A covered box is to be made from a rectangular sheet of cardboard measuring 35 inches by 56 inches. This is done by cutting out the shaded regions of the figure and then folding on the dotted lines.   What are the dimensions x, y, and z that maximize the volume?

Q: To evaluate the integral / V16 – x² dx, we use Select one: O x = 4 sec 0 O x = 4 sin 0 O x = 3 sin 0...

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Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 2n Σ 7...

A: We can test the convergence as below.

Q: Replace ? with an expression that will make the equation valid. d. x* +5 = ex +5? dx The missing exp...

A: Consider the expression  ddxex4+5=ex4+5   _

Q: y' - y = 2x? 3

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next ti...

Q: 1. f (x) = 5x – 4 2. f (x) = 4x? + 3x – 6 2x+7 3. f (x) = 3x

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Q: b. (2,1)

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Q: Question 3 Find the change in y = 2x -3 if the x changes from 3.3 to 3.5. А) 0.1 0.2 0.3 0.4

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Q: ☺ Find tue indefinile intgrel. cos (5@] do

A: ∫un du = un+1n+1+C ; where, 'C' is an integration constant.

Q: A- Graph the following functions and determine (domain, range) (1) y= sin/x/ (2) y= /x - 2/

A: since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: 7. Find the volume of the solid formed when the graph of the region bounded by y = e, x = 0, x = 2, ...

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find ...

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Q: Given Cost and Revenue functions C(q) = q° - 11q +51q + 5000 and R(q) = - 3q +2400q, what is the min...

A: Given query is to find minimum marginal cost.

Q: i- graph and Rined Demain and Range for yz sin'x- 3 ーhn Hi-z+ 3x3-5 2. - graph apel find Df f Rf for...

A: 1. y=sin2x-32. limx→∞4x3-2x2+13x3-53. y=-5sin2x Note:      Multiple questions are given, we are answ...

Q: Find a solution for y in terms of x that satisfies the differential equation and passes through the ...

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Q: Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solu...

A: We have to find the solution set for the following equations using guass Jordon method.

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. ,6x dx u = ...

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Q: 2 dx х3.4 а. x2.2

A: ∫1x2.2-2x3.4dx∫x-2.2dx-2∫x-3.4dxFormula: ∫xndx=xn+1n+1+C

Q: 4. y = x0sx

A: Take the logarithm then take derivative twice. 

Q: Solve the differential equation by using integrating factors. xy' = 3y + x2

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Q: Use long division to divide and use the result to factor the dividend completely. (5x2- 3x-14) (x- 2...

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Q: Find the total differential. z = e-X tan(y)

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Q: e in free space is 1 millimeters and h = 100 t 32 1 millimeters. (Round your answer to six decimal p...

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Q: Solve the homogeneous equation (x²+y²)dy + x²dx = 0 Please help.

A: x2+y2dy+x2dx=0rewrite in standard format x2+y2dy=-x2dxdydx=-x2x2+y2

Q: TT(e-1) В. 2.

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Q: 30. The radius of a puddle is claimed to be 12.0 inches, correct to within 0.01 inch. Use linear app...

A: This question is related to error and approximation, we will solve it using given information. 

Q: Consider the region between the curve y = sin(x) and the x-axis, between r = 0 and x = on is rotated...

A: To find the volume of S using cylindrical shells method. Given information: Let S be the solid obtai...

Q: ng - 0.25t measures the concentration, in of a drug in a person's system t hours after the drug is a...

A: Goven,             Ct=49.2te-0.25t measures the concentration in ngml, of a drug in a person's      ...

Q: TC If f(x) =, then f tan x II

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Q: The acceleration of an object (in m/s2) is given by the function a(t) = 9 sin(t). The initial veloci...

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Q: (a) e2tsin (wt +t/6)

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Q: ーズ 10. S- ex

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Q: Find the derivative of y = 3sin2x A 6 sin x B 6cos2x с) 6sec2x

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Q: (-1)n+l2nx" n2 + 3 Determine the interval of convergence of n=1

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Q: The planes I. and II, have equations IL : 6y+5z =-19, 5 II,: -x -4y+7z =1. State the normal vector o...

A: We have to find the normal vectors of the given planes.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

A: Given:   ∫17x-1x2+16 dx

Q: Question Select your answer. Find the derivative of f(x) = 5/I with respect to r. 2x 5 Answer

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Q: 3x2+- 8(y + 1) = 0

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Q: (a) Graph the function f(x) = 1/x (b) Hence, using translations, reflections etc., graph 1 f(x) = -1...

A: We have to draw the graph of the given functions according to the given information 

Q: Section 3.7 p. 343/345 # 364 Determine whether the improper integrals converge or diverge. If possib...

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Q: 3 cos(x)³ dx

A: We need to evaluate integral.

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the...

A: Given problem:- Find the maximum profit and the number of units that must be produced and sold in or...

Q: If   C(t)=50te^−0.5t measures the​ concentration, in ngml​, of a drug in a​ person's system t hours ...

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Q: 2) The graph of a function y = f(x) is given. Draw a graph of it's derivative %3D

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Q: Question The position of a car traveling along a highway is given by the function s(t) = - + 312+ 20...

A: Given query is to find the interval when car is slowing down.

Q: Find the centroid of the region shown in the figure. 1 1

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Q: The Taylor series expansion is given by: 00 (-1)" sin x= 2n +1 (2n + 1)! n= 0 Evaluate sin 44° using...

A: We will find all the asked values using Taylor series expansion as following.

Q: et cos(t) Ry = e' sin(t) for 0 <t < 5 Find the length of the curve (Hint: You can simplify the integ...

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Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx ...

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x...

Q: iven Cost and Revenue functions C(q) = q° - 10q“ +51q + 5000 and R(q) = - 3q“ + 2600q, what quantity...

A: Given query is to find the quantity to minimize the marginal cost.

Q: show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given di...

A: Given differential equation y''+4y=0  y1(t)=cos(2t)     , y2(t)=sin(2t)