A certain tank of depth 10 ft is a surface of revolution formed by rotating y = x² about its axis. If the tank is full of water, find the work done in pumping the water to the top of the tank until the depth of the remaining water is 6 ft.

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A: In this question, we need to evaluate the given integrals. Note : According to bartleby guidelines,…

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A: Given that y is

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A: Here, R→(t)=t2,1-t2,t, r(t)=cos t So, F→(t)=R→∘r(t)⇒F→(t)=R→(cos t)⇒F→(t)=cos2t,1-cos2t,cos…

Q: 1+x² 1. Find the area of the region bounded by the curve y=- 2x² and the lines y = 0, y = x, x = 2.

A: Given problem:-  1. Find the area of the region bounded by the curve y=(1+x2)/2x2 and the lines y =…

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Q: The volume of y = (3x+1)+,x=0, x=8,y=0 O (28/9) TL O (26/3) T O (1372/9) O (248/9) m 6 and x = = 2y

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A: First derivate with respect to t then derivate with respect to x to get desired result

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Q: Find all solutions to the given equation. In the choices, k runs through all integers. √3csc(x)+2=0…

A: We can find the answer as below.

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A: Product Rule of differentiation : d(u.v)dx = udvdx+dudxv. dxndx=n.xn-1

Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

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Q: 5. Given the Standard Equation the DE, Identify the roots * d²y d³ y dx³ dx² + dx - 2- m: 1+ √2,0…

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A: I am attaching image so that you understand each and every step.

Q: dx Evaluate ·S- x1/2 + +x213 A none of the choices B С) ℗ D E using rationalizing substitution. 3 ln…

A: Let's evaluate given integral by rationalizing substitution.

Q: Suppose cot(y) = - 3 4 and csc(y) > 0. What is the value of sin(y)? A B Ⓒ с I 415 315 -33 |

A: solution next step

Q: 4. Evaluate the following integral using cylindrical coordinates: LI [zd x dz dy dx

A: Let's evaluate given integral by using cylindrical coordinates.

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A: The integration of the integral is  1/(x1/2+x1/3).

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A: Graph :

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Q: d'y day + dx5 dx4 y = (C₁+C₂ + С3) ex +C4e²x+C5e-3x y = Cıe2* +Czxe-3x +C3е* + С4е* + С5е* OA) Ō d³…

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A: The objective of the question is evaluate the limit and choose the correct option.

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A: Solved below

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