Refer to the following figure, which displays a right circular cone along with the formulas for the volume V and the lateral surface area S. V The volume of a right circular cone is 48x cm3. Express the height as a function of the radius. h(r) =

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

A:

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: The temperature of points on a plate x2 + xy + y? <1 is modeled by the function f(x, y) = 25(x² +…

A: Given: The temperature of point on a plate x2+xy+y2≤1 is model by the function is : f(x, y)=25 x2+y2…

Q: Differentiate the following function. y = 6 e* (1+3 ex)2

A: To differentiate the given function :

Q: Graph the following equations and explain why they are not graphs of functions of x. a. ly| = x b.…

A: As per bartleby guidelines only one question is answered please upload the rest separately. The…

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 acceleration of a moving body is given by the function a = 6t +4. If the velocity after 4…

A: Given, Acceleration of the body  a=6t+4 Velocity after 4 seconds = 70m/s Displacement in that time =…

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 volume of the hot-air balloon from the previous 4 3 Tr If the radius is given by 3 problem is…

A:

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: Find dydx, where y is defined as a function of x implicitly by the equation below. −x2 +2x−4=−2y2 +y…

A: By differentiating and using the result that  derivative of  x^n is nx^(n-1), we get the required…

Q: Describe the impact the a-value has on the following function: y = 3(x – 1)2 +1 %3D

A:

Q: he sand is uneven whereby the surface height, in metres, measured fr ottom of the container, is…

A: In the given question, the concept of volume is applied. Volume The volume of Cuboid is given by…

Q: The height of a right cylinder is 3r, where r is the radius. Write a function f in simplest form…

A:

Q: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

A:

Q: AP to Suppose that the radius r and volume V = 4Tr³ of a sphere are differentiable functions of t.…

A:

Q: Evaluate the following. Your answers should be functions of x. favī 1. V4 – x dx,

A: SOLUTION-

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: Vhich of the following is NOT TRUE about the function f(x, y) = e² + e"?

A:

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: alculate L6 for f(x) = v5x + 2 over [1,3]. Give your answer to three decimal places.)

A:

Q: Express the given quantity as a function f(x) of one variable x. the perimeter of a rectangle of…

A: Given length = x  width= y

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: Differentiate the function with respect to the independent variable. f(s) = s* e5 +4 e

A:

Q: Your answer is incorrect. Differentiate the function P(t) = 5C'e. Assume that C is a constant. P'(t)…

A:

Q: (a) Define what it means by for y = f(x). %3D

A: In this question we have to define the meaning of dydx for y=fx

Q: 2. (x? + 2ху — 4у?)dx — (x? — 8ху — 4у?)dy %3D0 -

A:

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

A:

Q: Differentiate the following function. y =x(x5 +9) 3 dx

A: We have to find derivative

Q: The amount of light intensity on a point is given by the function t2 + 3t + 36 I(t : te (0, 15] t+3

A:

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…

A:

Q: The volume of a rectangular prism with a square base is fixed at 500 cm3. Determine the surface…

A: We know that volume of a rectangular prism is the product of area of the base and the height of the…

Q: Find the slope of the function at (1,-1) x^(2/3)- y^(2/3)- y= 1 m=? Round to 3 decimal places if…

A:

Q: Differentiate the following functions. eX+e=* y D .y= 2

A:

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

A:

Q: The length of a rectargle is 3 inches lorger than 4 times the width (x). Which is the arealy…

A: The length of rectangle is 3 inches longer than 4 times the width.

Q: Suppose you have the function f(x) = 3x2 + 4x + 2. %D - A) What is the exact value of the slope of…

A:

Q: Differentiate the function with respect to the independent variable. f(s) = s° e4 +3e f'(s) =D

A: Consider the given: fs=s3e4+3eDiffrentiate w.r.t.…

Q: H.W: Determine which the following functions are differentiable. a) f(z) ix ze.e 6) f(Z) =

A: Let us consider the complex function f(z)=u+iv then the function is differentiable if and only if…

Q: The number of bacteria in a culture is modeled by the function n(t)=30e^rt where t is in hours.…

A:

Q: Are the functions f= O(g) and g= O(f) true if the positive functions f(x) and g(x) increase at the…

A: Given data:     The given expression for the first function is: f=O(g). The expression for the…

Q: The height of a cylinder is four times its radius. Find a function that models the volume V of the…

A: We have to find the function that models the volume V of the cylinder in terms of its radius r where…

Q: The function, f, is given by the formula f (x) = x² + kx, where k is a positive constant. The…

A: given function is                                         f(x)=x2+kx point with abscissa…

Q: Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)

A: (a) 51 Linear approximation is obtained as Lx=fa+f'ax-a Consider the function fa=a. On…

Q: Consider the concentration, C, (in mg/liter) of a drug in the blood as a function of the amount of…

A:

Q: The amount of light intensity on a point is given by the function t2 + 2t + 16 I(t) te [0,14] t+2

A: In this question, we need to find the time of minimal intensity and the minimal intensity.

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

A:

Q: Determine where the function is (a) increasing, (b) decreasing, and (c) where the relative extrema…

A: Given:- F(x) = 21/√x To find:-  (a) increasing (b) decreasing. (c) where the relative extrema occur.…

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.