Develop an equation relating the rates at which the variables V and h are changing (dv/dt and dh/dt). O dV A) = 9th² dt dV TC B) dr = n²( dt ū D) dV dt dV dt 3πr 2 dt dh dt. dt. TC (dh 72 dt.

Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: Suppose the temperature of a metal plate is given by f (x, y) = the temperature of the metal plate…

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Q: Can you help me step by step?

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Q: dx -y = 5 dt dy = 3t dt 2x -

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A: We have given  F= G m1m2/r2  Where F is force of attraction , G is gravitational force which is…

Q: Indicate whether the following statement is true or false. The change of variable formula reads:…

A: We have to check whether the statement, "∬Dfx,ydxdy=∬D'fxu,v,yu,v∂x,y∂u,vdudv" is true or false. The…

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A: Given, y= cot(9x4-2x +8)   To find: y''

Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: 3. x dy + 6y = 3xyi dx

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Q: U= Find values of u, a, b, and C so that a = [³ In(+³) t b= dt = cb a Cu Cu du. C =

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Q: 11 FCF)dt= fCx) dx =- 43 then 1.

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Q: dv dt Find given ure, z=t", and y=-2+3t. Write answer in terms of the independent variable. = du dt

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Q: Find dx dt dy dt dy dx dx dt || 11 || dy dt dy dx x = 5t - 5ln(t), and y = 8t² - 8t -2

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Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.