If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by the equation shown belov 5900p C(p) = 100 - P Find the rate of change of C with respect to p. C'(P) = |

Q: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

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: If the instantaneous rate of change of f(x) at (5,-9) is 3, write the equation of the line tangent…

A: For equation of tangent, one have to use y-b=m(x-a)Where (a,b) is the point, m is the slope.

Q: With the given graph, estimate the instantaneous rate of change at x= -1 and show the steps. Next,…

A:

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

A:

Q: A balloon is deflating at a constant rate of 12 cm3 per second. When the volume of the balloon is…

A:

Q: By choosing small values for h, estimate the instantaneous rate of change of the function f(x) = x³…

A: Use the diffrention formula then simplify

Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: If the instantaneous rate of change of f(x) at (3, -5) is 9, write the equation of the line tangent…

A:

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: If the instantaneous rate of change of f(x) at (4, −9) is 8, write the equation of the line tangent…

A: From the given statement, the rate of change of f(x) at (4, –9) is 8.That is,  f′(x) = 8.

Q: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

A:

Q: In physics, the kinetic energy, K, of an object of mass m, moving at a velocity v, is given by the…

A: Given that kinetic energy K for an object of mass m and velocity V is given by K=(1/2)mv2. If mass…

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

A:

Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

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

A:

Q: If f(x) = 3x + 2x + 6, find the instantaneous rate of change of f(x) at x = 1. -

A: Topic - applications of derivativea Instantaneous Rate of change of f(x) at x is given by slope of…

Q: If f(x)=9x+6, find the instantaneous rate of change of f(x) at x=-5

A:

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: What is the rate of change of y with respect to x for this function?

A:

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

A:

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

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

A: First we will find value of y from given equation And differentiate wrt to t

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

A:

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

A:

Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 +…

A:

Q: tan(Cx) Va6+2 find the rate of change of P with respect to x, where C is a Given that P = constant.

A:

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

A:

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

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…

A:

Q: Find the equation of the line tangent to the graph of y = (x2 - x) ln (8x) at x = 2

A: Topic = Derivative

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

A:

Q: For f(x)=x^3​, the instantaneous rate of change is known to be 27  at x=3. Find the equation of…

A:

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

A:

Q: 7. If the rate of growth of a bacteria population is modeled by r(t) = 8e2t-1 thousand bacteria per…

A: Introduction: When a function is given, we determine the average value by integrating the function.…

Q: Suppose that f(x) = 5x² – 4. (A) Find the slope of the line tangent to f(x) at x = 5. (B Find the…

A:

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

A:

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the volt-age…

A: Separate the variables.

Q: A stuntman estimates the time T, in seconds, for him to fall x meters, 15. is T(x) = 0.54Vx. Find…

A: Instantaneous rate of change – It is the rate of change at each instant in time, not over a long…

Q: 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).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: 4. Find the slope of the line tangent to the graph of the equation -ey +y° = 7+ 2x at the point…

A: Given query is to find the slope of the tangent at given point.

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

A: .

Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah