Answer it correctly, neatly, and comprehensively.  Written answer only.  A rectangular box with open top and has a square base is a school project of two  senior high school students. However, they are wondering what would be the  minimum dimensions of their box if it will have a fixed volume of 62.5 cm³

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

A: Please refer to the image below

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A: I hope the perfect equation you mean is the exact differential equation. We use the exact…

Q: Find the general Solution of the following PDES Du -5X -3x = 2 +4, исx; c) = 32 + 2e du ду 3e Dx…

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Q: 1. y ecos(-2x) =

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Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx − (2xy + x²) dy…

A: A detailed solution is given below.

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Q: ferential √226

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A: Here we have to find the general solution of the given differential equation,  y'+2y=2ex…

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A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

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Q: y² = 8x, y = 2x; about y = 4.

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Q: 1. Prove the linearity principle (the homogeneous case). That is, if yn (t) is a solution of the…

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Q: ✓ Solve the following linear programming problem using the graphical method Min (Z)= 20X+30Y…

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Q: Given the vector function F(t) = (+1, 1-2t², 8t-4), find the are length of this curve on the…

A: Please refer to the image below

Q: e dx + (2y + xe") dy = 0

A: Given ey dx+2y+xey dy=0 Here M=ey and N=2y+xey ∂M∂y=ey  , ∂N∂x=ey Therefore,   ∂M∂y=∂N∂x is exact…

Q: O By direct partial integration, Solve the following PDES 8- аги axdy = CBX COSy? SXUCX,t) Ex u(x₂)…

A: The pde is solved using partial integration

Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it da da d. +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 4. Evaluate 12x+1 dx 5. Evaluate dx X 6. Evaluate [ 3x -¹ dx

A: To find the value of given integrals .

Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

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Q: An airplane takes off from an airport at sea level and its altitude (in feet) at time t (in seconds)…

A: The given equation is: h=3400lnt+1   ...1   As we know that; The Power Law: ddxxn=nxn-1 The Chain…

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A: Trigonometric series

Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: We have to set up the integral for volume.

Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

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Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

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Q: Solve for y at x=2: (x5 + 3y) dx - x dy=0; x=1, y=2

A: Rewrite the differential equation in standard form and solve it

Q: 1. Given the region bounded by the following functions as well as the x-axis: y= 2²/1₂ ² x= x = 4…

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A: Value of b is given.

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

A: The given indefinite integral is: I=∫dx4x+3   ...1   As we know the common integral. ∫1xdx=lnx+C

Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

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A: Given

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Q: Change the Cartesian integral to polar coordinate dy dx 171-72 حول من كا الا بولير -1 0

A: ∫-11∫01-x2dydxIn polar co-ordinates, Let  x = r cosθ    and    y= r sinθThen , r2 = x2+y2     and…

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A: Cayley Hamilton theorem and basic property of eigenvalues are used

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A: Use first derivative to sketch curve of function g(theta)

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

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Q: o classify the following PDES :- 227 ахг <-2 822 буду +2 82 дуг =x+3y 2 X •x2 Ихх - 2 xу Иху +ў Иуу…

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Q: luate 2 Af ² (x-1) 25 dx 7 S² √4+3x dx 1 x² (1+22³)5 dx esinx cosxdx O 플 the definite O inte

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Q: Find the maximum and minimum values of the function ㅠ g(0) = 60 - 7 sin(0) on the interval 0,…

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Q: Consider the function f(x) = 3x² − 8x + 6, 0 ≤ x ≤ 9. The absolute maximum of f(x) (on the given…

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Q: Solve the following using the inverse matrix method: (Show your solution) 13 3x + 2y 5 x + 4y 5x + y…

A: As per bartleby guidelines we only give first question answers.