Waste Management Company wants to construct a dumpster in the shape of a rectangular solid with no top whose length is four times its width. Its volume is fixed at 25.6 yd3. Find the dimensions of the dumpster that will minimize its surface area.

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

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Q: 2x² +2y? 11. Set up an integral that would calculate the volume of the solid bounded by the…

A: Given problem:- 11. Set up an integral that would calculate the volume of the solid bounded by the…

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Q: Suppose on Jan 1, 1997 Dave invested $2,000 into a bank account at 5% interest compounded…

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Q: 20) Solve the higher order initial-value problem y"=x+1/x;y(2) =1 and y '(2) = 0 1 7 7 1 15 + -- X-…

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Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

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Q: 2. The volume of the sun is 1.4 x 10 cubic kilometers and the volume of the earth is 1.1 x 102 cubic…

A: Earth mass

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Q: 1. The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3yt = 0. a) Calculate the value of…

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Q: 3/xyy' = 5

A: We have to solve the differential equation  3xyy' = 5.

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A:

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Q: Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

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Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

Q: Solve

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Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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Q: Evaluate F. dr. F(x, y) = 7xi + 8yj C: r(t) = ti + V4 - t²j, -2 sts 2

A: Use line integral concept

Q: Find the domain of r(t) and the value of r(to). Edit NOTE: Round your annwer to two decimal places…

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Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: We have to find the slope.

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: 5 4 3 2 1 -1 T/2 3T/2 -2 -3 -4 -5 The graph of the function f(x) : given above for the interval x E…

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Q: 8. c d 12 10 values of the areas bounded by the curve h', the derivative of h, and the x-axis on the…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Match the equation with its graph. 16 56

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain.

Q: cos x sinx dx- 3 COS

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Q: dx Ух — 12

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Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

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Q: 5 4 3 1 T1/2 3π/2 -1 -2 -3 + -4 -5 The graph of the function f(x) = cot x is given above for the…

A: Solution is given below:

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Q: y" –3y – 2y=0; x =0,y=0, y' =9,y' =0

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: 1 Given that 1 > x" with convergence in (-1, 1), find the power series for with center 1- 9x4 n=0 0.…

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Q: Which among the choices is NOT true about the continuity of f(x)? if x 1 X, メ, 2 f(x) = (2 – x), O…

A: Solution

Q: Evaluate lim,-(-- 7 - 10 + 4) | 4x3 O +∞ O -7 O -10 8.

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Q: Find T(t) and N(t) at the given point. r(t) = 5 cos(t)i+ 5 sin(t)j; t = 3 T 3. N(E) || ||

A: We have to find the unit tangent and normal

Q: (1+x, if x 2 %3D

A: