11 286. However, the numbers 15 and 70 don’t match these. 15 is the 5th triangular number, but 70 isn’t a triangular number, but is the sum of 15 and 55 (5th and 10th triangular numbers).</p>Word Problem Answershttps://www.mathhomeworkanswers.org/274075/how-many-tomatoes-will-be-in-each-the-fifth-and-seventh-piles?show=274089#a274089Wed, 27 May 2020 19:38:55 +0000Answered: Would you mind showing your work, such as how you got those answers?
https://www.mathhomeworkanswers.org/274086/would-you-mind-showing-your-work-such-how-you-got-those-answers?show=274088#a274088
<p style="text-align: justify;">For the graph part, you use the answers to parts (1) to (4) to help you draw the graph. The x intercepts in (1) are -3 and 0, so on your axes, write a small cross at (-3,0) and on the origin (0,0) which is also the y intercept (2). The axis of symmetry is a vertical line through the point (-1½,0), so mark this point on the x axis and draw a vertical line (parallel to the y-axis) through the point. The parabola (curve) is symmetrical about this line, in other words, the line acts as a mirror, reflecting half the curve.</p>
<p style="text-align: justify;">On this axis of symmetry is the vertex where y=-9, so it’s the point (-1½,-9). This vertex is the lowest point on the U-shaped curve (parabola) and the curve must pass through all the points you marked earlier.</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/274086/would-you-mind-showing-your-work-such-how-you-got-those-answers?show=274088#a274088Wed, 27 May 2020 18:42:18 +0000Answered: Why is the square root of 12 simplified by "4", and not "6" or "3"?
https://www.mathhomeworkanswers.org/274062/why-is-the-square-root-of-12-simplified-by-4-and-not-6-or-3?show=274085#a274085
<p style="text-align: justify;">√12=√(2×2×3)=√(2×2)×√3=2√3. To simplify the square root of n, you are looking for the largest perfect square which is a factor of n. When n=12, the largest such factor is 4, because it’s the largest perfect square, whereas 3 and 6 are not perfect squares.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/274062/why-is-the-square-root-of-12-simplified-by-4-and-not-6-or-3?show=274085#a274085Wed, 27 May 2020 18:10:37 +0000Answered: y = 4x² + 12x
https://www.mathhomeworkanswers.org/274083/y-4x%C2%B2-12x?show=274084#a274084
<p style="text-align:justify">(1) 4x²+12x=4x(x+3)=0, x=0, x=-3 are the x intercepts.</p>
<p style="text-align:justify">(2) y=0 is the y-intercept (plug x=0 into 4x²+12x).</p>
<p style="text-align:justify">(3) y=4(x²+3x+9/4-9/4)=4(x+3/2)²-9, the vertex is at (-3/2,-9) so the axis of symmetry is x=-3/2.</p>
<p>(4) y=-9</p>
<p>(5) Graph:</p>
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=3948435071823089058" style="height:711px; width:550px"></p>
<p> </p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/274083/y-4x%C2%B2-12x?show=274084#a274084Wed, 27 May 2020 18:00:31 +0000Answered: antidifferentiate sin4 x.
https://www.mathhomeworkanswers.org/274031/antidifferentiate-sin4-x?show=274082#a274082
<p style="text-align: justify;">cos(2x)=1-2sin²(x), sin²(x)=½(1-cos(2x)), sin⁴(x)=¼(1-2cos(2x)+cos²(2x)).</p>
<p style="text-align: justify;">cos(4x)=2cos²(2x)-1, cos²(2x)=½(cos(4x)+1) so:</p>
<p style="text-align: justify;">sin⁴(x)=¼(1-2cos(2x)+½(cos(4x)+1)=⅛(2-4cos(2x)+cos(4x)+1)=⅛(3-4cos(2x)+cos(4x)).</p>
<p style="text-align: justify;">Each term in this expression can be integrated (antidifferentiated)</p>
<p style="text-align: justify;">The antiderivative of sin⁴(x)=⅛(3x-2sin(2x)+¼sin(4x))+c, where c is a constant.</p>
<p style="text-align: justify;">So ∫sin⁴(x)dx=(1/32)(12x-8sin(2x)+sin(4x))+c.</p>
<p style="text-align: justify;"> </p>Calculus Answershttps://www.mathhomeworkanswers.org/274031/antidifferentiate-sin4-x?show=274082#a274082Wed, 27 May 2020 17:09:50 +0000Answered: combination
https://www.mathhomeworkanswers.org/274069/combination?show=274080#a274080
36000Other Math Topicshttps://www.mathhomeworkanswers.org/274069/combination?show=274080#a274080Wed, 27 May 2020 17:00:04 +0000Answered: There are 53 chairs set up in the gym for an assembly. After the assembly, all the chairs will be put away on racks that hold 5 chairs. How many racks are needed?
https://www.mathhomeworkanswers.org/274048/chairs-assembly-assembly-chairs-racks-chairs-racks-needed?show=274059#a274059
<p style="text-align: justify;">10 racks will hold 50 chairs (10×5=50), leaving 3 chairs to go onto another rack, making 11 racks.</p>https://www.mathhomeworkanswers.org/274048/chairs-assembly-assembly-chairs-racks-chairs-racks-needed?show=274059#a274059Tue, 26 May 2020 20:41:06 +0000Answered: Solve equations constant both sides n+7=4
https://www.mathhomeworkanswers.org/274047/solve-equations-constant-both-sides-n-7-4?show=274058#a274058
<p style="text-align: justify;">n+7=4. Add -7 to each side: n=-3.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/274047/solve-equations-constant-both-sides-n-7-4?show=274058#a274058Tue, 26 May 2020 20:37:58 +0000Answered: a(2a²-a-4)-a(a-3)2a
https://www.mathhomeworkanswers.org/274052/a-2a%C2%B2-a-4-a-a-3-2a?show=274057#a274057
<p style="text-align: justify;">Expand the parentheses: 2a³-a²-4a-2a³+6a²=5a²-4a which can also be written a(5a-4).</p>Calculus Answershttps://www.mathhomeworkanswers.org/274052/a-2a%C2%B2-a-4-a-a-3-2a?show=274057#a274057Tue, 26 May 2020 20:35:33 +0000Answered: Given 3<a<4, 4<b<5 Find: a-b/2a
https://www.mathhomeworkanswers.org/274055/given-3-a-4-4-b-5-find-a-b-2a?show=274056#a274056
<p style="text-align: justify;">(a-b)/2a=½-b/2a; 6<2a<8. If we take the limits of (2a,b) we get (6,4), (6,5), (8,4), (8,5)</p>
<p style="text-align: justify;">For each of these, calculate ½-b/2a=-⅙, -⅓, 0, -⅛. The smallest of these is -⅓ and the largest is 0, so -⅓<(a-b)/2a<0.</p>https://www.mathhomeworkanswers.org/274055/given-3-a-4-4-b-5-find-a-b-2a?show=274056#a274056Tue, 26 May 2020 20:31:42 +0000Answered: 7(2x + 6y)
https://www.mathhomeworkanswers.org/70726/7-2x-6y?show=274053#a274053
4x+7yPre-Algebra Answershttps://www.mathhomeworkanswers.org/70726/7-2x-6y?show=274053#a274053Tue, 26 May 2020 18:57:54 +0000U: R³ -> R³ , U(x, y, z) = (5x+8y+16z,4x+y+8z,-4x-4y-11z) is a lineer transformation, find the functions that accept U as a root.
https://www.mathhomeworkanswers.org/274050/lineer-transformation-find-the-functions-that-accept-root
The topics are Linear Operators and Linear Transformations. Please tell me if i made some mistakes while translating the question to english if or there is something that doesn't make sense.Other Math Topicshttps://www.mathhomeworkanswers.org/274050/lineer-transformation-find-the-functions-that-accept-rootTue, 26 May 2020 18:08:32 +0000Answered: f(x)=x+3,x<0
https://www.mathhomeworkanswers.org/273877/f-x-x-3-x-0?show=274044#a274044
f(x)=x+3, x<0 so x+3<3, and f(x)<3.https://www.mathhomeworkanswers.org/273877/f-x-x-3-x-0?show=274044#a274044Tue, 26 May 2020 13:16:15 +0000Answered: Is 0.138 a higher number than0.50
https://www.mathhomeworkanswers.org/274028/is-0-138-a-higher-number-than0-50?show=274037#a274037
<p style="text-align: justify;">Multiply each by 1000: 138, 500, so 0.50 is larger.</p>Calculus Answershttps://www.mathhomeworkanswers.org/274028/is-0-138-a-higher-number-than0-50?show=274037#a274037Tue, 26 May 2020 08:51:17 +0000Answered: The graph of the distribution of the numbers of children in Canadian families is
https://www.mathhomeworkanswers.org/273901/the-graph-distribution-numbers-children-canadian-families?show=274035#a274035
<p style="text-align: justify;">No data has been provided so I have to guess the most likely distribution.</p>
<p style="text-align: justify;">If the range of numbers is 6 and most families have 2 children there would be a low modal value. The bulk of data would be around this value of 2, tailing off between 2 and 6, creating a positive skew. On this basis, answer a would apply.</p>
<p style="text-align: justify;"> </p>https://www.mathhomeworkanswers.org/273901/the-graph-distribution-numbers-children-canadian-families?show=274035#a274035Tue, 26 May 2020 08:46:59 +0000Answered: what is (x-5)(x-5)?
https://www.mathhomeworkanswers.org/23254/what-is-x-5-x-5?show=274032#a274032
the answer is x^2- 10x-25.Algebra 1 Answershttps://www.mathhomeworkanswers.org/23254/what-is-x-5-x-5?show=274032#a274032Tue, 26 May 2020 02:17:11 +0000Answered: Which fraction is equivalent to 5/20?
https://www.mathhomeworkanswers.org/209818/which-fraction-is-equivalent-to-5-20?show=274029#a274029
25/100Pre-Algebra Answershttps://www.mathhomeworkanswers.org/209818/which-fraction-is-equivalent-to-5-20?show=274029#a274029Tue, 26 May 2020 02:07:33 +0000Answered: Suppose the Sun casts light that makes an angle of 40∘ with the horizontal. Determine the length of the shadow of a 1.8 metre tall person to one decimal place.
https://www.mathhomeworkanswers.org/274024/suppose-horizontal-determine-length-shadow-person-decimal?show=274026#a274026
<p style="text-align: justify;">The person represents the vertical leg of a right triangle opposite to the 40° angle. The shadow is the leg adjacent to the angle. tan40=1.8/s where s is the shadow length. Therefore s=1.8/tan40=2.1m to 1 decimal place.</p>Trigonometry Answershttps://www.mathhomeworkanswers.org/274024/suppose-horizontal-determine-length-shadow-person-decimal?show=274026#a274026Mon, 25 May 2020 22:23:22 +0000Answered: Factor out -1 from the expression x^2-x-1
https://www.mathhomeworkanswers.org/274023/factor-out-1-from-the-expression-x-2-x-1?show=274025#a274025
<p style="text-align: justify;">-1(-x²+x+1)</p>Algebra 2 Answershttps://www.mathhomeworkanswers.org/274023/factor-out-1-from-the-expression-x-2-x-1?show=274025#a274025Mon, 25 May 2020 22:18:09 +0000Answered: angle of elevation
https://www.mathhomeworkanswers.org/12857/angle-of-elevation?show=274022#a274022
<p style="text-align:justify"><span style="font-size:16px">We can relate the horizontal extension x of the string to the angle of elevation θ: tanθ=100/x. Differentiate with respect to time t: sec²θdθ/dt=-(100/x²)dx/dt.</span></p>
<p style="text-align:justify"><span style="font-size:16px">dθ/dt is the rate of change of the angle of elevation, and dx/dt is the horizontal rate of change of the length of the string, which is 10 ft/s. Therefore sec²θdθ/dt=-(100/x²)(10)=-1000/x².</span></p>
<p style="text-align:justify"><span style="font-size:16px">When θ=30°, x=100cotθ=100√3 feet (this is the horizontal ground distance to a point directly beneath the kite, not the length of the kite string). We plug in (x,θ)=(100√3,30): </span></p>
<p style="text-align:justify"><span style="font-size:16px">sec²θdθ/dt=1000/(100√3)²=-1/30, sec²30=4/3, and dθ/dt=-1/30×¾=-1/40=-0.025°/s approx. This means that the rate of change is a decrease in the angle of elevation which is 0.025 degrees per second at the instantaneous point where the angle of elevation was 30°. At this point, the length of the string was 200 feet (at an angle of 30°), but the string is extended horizontally, not at an angle of 30°.</span></p>
<p style="text-align:justify"><span style="font-size:16px">Alternative solution using x=100cotθ, dx/dt=-100cosec²θdθ/dt.</span></p>
<p style="text-align:justify"><span style="font-size:16px">dx/dt=10, θ=30°, 10=-100×4dθ/dt, so dθ/dt=-1/40 degrees per second.</span></p>Calculus Answershttps://www.mathhomeworkanswers.org/12857/angle-of-elevation?show=274022#a274022Mon, 25 May 2020 20:32:36 +0000Answered: Is there anyway I can get a mathematical equation that can lead me to this answer 61547098E5
https://www.mathhomeworkanswers.org/274018/there-anyway-mathematical-equation-that-answer-61547098e5?show=274020#a274020
<p style="text-align: justify;">6.1547098E12=61547098E5=6,154,709,800,000.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/274018/there-anyway-mathematical-equation-that-answer-61547098e5?show=274020#a274020Mon, 25 May 2020 19:22:38 +0000Answered: If (,y) = ^/ find (1,1)
https://www.mathhomeworkanswers.org/273911/if-y-find-1-1?show=274019#a274019
<p style="text-align: justify;">(1,1)=1^y/1=1?</p>Calculus Answershttps://www.mathhomeworkanswers.org/273911/if-y-find-1-1?show=274019#a274019Mon, 25 May 2020 19:14:59 +0000Answered: If (,) = / find (1,1)
https://www.mathhomeworkanswers.org/273910/if-find-1-1?show=274017#a274017
(1,1)=1/1=1?Calculus Answershttps://www.mathhomeworkanswers.org/273910/if-find-1-1?show=274017#a274017Mon, 25 May 2020 19:13:10 +0000Answered: What is the number, if k% of it is 2a?
https://www.mathhomeworkanswers.org/274015/what-is-the-number-if-k%25-of-it-is-2a?show=274016#a274016
<p style="text-align:justify">If the number is x, then kx/100=2a. Therefore x=200a/k.</p>
<p style="text-align:justify">Let a=24 and k=25, then we have x=(200)(24)/25=192.</p>
<p style="text-align:justify">So 25% of 192=192/4=48 which is 2×24=2a.</p>https://www.mathhomeworkanswers.org/274015/what-is-the-number-if-k%25-of-it-is-2a?show=274016#a274016Mon, 25 May 2020 18:59:21 +0000Answered: Two observer p and q 32m apart on the same horizontal ground and the same side of a kite (k), observed the kite at angle of elevation 27° and 48° respectively, calculate correct to 1 decimal place
https://www.mathhomeworkanswers.org/274008/observer-horizontal-observed-elevation-respectively-calculate?show=274010#a274010
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=15006439410730822327" style="height:298px; width:550px"></p>
<p style="text-align:justify">Let’s call h the height of the kite. And let x be the distance between observer Q and a position N on the ground directly beneath the kite (that is, a distance h below the kite).</p>
<p style="text-align:justify">We can write two equations based on the tangents of the two angles. The distance of observer P from N is 32+x. We have two triangles: PKN and QKN, where KN=h, QN=x, PN=32+x.</p>
<p style="text-align:justify">tan(48)=h/x and tan(27)=h/(32+x). Therefore h=xtan(48), so tan(27)=xtan(48)/(32+x), (32+x)tan(27)=xtan(48), 32tan(27)+xtan(27)=xtan(48), x(tan(48)-tan(27))=32tan(27), and x=32tan(27)/(tan(48)-tan(27))=27.1m to 1 decimal place.</p>
<p style="text-align:justify">(i) h=xtan(48)=30.1m</p>
<p style="text-align:justify">(ii) sin(27)=KN/PK=h/PK, so PK, the distance between the kite and observer P=h/sin(27)=66.4m.</p>Trigonometry Answershttps://www.mathhomeworkanswers.org/274008/observer-horizontal-observed-elevation-respectively-calculate?show=274010#a274010Mon, 25 May 2020 11:16:18 +0000Answered: Explain the pattern
https://www.mathhomeworkanswers.org/273999/explain-the-pattern?show=274002#a274002
<p style="text-align:justify">First series: the terms are generated by dividing alternatively by -2 then 2:</p>
<p style="text-align:justify">4/3÷(-2)=-2/3, -2/3÷2=-1/3, -1/3÷(-2)=1/6, 1/6÷2=1/12, 1/12÷(-2)=-1/24, -1/24÷2=-1/48, ...</p>
<p style="text-align:justify">Second series: reverse Fibonacci: subtract the second term from the first to get the next:</p>
<p style="text-align:justify">24/4-15/4=9/4, 15/4-9/4=6/4, 9-6/4=3/4, 6/4-3/4=3/4, 3/4-3/4=0 (the term 6/4, or 3/2, appears to be missing).</p>
<p style="text-align:justify">Third series: starting by subtracting 3/2 from the first time and doubling this to 3, then 6, and so on, we get successive terms: -5/2-3/2=-4, -4-3=-7, -7-6=-13, -13-12=-25, -25-24=-49, ...</p>
<p style="text-align:justify">Fourth series: geometric with common ratio -3/2, that is, each successive term is -3/2 times the previous term.</p>
<p style="text-align:justify">Fifth series: to get the next term, invert the fraction and add 1 to the numerator and denominator. I think the series should be:</p>
<p style="text-align:justify">3/7(→7/3)→8/4(→4/8)→5/9(→9/5)→10/6 (5/3)</p>
<p style="text-align:justify">(→6/10)→7/11(→11/7)→12/8 (not 12/18)(→8/12)→9/13</p>
<p style="text-align:justify">Sixth series: the difference between terms starts at 12, then increases by 20 to 32, 52, 72, making the next term 198+92=290 not 2810.</p>
<p style="text-align:justify"> </p>Other Math Topicshttps://www.mathhomeworkanswers.org/273999/explain-the-pattern?show=274002#a274002Sun, 24 May 2020 14:49:06 +0000Answered: Find the angle between the lines whose Direction cosines are given by the equation 3 L + m + 5 n =0 and 6mn- 2nl+5l=0
https://www.mathhomeworkanswers.org/273989/angle-between-lines-whose-direction-cosines-given-equation?show=274000#a274000
<p style="text-align:justify"><span style="font-size:14px">Assuming that each line shares common direction cosines defined by the equations, and adding to the given equations L²+M²+N²=1 (I’ve used uppercase versions of the direction cosines to avoid ambiguities), we have three equations with three unknowns, which is sufficient to find the individual direction cosines. Without this assumption there would be insufficient information to define the line vectors.</span></p>
<p style="text-align:justify"><span style="font-size:14px">So we have:</span></p>
<p style="text-align:justify"><span style="font-size:14px">(1) 3L+M+5N=0⇒M=-(3L+5N);</span></p>
<p style="text-align:justify"><span style="font-size:14px">(2) 6MN-2NL+5L=0⇒-6(3L+5N)N-2NL+5L=0, -20NL-30N²+5L=0, L(1-4N)=6N², L=6N²/(1-4N)⇒M=-(18N²/(1-4N)+5N)=N(2N-5)/(1-4N);</span></p>
<p style="text-align:justify"><span style="font-size:14px">(3) L²+M²+N²=1⇒</span></p>
<p style="text-align:justify"><span style="font-size:14px">36N⁴/(1-4N)²+(18N²/(1-4N)+5N)²+N²=1,</span></p>
<p style="text-align:justify"><span style="font-size:14px">36N⁴+N²(2N-5)²+N²(1-4N)²=(1-4N)²,</span></p>
<p style="text-align:justify"><span style="font-size:14px">36N⁴+4N⁴-20N³+25N²+N²-8N³+16N⁴=1-8N+16N²,</span></p>
<p style="text-align:justify"><span style="font-size:14px">56N⁴-28N³+10N²+8N-1=0.</span></p>
<p style="text-align:justify"><span style="font-size:14px">This quartic can be solved using Newton’s Method and approximations of the solution as initial values: -0.35 and 0.15 (from a graph and using the Intermediate Value Theorem).</span></p>
<p style="text-align:justify"><span style="font-size:14px">N₁=-0.3754, N₂=0.1130,</span></p>
<p style="text-align:justify"><span style="font-size:14px">L₁=0.1397, L₂=0.3380,</span></p>
<p style="text-align:justify"><span style="font-size:14px">M₁=-0.9837, M₂=0.8630 (approx figures).</span></p>
<p style="text-align:justify"><span style="font-size:14px">Thus there are two solutions (only), presumably one for each line.</span></p>
<p style="text-align:justify"><span style="font-size:14px">(L₁,M₁,N₁) defines the unit vector for one line and (L₂,M₂,N₂) defines the unit vector for the other line. The dot product of these gives the cosine of the angle θ between them, so θ=arccos(L₁L₂+M₁M₂+N₁N₂)=arccos(-0.8442)=147.58° or 2.5758 radians.</span></p>Geometry Answershttps://www.mathhomeworkanswers.org/273989/angle-between-lines-whose-direction-cosines-given-equation?show=274000#a274000Sun, 24 May 2020 14:08:33 +0000Answered: MY name is Arham I want to know my name in math.
https://www.mathhomeworkanswers.org/273986/my-name-is-arham-i-want-to-know-my-name-in-math?show=273987#a273987
<p style="text-align: justify;">Your name is either 17070012 or 303536</p>https://www.mathhomeworkanswers.org/273986/my-name-is-arham-i-want-to-know-my-name-in-math?show=273987#a273987Sat, 23 May 2020 14:55:28 +0000Answered: Which of the following is equivalent to 1/log3(m) ?
https://www.mathhomeworkanswers.org/260467/which-of-the-following-is-equivalent-to-1-log3-m?show=273976#a273976
Log m (3)Algebra 2 Answershttps://www.mathhomeworkanswers.org/260467/which-of-the-following-is-equivalent-to-1-log3-m?show=273976#a273976Sat, 23 May 2020 03:05:18 +0000Answered: How much is the most valuable watch worth?
https://www.mathhomeworkanswers.org/273966/how-much-is-the-most-valuable-watch-worth?show=273970#a273970
<p style="text-align:justify">If one watch has value £x, the other is worth 200-x pounds.</p>
<p style="text-align:justify">The difference in their value is 200-x-x=200-2x=64, so 2x=200-64=£136, x=136/2=£68. The other watch is worth 200-68=£132, so this is the more valuable watch.</p>
<p style="text-align:justify"> </p>https://www.mathhomeworkanswers.org/273966/how-much-is-the-most-valuable-watch-worth?show=273970#a273970Fri, 22 May 2020 16:59:23 +0000Answered: How to simplify (10^2 x y^2)^3
https://www.mathhomeworkanswers.org/273965/how-to-simplify-10-2-x-y-2-3?show=273969#a273969
<p style="text-align: justify;">(10²)³(y²)³=10⁶×y⁶=1000000y⁶</p>Other Math Topicshttps://www.mathhomeworkanswers.org/273965/how-to-simplify-10-2-x-y-2-3?show=273969#a273969Fri, 22 May 2020 16:53:03 +0000Answered: What is x+x-x=15. Solve for x
https://www.mathhomeworkanswers.org/273952/what-is-x-x-x-15-solve-for-x?show=273968#a273968
<p style="text-align: justify;">Two x’s cancel out leaving x=15.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/273952/what-is-x-x-x-15-solve-for-x?show=273968#a273968Fri, 22 May 2020 16:49:56 +0000Answered: What number is halfway between 0.6 and 0.7
https://www.mathhomeworkanswers.org/251362/what-number-is-halfway-between-0-6-and-0-7?show=273947#a273947
<p><img alt="crying" src="https://www.mathhomeworkanswers.org/qa-plugin/ckeditor4/plugins/smiley/images/cry_smile.gif" style="height:20px; width:20px" title="crying">bulling</p>Other Math Topicshttps://www.mathhomeworkanswers.org/251362/what-number-is-halfway-between-0-6-and-0-7?show=273947#a273947Fri, 22 May 2020 04:45:04 +0000Answered: 0.9 is the same as 9
https://www.mathhomeworkanswers.org/266047/0-9-is-the-same-as-9?show=273930#a273930
<blockquote>
<p style="text-align: justify; margin-left: 40px;"><span style="text-decoration: line-through;">yes<u><em><strong> boi it issss boiii<img alt="" src="ssjwjssjwswssws" style="border-style:solid; border-width:12222px; margin-left:2px; margin-right:2px"></strong></em></u></span></p>
</blockquote>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/266047/0-9-is-the-same-as-9?show=273930#a273930Thu, 21 May 2020 14:06:06 +0000Answered: Pre- calc question
https://www.mathhomeworkanswers.org/273921/pre-calc-question?show=273928#a273928
<p style="text-align: justify;">If 40 people contribute, the amount raised is $4000, because each contributes $100.</p>
<p style="text-align: justify;">The question doesn’t say what happens if more or fewer than 40 contribute, so the question seems open to different interpretations.</p>
<p style="text-align: justify;">Let’s suppose the first contributor contributes $99, so 4 additional people contribute, making 5 in all. If each of these contributes $99, the total amount contributed so far is 99+4×99=$495. But for each of these 4 people, 4 more contributors are added, making 16 contributors. So far, this would make 21 contributors and $2,079 if the new additions each contributed $99. With no limit on the number of contributors, the total contributions is unlimited, if the pattern continues. The equation would be 33(4ⁿ-1), where n is the number of “generations” of contributors. 2079=33(4³-1) for n=3.</p>
<p style="text-align: justify;">Now, let’s suppose that the first contributor contributes $90, so 10 additional people contribute, making 11 in all. If each new contributor contributes $90, then $990 would be raised so far. But each new contributor brings in a further 10 contributors, making a total so far of 111. The equation would be 10(10ⁿ-1) for an indefinite succession of contributors.</p>
<p style="text-align: justify;">Another interpretation would be to put a limit on the number of contributors. The question doesn’t give a maximum, but just states that, if there are 40, each contributes $100.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/273921/pre-calc-question?show=273928#a273928Thu, 21 May 2020 12:37:30 +0000Answered: which 3 square numbers add to make another square number
https://www.mathhomeworkanswers.org/51603/which-3-square-numbers-add-to-make-another-square-number?show=273906#a273906
2 squared + 3 squared +6 squared = 49 whose square root = 7Algebra 1 Answershttps://www.mathhomeworkanswers.org/51603/which-3-square-numbers-add-to-make-another-square-number?show=273906#a273906Thu, 21 May 2020 10:38:14 +0000Answered: Jake cut a 40 inch board into two pieces and painted one purple and the other orange. The purple board is 4 inches longer than the orange board. How long is each board?
https://www.mathhomeworkanswers.org/273915/pieces-painted-purple-orange-purple-inches-longer-orange-board?show=273916#a273916
Let the length of the orange board be x inches.<br />
<br />
Then the length of the purple board will be x+4 inches.<br />
<br />
x+x+4=40<br />
<br />
2x+4=40<br />
<br />
2x=40-4<br />
<br />
2x=36<br />
<br />
x=36/2<br />
<br />
x=18<br />
<br />
Orange board length is18 inches and purple board length is 22 inches .Pre-Algebra Answershttps://www.mathhomeworkanswers.org/273915/pieces-painted-purple-orange-purple-inches-longer-orange-board?show=273916#a273916Thu, 21 May 2020 02:22:51 +0000Answered: 12 3/4 length board is going to be divided into 4 pieces, then those pieces are divided in half, what is the length of each piece?
https://www.mathhomeworkanswers.org/273907/length-board-divided-pieces-those-pieces-divided-length-piece?show=273914#a273914
<p style="text-align: justify;">12¾ divided by 4 then halved is 12¾ divided by 8=51/4÷8=51/32=1¹⁹⁄₃₂ or 1.59375.</p>https://www.mathhomeworkanswers.org/273907/length-board-divided-pieces-those-pieces-divided-length-piece?show=273914#a273914Wed, 20 May 2020 23:12:11 +0000Finding critical point
https://www.mathhomeworkanswers.org/273909/finding-critical-point
I need some help please. Find and classify the critical point of (,) = 2 + 2 + 4 − 8 − 12Calculus Answershttps://www.mathhomeworkanswers.org/273909/finding-critical-pointWed, 20 May 2020 19:04:35 +0000Answered: Determine the probability that a board selected at random will be at least 10 ft long.
https://www.mathhomeworkanswers.org/273900/determine-probability-that-board-selected-random-will-least?show=273903#a273903
<p style="text-align: justify;">The uniform distribution is represented by a rectangle with base length 12-6=6 and height 1/(12-6)=1/6, making the area=1, the total of all probabilities. 10ft is 2/3 of the distance (and area) between 6 and 12 feet, so that’s a probability of 2/3, answer d, because the total of probabilities for ≥10 is the area split off by a vertical line drawn at x=10, where x ranges from 6 to 12. (10-6)/(12-6)=4/6=2/3.</p>https://www.mathhomeworkanswers.org/273900/determine-probability-that-board-selected-random-will-least?show=273903#a273903Wed, 20 May 2020 13:47:51 +0000Answered: Describe the graph of this distribution.
https://www.mathhomeworkanswers.org/273899/describe-the-graph-of-this-distribution?show=273902#a273902
<p style="text-align: justify;">The graph is a rectangle. The lower limit of the graph is 6 and the upper limit is 12, because the distribution is uniform. The base length is 12-6=6. The height is 1/6, the same probability for all lengths. The area of the rectangle is 1 including all probabilities. The graph can be represented by a piecewise function f(x)=</p>
<p style="text-align: justify;">{ 1/6 | 6≤x≤12</p>
<p style="text-align: justify;">{ 0 | x<6 or x>12</p>
<p style="text-align: justify;">Answer d is probably applicable.</p>
<p style="text-align: justify;"> </p>https://www.mathhomeworkanswers.org/273899/describe-the-graph-of-this-distribution?show=273902#a273902Wed, 20 May 2020 13:39:40 +0000Answered: Find the equations of the lines that are tangent and normal to the curve e^ x + y^ 2 = 2 at the point (0, 1).
https://www.mathhomeworkanswers.org/273866/find-the-equations-lines-that-tangent-normal-curve-the-point?show=273879#a273879
<p style="text-align:justify">eˣ+y²=2,</p>
<p style="text-align:justify">eˣ+2yy'=0,</p>
<p style="text-align:justify">2yy'=-eˣ.</p>
<p style="text-align:justify">At (0,1): 2y'=-1, y'=-½, so the tangent line has a slope -½, and the normal has a slope -1/(-½)=2.</p>
<p style="text-align:justify">Use slope/intercept to get the tangent line and normal line equations:</p>
<p style="text-align:justify">TANGENT: y-1=-x/2, y=-x/2+1</p>
<p style="text-align:justify">NORMAL: y-1=2x, y=2x+1</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9940561672866796153" style="height:259px; width:350px"></p>
<p style="text-align:justify">Curve is in red; the tangent line is blue and the normal line is green.</p>Calculus Answershttps://www.mathhomeworkanswers.org/273866/find-the-equations-lines-that-tangent-normal-curve-the-point?show=273879#a273879Tue, 19 May 2020 22:14:04 +0000Answered: area of isosceles triangle 30, 30, 120 angles, 2 sides are 6"
https://www.mathhomeworkanswers.org/53438/area-of-isosceles-triangle-30-30-120-angles-2-sides-are-6?show=273878#a273878
<p><span style="font-family:courier new,courier,monospace">so first you put one side on then the other side and then you have your answer. The answer is 1234567890 do you like scooby doooooooooo me does :) hahahahahahavavbabahahahahhahahahahahahahahahahahahahahahhahahwhw see ya</span></p>Geometry Answershttps://www.mathhomeworkanswers.org/53438/area-of-isosceles-triangle-30-30-120-angles-2-sides-are-6?show=273878#a273878Tue, 19 May 2020 20:42:16 +0000GEOMETRY QUIZ
https://www.mathhomeworkanswers.org/273876/geometry-quiz
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=14507592130494358406" style="height:337px; width:600px"> This is a screenshot of the quiz there are 2 more problems after I get an answer for these thanks!</p>Geometry Answershttps://www.mathhomeworkanswers.org/273876/geometry-quizTue, 19 May 2020 19:21:28 +0000Answered: 908,400 in scientific notation
https://www.mathhomeworkanswers.org/273845/908-400-in-scientific-notation?show=273875#a273875
<p style="text-align: justify;">9.084×10⁵ which can be written 9.084e5 or 9.084E5.</p>https://www.mathhomeworkanswers.org/273845/908-400-in-scientific-notation?show=273875#a273875Tue, 19 May 2020 18:51:52 +0000Answered: Ken has $60, and he wants to buy at least 8 plants for his garden. Plants A is $6, and Plants B is $10.
https://www.mathhomeworkanswers.org/273870/ken-has-and-wants-least-plants-for-his-garden-plants-and-plants?show=273874#a273874
<p style="text-align:justify">Let A be the number of Plant A plants and B the number of Plant B plants.</p>
<p style="text-align:justify">First inequality: A+B≥8. The total cost of the plants = 6A+10B and cannot exceed $60, so the second inequality is 6A+10B≤60, which simplifies to 3A+5B≤30.</p>
<p style="text-align:justify"><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=15263944326203299787" style="height:260px; width:350px"></p>
<p style="text-align:justify">In the above graph Plant B is the vertical axis and Plant A the horizontal axis.</p>
<p style="text-align:justify">The pink line and shading represents the quantity of the plants while the blue line and shading represents the cost of the plants. The dark shading is the region where both inequalities are true. The intersection of the lines is where equality is satisfied, that is, A+B=8 and 6A+10B=60. This happens when A=5 and B=3. The rest of the dark shaded area above the horizontal axis contains all the values of A and B where both inequalities are satisfied.</p>
<p style="text-align:justify"> </p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/273870/ken-has-and-wants-least-plants-for-his-garden-plants-and-plants?show=273874#a273874Tue, 19 May 2020 18:27:08 +0000