8. Area Find a function that models the surface area S of a cube in terms of its volume V.

Q: The price P (in dollars) of a used car is a function of its initial cost C (in dollars) and its age…

A: P is the price of a used car and A is the age, the unit of P is in dollar and that of A is year.

Q: A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the…

A: given: edge=2ft rate of edge increasing=5ftt/min

Q: Consider the following problem: A box with an open top is to be constructed from a square piece of…

A:

Q: As coal deposits are depleted, it becomes necessary to strip-mine larger areas for each ton of coal.…

A: Answer is mentioned below

Q: E Homework: Sec. 2.1 HW Part 1 öf 3 From a 15-cm by 15-cm piece of cardboard, square cormers are cut…

A:

Q: A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover…

A:

Q: Find the composite function N(T(t)): N(T(t)) %3D Find the number of bacteria after 0.6 hours. Give…

A: Given that : The number of bacteria is a refrigerated food product is given by N(T) = 29T2 - 116 T +…

Q: Upload your work and answer to the following question: A ball is thrown into the air with an initial…

A: Velocity: h(t)=-16t2+48t+4h'(t)=v(t)=-32t+48v(t)=0(i)When 2 seconds has passed the height will…

Q: Select the best answer for the question. 11. The function f(x) = 4mx2 describes the volume, f(x), of…

A: Given:- f(x) = 4πx2 f(x) = volume of right circular cylinder  Radius x feet, Height 4 feet  To…

Q: A right cylinder with height y and radius x is used to store wheat. The top and bottom of the…

A: We need to find the equation of volume in function of x and y .and value of V(10,2)

Q: Suppose a pizza has just been taken out of an oven to cool. The temperature, H, of the pizza…

A:

Q: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic…

A:

Q: A cube has an edge of 4 feet. The edge is increasing at the rate of 2 feet per minute. Express the…

A:

Q: A daycare center has 30 ft of dividers with which to enclose a rectangular play space in a corner of…

A:

Q: In the problem you are asked to find a function that models a real life situation. Use the…

A: Given, The height of a cylinder is four times its radius. To find a function that models the volume…

Q: A projectile is shot upward from the surface of Earth with an initial velocity of 127 meters per…

A:

Q: The attached figure shows water running into a container in the shape of a cone. The radius of the…

A: Given:Radius of the cone r=6 feetHeight of the cone h=12 feetVolume of the cone  V=13πr2h

Q: Use the function of a function rule to determine the rate of change of volume a being filled by…

A: Given Radius of changes water at 0.6cm/sRadius of sphere=6cm

Q: i want to build a fence in a square patch. The fencing for the east and west sides is $5 oper foot…

A:

Q: The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original…

A: Given: E=2×1010(r-10000r) where E is energy in Joules           r is the radius in kilometers

Q: - SCx³ – 2x²) (÷ – 5) dx

A:

Q: The function H gives the height, above the ground, of a point on a spinning wheel. The function A…

A: Given that H gives the height , above the ground of a point on a spinning wheel and A gives the…

Q: A right circular cone is known to have a height (h) that is four times its radius (r). (a) Write a…

A: Given a right circular cone has height h that is four times the radius r

Q: In this problem you are asked to find a function that models a real-life situation and then use the…

A: A box with an open top is to be constructed from a rectangular piece of  cardboard with dimension 14…

Q: We encounter the composition h(T) = L(A(T)) with L and A defined as: A, the amount of ice stored in…

A: a) As the temperature increases, i.e., dT is small but positive, we must have a lesser amount of ice…

Q: In the problem you are asked to find a function that models a real life situation. Use the…

A: Given, Equilateral triangle of area A sides of triangle are x we know area of triangle is A=34a2…

Q: The function given below gives the cost to manufacture x items. Estimate (using h = 0.0001) the…

A:

Q: Find the average rate of change of the function f(x) = Vx from x, = 9 to x2 = 25. ... The average…

A:

Q: Consider the following problem: A box with an open top is to be constructed from a square piece of…

A: Consider the following problem: A box with an open top is to be constructed from a square piece of…

Q: The volume of a cylindrical canister is given by the formula V=nr^2h Part1. Write a function f(V) to…

A: The volume of a cylindrical canister is given by the formula V=nr^2h Part1. We have to write a…

Q: The function given below gives the cost to manufacture x items. Estimate (using h = 0.0001, the…

A: We have to find C'(120)  We will use the limit definition of the derivative. For that we have to…

Q: There are many square prisms with volume 125 in Let w represent the side length of the square base…

A: Given volume of square prism  =125 in3 Volume of prism   V  = w2h  ,  w =width, h =height  Surface…

Q: Now that you have deeper understanding of the topic, you are ready to solve the problems below. Let…

A: To write the function rule

Q: A cube has an edge of 5 feet. The edge is increasing at the rate of 4 feet per minute. Express the…

A:

Q: A research lab grows a type of bacterium in culture in a circular region. The radius of the circle,…

A:

Q: Given f(x) find the average rate of change of f(x) on the interval 4, 4 + h]. %3D x + 6 Your answer…

A:

Q: After a pebble has been thrown in still water, ripples form and spread outward in a shape that is…

A:

Q: Yこ cot 2.

A: Given: y=cot-1 x2-2xTo find the derivative of y with respect to xFormula: cot-1x'=-11+x2x'=12x ;…

Q: The function given below gives the cost to manufacture x items. Estimate (using h = 0.0001) the %3D…

A: Use simple formula of instantaneous rate of change

Q: A Spherical ballon is being filled with air. The radius of the Sphere {nitially is Ift & is grawing…

A: Given: A spherical balloon is being inflated with air. The radius of the sphere initially is 11 ft…

Q: Managing fuel costs is always a challenge in the airline industry as the price of jet fuel can be…

A: a From the table, F50=55 and F70=65. From t=50 to t=70 the graph has constant slope. So, at t=60 it…

Q: The Happy-Go-Lucky toy company found that the rate its revenue is changing, measured in hundreds of…

A: Given

Q: Francine throws a wrench into the air from the bottom of a trench 10 feet deep. Its height t seconds…

A: Definition used -               The maximum height for a quadratic equation -                 We…

Q: An isosceles triangle has a perimeter of 8 cm. Find a function that models its area A in terms of…

A: given that an isosceles triangle has a perimeter of 8 cm.

Q: Differentiate the function y=ln8x 2−3x+1. y′=nothing

A:

Q: 1)  Determine the average rate of change between r = 10 000 km and r = 15 000 km. 2)  Determine the…

A: We are given E=2×1010r-10000r=2×10101-10000r Rate of change between r=10000 and r=15000…

Q: A particle travels along a horizontal line according to the function s(t) = -3t° + t + 3t – 2 where…

A: By differentiating the s(t) we get the velocity function

Q: Answer: A carpenter wants to make a rectangular bookcase like the one shown here. It should have a…

A:

Q: A cube has an edge of 3 feet. The edge is increasing at the rate of 5 feet per minute. Express the…

A: Using formula,Volume of cube = (edge) 3 solve it.

Q: Consumers buy x watches at $p by function x=(5000)/(0.2p+1). Find demand and instantaneous rate of…

A:

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.