How do you find the kinetic energy of a tennis ball that is served with a speed of v m/sec is given by f(v) Joules. Values for the function f are shown in the table below. Estimate f'(55) with units?

Q: Anti-derivative of this function:  h(θ) = 4 csc θ cot θ + 2 sec2 θ

A: Indefinite Integration

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: · The carbon monoxide level in a city is given by c(p)=0.04p" +2 ppm (parts per million), where p is…

A: To solve the given derivative problem.

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm/ min.…

A:

Q: There was a girl in a class studying math with, of course, a math teacher. This girl's name is…

A: Given query is to find the amount converted in two hours.

Q: (a) Find the average rate of change of y with respect to x over the interval [xo, x1]. (b) Find the…

A: Here, We are going to solve only the first three subparts of question number 7 and for the remaining…

Q: le's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A:

Q: Find the first derivative of y = ( ex – e –x ) /  (ex  + e –x ) and y = ln [ x  +  √ (x2  + 1) ]…

A:

Q: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: Given problem:- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a…

Q: Find the equation of the line tangent to the graph of y = 4 ln(x) at a = 2. Enter exact values.…

A: detailed solution is given below

Q: An object is tossed into the air vertically from ground level with initial velocity v0 ft/s at time…

A:

Q: 1) Find the derivative of the function g(x) = (arctan x)3, first showing how to get the d formula…

A: As per guideline we have solve only one question

Q: A water balloon of mass 890 grams is rolled on level ground with an initial velocity of 38 meters…

A: (a) given balloon of mass M=890 gram initial velocity V0=38 meters per second according to question…

Q: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 7 volts is…

A: Given that , V = 7 volts R' = 0.1 ohms R = 4 ohms I' = ?

Q: A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: Given: dQdt=-rQ for Q is the amount present at time t. 100 mg reduce to 82.04 mg in 1 week, the…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att= 0, fresh…

A:

Q: 15. Find the average rate of change of the function f(x) - - 3x between the points (-2,14) and…

A: Average rate of change of a function between two points is change in output divided by change in…

Q: According to Kleiber’s Law, the metabolic rate P (in kilocalories per day) and body mass mm (in…

A:

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

A:

Q: A box with a square base and open top must have a volume of 296352 cm. We wish to find the…

A:

Q: The tank shown in the figure was filled with 100 liters of substance A in a concentration of 10g /…

A: Given: The tank having 100 liters of substance A in a concentration of 10g / L. Material A is fed…

Q: dium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: since it is given that, Sodium chlorate crystals are easy to grow in the shape of cubes by allowing…

Q: dy Part II: Find the derivative ) implicitly. Show all work. dx 11. e" – 4x³ + 5y? = 10

A:

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att = 0, fresh…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: A roast turkey is taken from an oven when Its temperature has reached 185F and Is placed on a table…

A: Follow step 2.

Q: 13. A motorcycle is moving at 30 m/s when the rider applies the brakes, giving Che motorcycle a…

A: Consider the given information. If the acceleration is constant then we can use these equations.…

Q: 5. Find the average rate of change of the function f(x)= cos² x from x =- x = ". Use to - exact…

A: Rate of change=f(b)-f(a)b-a Given:  f(x)=cos2x, x=-π6,π4

Q: The average rate of change of h(x) over the interval [a, b] is zero and b > a. Part A: What can we…

A: A) The average rate of change = change in outputchange in input…

Q: 20. Il: Antiderivatives A car is being driven at a rate of 40 mph when the brakes are applied. The…

A: We have to find the time taken by car to stop.

Q: A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: If Q(t) is the amount present at time t, then dQ/dt = −rQ, where r > 0 is the decay rate.…

Q: A formula for the drag force is F = dv² (found to be valid for a large regime of data), where F is…

A:

Q: Solve the problem. Find the derivative of the function f(x y) = x² + xy + y² at the point (6, 7) in…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Molar volume is a function of temperature and the pressure or V = f (T, P) ; and its total…

A:

Q: A basketball is thrown for a 3-point shot. The height of the basketball (in meters) is given by the…

A: To find the height from which the basketball is thrown, average velocity, instantaneous velocity and…

Q: an object is moving in than positive x direction slowing at a rate of 2.93 m/s^2. After moving…

A: To find the initial speed

Q: Exercise 4 Water drains from the conical tank at the rate of 5 fi / min shown as in figure. (i) What…

A:

Q: The function of position of an object in motion with respect to time is obtained by fa] a.…

A: By integrating the acceleration with respect to time we get the velocity of an object. dx/dt…

Q: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: The Worldometers website (www.worldometers.info.) estimates that as of July 2015, the Philippine…

A: Use the information given in the model to find the equation. It is given that the population changes…

Q: A bacteria culture is known to grow at a rate proportional to the amount present. After one hour,…

A: For the solution of the problem follow the next steps.

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.05 cm /…

A: Area =πr² Find dA/dt when r=56 cm

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

A: Given problem:- A potter forms a piece of clay into a cylinder. As she rolls it, the length, L, of…

Q: The tangent line to the graph of y=f(x) at the point (7,55) has the equation y=8x−1 (a) Find f′(7)…

A:

Q: Find y"by implicit differentiation of x3 + y3 = 1.

A: x3+y3=1 ddxx3+y3=ddx(1) 3x2+3y2dydx=0 dydx=-x2y2

Q: a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down…

A: We have to use formula for volume and surface are of a sphere in terms of radius (r) .  Volume…

Q: What is the result of integrating a population growth rate between two times t= a and t=b, where…

A:

Q: Vr2 + 1 VI+1 Calculate the derivative of the function y = log3

A:

Q: Water is flowing at constant rate of 120 cc/sec in a hemispherical bowl with radius 18 cm. If the…

A: ANSWER: Option a) 0.1669 cm/s

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: