The revenue and the cost rate of Gold Star mining operation are, respectively 1 R'(t) = 19 – tz and C'(t) = 3 + 3t? where t is measured in years and R and C are measured in millions of dollars. Determine how long the operation should continue to maximize profit. Find the profit that can be generated during this period. Ignore any fixed costs.

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

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A:

Q: Assumee thát ic COst C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. t…

A: given cost functio cx=25600+100x=0.1x2

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A:

Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

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Q: Evaluate.cuse C for the Constant of integration). 40 t6x-X dx

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Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Find dy/dx by implicit differentiation. x3 + y3 =1

A: The equation: x3+y3=1

Q: find dy/dx by implicit differentiation.   1. x2 + xy + y2 - 5x = 2    2. 5x^(4/5) + 10y^(6/5)=15

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Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: Find dy/dx by implicit differentiation. x2 + y2 = 9

A:

Q: The Strikers Technologies Company determines that the marginal cost for their MaxiPak flash disks is…

A: We will integrate the function with respect to x and then find the general solution. Next, for…

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A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

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: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: یک 2. G(x) = L tanz et et +3 -dt

A:

Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. y= ;d'y/dx 2. Y = (7x + 2)S ;y"…

A:

Q: Find the total derivative dy dw. Y=3x+2w+5z x=4 In(w*) z=e43x³

A: Given, y=3x+2w+5z2x=4ln(w2)z=e-z+3x-3

Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

Q: determine dy/dx of the implicit function: 2x2y-sinxy2+e-xy=10

A: Given implicit function is  2x2y-sinxy2+e-xy=10 To find: dydx

Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: find the soution of' the differential eq. System X= 3X+44 9=X+3y %3D

A: Given differential equations are                                     dxdt=3x+4y,dydt=x+3y…

Q: Find the derivative. 8) y =V4x +2 dy dxN4x + 2 =N4x + 2 A) dy В) dx 4 1 N4x + 2 dy C) dx dy D) dx 8…

A: SOLUTION-

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: Second derivative of dy/dx = (2t+1)/(2t) x=t^2 + 1, y=t^2 +t

A: Given that dydx=2t+12tand x=t2+1,y=t2+tThen dydx=dydtdxdtAs dydt=2t+1,dxdt=2tso dydx=2t+12tNow…

Q: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

A:

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: dy Y = y° dx 'x

A: As per guidelines,we will solve only first question.

Q: Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr/ dx = 2…

A: To determine the expected revenue from a production run.

Q: Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr dx = 2 -…

A: To Determine:  How much money should the company expect from a production run of x = 3 thousand…

Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

A:

Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A: A heat-seeking particle is located at the point 2,3 on a flat metal plate whose temperature at a…

Q: Find the indicated derivative. dy dt for y=(2.7t-4t)(3t+1.6)

A:

Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

A:

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

A:

Q: Find dy/dx by implicit differentiation. 2) x3 - 2y2 = 1 4y B) x2 + 1 A) 4y C) 2y D) x2

A: solve the following

Q: y" – 4y' +4y = 0; y(0) =-1, y'(0) = 0

A: We have to solve the differential equation…

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

A:

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

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Q: Differentiate the function. 1 y3= (2x +3) dy dx

A:

Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A:

Q: Confirm the approximations by using the linear approximation at x = 0

A: