A mining expert estimates that the production growth rate of copper overtime, or ,is given by dt' dy -3t?y + 6t2 dt where, y is copper production and t is unit of (continuous) time. The mining expert would like to determine the level of copper production overtime (y(t)). Given the above information, answer the following questions:

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: dx dy at z = - 5 if y = 3x-3 and dt Find -1. dt dx dt

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Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find partial derivative af dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Can i get help step by step please

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: The equation of path is y=2x2+7. Also dxdt=4 cm/sec

Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: The given function is  y = 2x2 + 1; dx/dt = 2 centimeters per second

Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: The integrating factor of the linear DE of order one + y csc x = sin x is dx

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Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: Given y=2x2+1 , dxdt=2 centimeters per second .A point is moving along the graph of the given…

Q: # 5) If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2. # 9) If a snowball melts so that its…

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Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: ,dz Find ifz = xy2 +x²y, y = ln x - dt

A: We are given : z=xy2+x2y and y=ln x⇒z=x(ln x)2+x2 ln x

Q: a) How is ds/dt related to dx/dt if y is constant? ds/dt=___(dx/dt)

A: Consider a function S with variable x and y as constant. S=fx+ywhere, fx=function with x as…

Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ---->1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: 2. Use the 4th-order Runge-Kutta method to integrate dx = t - sinx dt given x(0) = 1, using a step…

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Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA dx

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Q: The Integrating factor of the equation (x²y³ + xy) dy dx 1 is

A: We have to find the integration factor of the equation x2y3+xydydx=1. We know that integrating…

Q: Find for the equation below. dy dt

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Q: What is an integrating factor of the DE dy/dx = (y + y^2) / x ?

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: Given: y = (In x)* , find dy/dx.

A: Given, y=logxx take log both side logy=xloglogx now derivate both side…

Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

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Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

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Q: at is the integrating factor of the given differential uation? (2y3 – x*)dx + 3x²ydy = 0

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Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

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Q: dy dt II

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: The function is y=2x2+3   & dxdt=4 centimeter per second By using the chain rule Chain rule:…

Q: Find the differential dy of the x + 1 y = 4х — 5 dy =

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Q: Let x > 0 and b > 0. Show that

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Q: Can i get help step by step please

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.