The volume V of a right circular cylinder is given by the formula V = 1/3ar²h where r is the radius and h is the height. a. Find a formula for the instantaneous rate of change of V with respect to h if h changes and r remains constant. b. Find a formula for the instantaneous rate of change of V with respect to rif r changes and h remains constant. c. Suppose thath has a constant value of 4 inch, but r varies. Find the rate of change of V with respect to r at the point where r is 6 inch d. Suppose that r has a constant value of 8 inch, but h varies. Find the instantaneous rate of change of V with respect to h at the point where h = 10 inch.

Q: Given the area of a circle A=πr^2, find the rate of change of diameter d if dA/dt=3cm/min and the…

A: To find: The rate of change of the diameter d. Given: The rate of change of area is dAdt=3…

Q: The base radius, r, of a cylinder is decreasing at a rate of 0,2cm/s while its height, h, is…

A:

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of o, is related to its pressure p (in…

A: NOTE: Refresh your page if you can't see any equations. . on the interval [8,11], the average rate…

Q: The rate at which ice is melting in a pond is given by R (t) = V1+ 2', where Ris measured in cubic…

A: We use substitution method to solve integration to find out amount of ice melting in first 5 minutes

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar²h where r is the radius…

A: a. The instantaneous rate of change V with respect to h is dVdh. Consider the formula V=13πr2h and…

Q: Determine by approximately what percentage the volume V of a right circular cylinder increases if…

A:

Q: A rectangular water tank is being filled at the constant rate of 35lt/s. The base of the tank has…

A: From the above information,  A rectangular water tank is filled at the constant rate, dVdt=35 lt/sec…

Q: If the rate of change of the side length of an equilateral triangle is 2br / sec, what is the rate…

A: Please rate and feel free to ask any query about any part of the question.  I have used applications…

Q: Find the rate of change of area of the square in m/s with respect to its side when the sides, s, is…

A:

Q: The radius, r, of a circle is decreasing at a rate of 4 cm/sec. Find the rate of change of the area,…

A:

Q: How do you solve?

A: Given, Side of square= x x(t)= 3t+1 Therefore, Area= (3t+1)*(3t+1) A(t)= 9t²+6t+1

Q: For what values of x is the instantaneous rate of change of the graph of y = sin x equal to 0? O and…

A: See solution below

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar h where r is the radius…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in…

A:

Q: Assuming a constant temperature, match the change in volume that a gas occupies to the change in the…

A:

Q: Suppose a particle’s position is given by f (t) = −2 / t, where t is measured in seconds and f (t)…

A: Given: ft=-2t

Q: If the area of a healing wound changes at a rate given approximately by dA 4 for 1 <t<10 is in days…

A:

Q: The length of a rectangle is 5t+5 and its height is , where t is time in seconds and the dimensions…

A:

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths a and y, and assume that a…

A: let l be the diagonal of a rectangle and x and y are the length and breadth of a rectangle  as we…

Q: The radius of a sphere decreases at the rate of 2 m/s. when the radius is 7m, then the rate of…

A: In this question we have to find the rate of change in the surface area of a sphere decreases.

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the…

A: Solve for the length of ladder

Q: The area of a square with sides of length s is given by A = s². Find the rate of change of the area…

A:

Q: Suppose that D = √x² + y² is the length of the diagonal of a rectangle whose sides have lengths x…

A: To find the formula for the rate of change of D with respect to x, differentiate D=x2+y2, using the…

Q: Enter the exact answers. (a) Find the average rate of change of y = - with respect to x over the…

A: Given: y=1x2   ,5,6

Q: The volume V of a right circular cylinder is given by the formula V = Tr'h, where r is the radius…

A:

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar²h where r is the radius…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The length of a rectangle is given by 4t−3 and its height is (2t)1/3, where t is time in seconds and…

A: Given, The length of the rectangle is 4t - 3 and it's height is (2t)13.

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: During a certain 12-hour period the temperature at time t (measured in hours from the start of the…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is…

A: Given equation is PV=8.31T Also given that, dTdt=0.21dPdt=0.05P=17T=304 So,…

Q: A NASA spacecraft measures the rate R of at which atmospheric pressure on Mars decreases with…

A: Unit Conversion Formula:

Q: The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and…

A: Given that the volume V of a right circular cylinder is given by the formula V =(pi)r2h, where r is…

Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

A:

Q: The volume of a cube is increasing at a rate of 56 in3/sec. At what rate is the length of each edge…

A: It is given that volume of cube V=x3 rate of volume increasing at dVdt=56 in3/sec The edge of the…

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is related to its pressure p (in…

A: Vp=1p

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar²h where r is the radius…

A:

Q: Under certain conditions, the efficiency e (in %) of an internal combustion engine is given by E =…

A:

Q: For many species of fish, the allometric relationship between the weight W and the length L is…

A: Here the given that, the allometric relationship between the weight W and the length L is…

Q: The volume V = Tr of a spherical balloon changes with the radius. a. At what rate (in/in) does the…

A: Given: V=43πr3

Q: The sides of a cube increase at a rate of R cm/s. When the sides have a length of 2 cm, the rate of…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the…

A: Solution is in step 2 Option A is correct answer.

Q: If a tank holds 3000 gallons of water, which drains from the bottom of the tank in 20 minutes, then…

A:

Q: The width of a rectangle is increasing at rate of 2cm/sec while the length increases at 3cm/sec. At…

A:

Q: The volume V of a right circular cone of radius r and height h is given by V = Tr²h. Find a formula…

A: To find the instantaneous rate of change:

Q: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: If it begins to decelerate at the rate of a=(-0.5v/2) m/s², where v is in m/s, determine the…

A: To find the distance travels by the particle before it stops. Given that: Initial velocity of the…

Q: dC The rate of change in the concentration of a drug with respect to time in a user's blood is given…

A:

Exponential Growth Model

The relation that represents an exponential function is: