9. Suppose an object is moving along a path described by; f(t) = t - 6t, where f (t) is measured in meters and time in seconds. What is the object's instantaneous rate of change at time t = 4 sec?

Q: Given the rate of change of a quantity Q and its initial value Q(0), explain how to find the value…

A: Given: the rate of change of a quantity Q and its initial value Q(0), To find: the value of Q at a…

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

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: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e

A: To find the instantaneous rate of change at indicated point:f(x)=ex;x=e. Solution: we know, the…

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: 4.) The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x? + 10x + 5000.…

A:

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 (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: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: .

A: We will find the temperature.

Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

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

A:

Q: 3. fox =V X at X T6

A:

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: Suppose y varies at a constant rate of change of 4 with respect to x (so that Δy=4⋅Δx ), and when…

A: topic - linear equation in two variables

Q: 14. Find the rate of change of y= (2x' +6x +4) at x =-1.

A:

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

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: The impedance Z (ohms) in aseries circuit is related to the resistance R (ohms) and reactanceX…

A: Given that The impedance Z (ohms) in a series circuit is related to the resistance R (ohms) and…

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

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

A:

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

A:

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: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

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: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 8. Use the difference quotient to find the approximate instantaneous rate of change for the function…

A:

Q: 9. Suppose an object is moving along a path described by; f(t) = t° – 6t, where f (t) is measured in…

A:

Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

A:

Q: 5. Assume that an airplane is flying toward you at a constant height of 2 miles and at a speed of…

A: Here we solve this question using differentiation and basic trigonometric formulas.…

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: If the instantaneous rate of change of f(x) at (9, -7) is 6, write the equation of the line tangent…

A:

Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

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

A:

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

A:

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

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…

A:

Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

A:

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

A:

Q: 7. If f (t) = -t2 + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A:

Exponential Growth Model

The relation that represents an exponential function is: