If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: Given An environmentalist find that a certain types of tree grows in such a way that its height h(t)…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: Suppose x and y are functions of third variable t. In the equation x+y=45, what are the values of…

A: The given equation is: x2+y2=45   .....(1) When x = 3, 32+y2=45y2=45-9y2=36y=±6

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

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Q: A study of a certain Subanen community suggests thatt years from now, the average level of carbon…

A: Given query is to find the rate of change of carbon monoxide after 2 years.

Q: Locate the relative extrema of y = ln(x2 + 2x + 3).

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: 7) The rate of water flowing in a tank is given by: R(t) = 0.5t* + 20t Gallons/minutes. How much…

A:

Q: find the rate of change. The reciprocal 1/x with respect to x when x = 1, 2, 3

A: The rate of change of a function is the value of the derivative of the function; thus, let the…

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

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Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: 2. The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: As per our limit we can answer only the first question. If you want other questions to be answered…

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: One model for the way diseases die out when properly treated assumes that the rate dy/dt at which…

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Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

A:

Q: 10 If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does S g'(x)dx…

A: Given, g'(x) is the rate of growth of redwood tree in feet per year now, We have to define…

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: Suppose the constant rate of change y with respect to x is -2.5 and we know that y=-6.75 when x=1.5…

A: Given,The constant rate of change of y with respect to x = -2.5.We know that,Slope = rate of change…

Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О

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Q: The radius of a right circular cylinder is given by √(t + 2) and its height is 1/2√t, where t is…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

Q: Suppose x and y are functions of third variable t. In the equation +y²=45, what are the values of…

A: First we will differentiate the given equation with respect to t using the chain rule of…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: We have to determine the time necessary for the number of bacteria to triple.

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

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Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

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Q: A snowball melts in such a way that the rate of change in its volume is proportional to its surface…

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Q: The radius of a right circular cylinder is increasing at the rate of 8 in/sec while the height is…

A: Given- drdt=8 in/sec and dhdt=-3 in/sec To Find- The rate of the volume changing when r= 7 in and…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

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Q: Suppose x and y are functions of third variable t. In the equation +y=45, what are the values of the…

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Q: The derivative of y=eSinh/x +cosh¬/x equals

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Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

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Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

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Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Exponential Growth Model

The relation that represents an exponential function is: