A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 7 feet.

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A: The given DE is: xy3dx+(y+1)e-xdy=0...(1)

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A: Given problem:-

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A: We can find Inverse of the matrix by using Gaussian elimination method and also apply Row operation ...

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Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

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Q: find A-1 using Gaussian elimination and check the resul 3 -2 [1 1) A = |1 2 4. 27 1 1 Ans: A-1 = -2 ...

A: Explanation of the answer is as follows

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A: Vector

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Q: Find f. f"(x) = cos(x), f(0) = 6, f'(0) = 4, f"(0) = 9 f(x) =

A: We can find the value of f(x) as below.

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A: To states whether true or false. For every continuous non linear function, there is a value of x tha...

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A: Given, g(1)= -1 g'(x)= √(x²+15) g'(1)= √16= 4

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

A:

Q: A. Write the missing term/s in the given series of numbers. 1. Find the next three terms in: -14 -10...

A: 1.      -14,-10,-6,-2,_,_,_ -14+4=-10-10+4=-  6    -6+4=-  2   -2+4=      2        2+4=      6      ...

Q: Show that f x) = Ix- 5| is NOT differentiable at 5 by using the definitien of the derivative, (Start...

A: Definition of derivative:f'(x)=limh→0 f(x+h)-f(x)hf(x)=x-5f(x)=5-x,  x<5x-5,  x≥5L.H.S. limit:x&l...

Q: 12 17 Find p, q if s" f(x) dx + fi2 f(x) dx = " f(x) dx. (Give your answers as whole or exact number...

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Q: Se xe" ds. Cis the line segment from (0, 0, 0) to (1, 2, 3)

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

Q: Give The 15T four nonzero Ternm oF Me Serbes abour ) He) =

A: Given:fx=excos3x

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A:

Q: use Gaussian Jordan 2メ+4y+ 6Z = 18 4x+ Sy + 6Z = 24 3x + Y -2Z =4 thy answer should be like this: 10...

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Q: The Furmetion fla)=t kininen as Taylor series abaut x =0 4s derwamine ite series elow end nerite our...

A: a) fx=8e2xb) gx=9x5e-1 x

Q: Use the table below to find: (f o g)(10) = (go f)(7) = %3D %3D (f o f)(2) = (9 o g)(9) = || -9 -7 -4...

A: Use the table 

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A: 3xy ^ 2dx + (3x ^ 2y + 4y ^ 2) dy = 0  

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Q: 2. f(x) = V-3x+ – 2

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Q: - partial fraction 1 -dx x(x² +1}

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Q: Rion to 2%3D8

A: Solution :Derivative with implicite diffrantiation Given  : x2y+y2=8

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Q: 1. D + The region D above lies between the two red lines and the red parabola y ?. It can be describ...

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Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: x'(2 - x)? dx

A: Let,I=∫ x32-x212dxSubstitute  u=2-x2Differentiate du=-2xdxAnd x2=2-udu-2=x.dxI=∫ x32-x212dxI=∫ x22-x...

Q: 2. For the following complex numbers; peform the indicated operations. Expressresultsin rectangular ...

A: Given:  za=-2-5izb=2.15e4.18izc=1.75cos165°+isin165°zd=0.745∠-36°ze=1+3izf=0.953cos324°+isin324°zg=2...

Q: 2x2; yい= - | %3D

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Q: 1) Linearize: 3x arourd 天=l %3D

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Q: VII. Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0 2. ...

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Q: Given vectors u = (3, –6) and v = (-6, 2) , find the difference v – u and represent the difference g...

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Q: h(x, y, z) = xyz, P(3, 2, 6), v =

A: We will find the directional derivative. 

Q: Determine the coterminal angle of 0 that is in the interval [0, 27) 307л 0 = 3

A: The answer to this question can be obtained by changing the angle in radians into degrees and then d...

Q: Find f'(x). f(x) = (3x° + 2) * f'(x) = %3D

A: