The height of a cylinder is four times its radius. Find a function that models the volume V of the cylinder in terms of its radius r.

Q: Differentiate the function. h(t) = Vt - 3et

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Q: Differentiate the function with respect to the independent variable. f(x) = %9+ 3x? %3D f'(x) =O

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Q: The parent function f(x)= Jx is compressed vertically %3D by a factor of 1/4, and translated 6 units…

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Q: The height of a right cylinder is 4r, where r is the radius. Write a function f in simplest form…

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Q: What function should be used to maximize the volume of an open box whose surface area is equal to 20…

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Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

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Q: From a 27-cm by 27-cm piece of cardboard, square cormers are cut out so that the sides can be folded…

A: From a 27 cm by 27 cm piece of cardboard, square corners are cut out so that the sides can be folded…

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

Q: The volume V of a right circular cylinder of height h and radius r is V = πr 2 h. If the height is…

A: Given: The volume of a right circular cylinder is, V=πr2h . Here, h is the height of the cylinder…

Q: determine where the function is concave upward and where it is concave downward  F(x)= 5 cube root…

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Q: The deeper you are under water; the less sunlight reaches you. The percent of sunlight, P, that…

A: We will modern the following question by the function in next step.

Q: Refer to the following figure, which displays a right circular cone along with the formulas for the…

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Q: Describe the domain of the function f(x, y) = ln(7−x−y).

A: (18)

Q: d (x+;

A: Here we use chain rule of differenciation.

Q: The function f(x) = (4/3) πx3 describes the volume, f(x), of a sphere of radius x inches. If the…

A: fx=43πx3 Differentiating with respect to x, we get f'x=ddx43πx3=43π·3x2            ∵dxndx=nxn-1=4πx2

Q: The height of a right cylinder is 2r , where r is the radius. Write a function f in simplest form…

A: Since, it is given that the height of a right cylinder is 2r.Our Aim is to write a function f in…

Q: The cubic function that is the best fit for the data, with y equal to the number of millions of…

A: Given,            The cubic function that is the best fit for the data, with y equal to the number…

Q: A conservation commission estimates the reproduction function for rainbow trout in a large lake to…

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Q: A spherical balloon with radius r inches has volume V(r) =Tr'. Find a function that represents the…

A: First, we are given the formula for the volume of a sphere…

Q: The surface area of an enclosed rectangular prism with a square base is 144 square centimeters.…

A: Suppose length , breadth  and height of rectangular solid(Cuboid) be l , b and h .Then ; Surface…

Q: The volume V of a right circular cone is V = (1/3)πr 2 h. If the height is twice the radius, express…

A: We have to express the volume V of a right circular cone as function of r if height is twice the…

Q: For a host - parasite relation, it was determined that when the host density (number of hosts per…

A: y = 1000 x10 + 43 x,where,y = No. of hosts that have parasite,x = No. of hosts per unit area

Q: Differentiate the function. z = A + Bcos y

A: We know that d/dx(xn)=nxn-1 d/dx(cosx)=-sin(X)

Q: Determine where the function ?(x) = √2x2 − x − 3 is NOT differentiable. (All under square root)

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Q: Determine whether the function is differentiable at x = 2.

A: Given: f(x)=x2+2x<22xx≥2 To determine: Given function is differentiable at x=2 or not.

Q: x+1 3 y = x–1

A: Given:  y=x+1x-13    Differentating with respect to xdydx=ddxx+1x-13        =ddxx+13x-13      Using…

Q: The volume V of a right circular cone is If the height is twice the radius, express the volume V as…

A: The height is twice the radius

Q: The volume V of a right circular cylinder of height h and radius r is V= π r 2h. If the height is…

A: Volume of a right circular cylinder = V = π r2 h where r is radius of cylinder  and h is height of…

Q: The length of a rectangle is 3 inches longer than 4 times the width (x). Which is the area (y)…

A: We have to find area y as function of x if length of the rectangle is 3 inches longer than 4 times…

Q: The main part of a trumpet has a shape given by rotating the function f(x)=1+x3/1000 about the…

A: The main part of a trumpet has a shape given by rotating the function f(x)=1+x31000 about the x-axis…

Q: A company sells an inexpensive accounting program for home computers. If it can sell x programs per…

A: Revenue per week=Number of items sold per week×Cost per item

Q: Differentiate the function.   y=e^0.5t

A: Refer to the question, we have to find the derivative of the provided function y = e^0.5t.

Q: y = V4x3 –6

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Q: A rectangular box with no top is to have a square base and a volume of 30 ft. The material for the…

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Q: If x is large, which function grows faster, f(x) g(x) = x2? %3D

A: The given function is fx=2x   and  gx=x2

Q: Apply the definition to differentiate the following functions: 1- y = ₁

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Q: Differentiate the function. y = V x2 + 2x

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Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

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Q: From a 27-cm by 27-cm piece of cardboard, square cormers are cut out so that the sides can be folded…

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Q: In the theory of relativity, the mass of a particle with speed v is m = f(v) = (m0) /…

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Q: If an object moves along a line so that it is at y=f(x)=3x2−2x at time x​ (in seconds), find the…

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Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

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Q: Differentiate the function. 18. y = Vx (2 + x)

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Q: The average change of the function y = √x from x = 4 to x =16 is _________________ ?

A: The given function y=sqrt(x). We need to find the average change of function over interval [4,16].

Q: The function f(x) = 3x + 10 has a vertical shift of how many units? %3D

A: The graph of the given parabola equation is

Q: What function should be used to maximize the volume of a closed box whose surface area is equal to…

A: From the given figure, the volume of box is V=x2 h. Given that the surface area of the box is 16.…

Q: The length of a rectangle is 3 inches longer than 4 times the width (x). Which is the area (y)…

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Q: An open rectangular box with a square base has a volume V = x²h where x is the length of a side of…

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Q: Find the domain of the function flx, yl= %3D

A: Explanation is given below...

Q: From a 12-cm by 12-cm piece of cardboard, square comers are cut out so that the sides can be folded…

A: Given:  From a 12‐cm by 12‐cm piece of cardboard, square corners are cut out so that the sides can…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.