54. An 8 foot long ladder is leaned against the side of a two-story house. Let x be the distancebetween the bottom of the house and the bottom of the ladder. Write the formula for the functionf(x) that gives the height (distance above the ground) at which the top of the ladder touches thehouses

Given,Length of the ladder is 8 foot.Let x be the distance between the foot of the house and the…

Answered: 54. An 8 foot long ladder is leaned…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Jeremy purchases a boat for the price of $31 950. The boat depreciates in value by 19% per year. The function that models its value over time is V(x) = 31950(0.81)*, where V is the value of the boat after x years. a) What is the value of the boat after 4 years? b) When will the boat be worth less than $10 000? c) Another boat made by a different company that costs $31 950, depreciates at a faster rate. If its value after 5 years is $8500, what is the rate of depreciation?
b. The temperature (in degrees Fahrenheit) can be approximated by the function c(x) = = + 40, where 4 x is the number of cricket chirps in 1 minute. What is the temperature for 60 chirps per minute? 100 chirps per minute? Use function notation to express these values. The temperature for 60 chirps per minute is c(I degrees Fahrenheit. %3D The temperature for 100 chirps per minute is c( degrees Fahrenheit.
Derive the following function 6. y = 23x²
A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) = Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Submit Answer
A rectangular parcel of land has width, w feet. The length of the diagonal, d, between opposite corners is 18 feet more than the length of the parcel. Note that d is lowercase. (a) Express the length, L, of the parcel as a function of d. (b) Express the width, w, of the parcel as a function of d. (c) Express the area, A, of the parcel as a function of d. L = W = A = (d) Suppose a fence is to be built around the perimeter of the rectangular parcel of land. The fencing material will cost $25 per foot. Express the total cost, C, of fencing the parcel as a function of d. C =
The amount of water in a tub increases at a constant rate. After 5 minutes of filling, the amount of water in the tub is 18.75 gallons. After 14.2 minutes of filling, the amount of water in the tub is 33.93 gallons. A) Determine the function f that models the amount of water in the tub with respect to the number of minutes that tub has been filling. Define any variables used. B) Evaluate f (11.2) and explain the meaning in the context of the problem. C) Determine the vertical intercept and explain the meaning in the context of the problem. D) Determine the horizontal intercept and explain the meaning in the context of the problem. E) Assuming the tub has a capacity of 40 gallons, determine the practical domain and range of the function. f) Determine the formula for the inverse function f ^-1. g) Evaluate f^-1 (11.2) and explain the meaning in the context of the problem.
How do you use a formula to express a record time (63.2 seconds) as a function since 1950? (t=time in years since 1950 and R = record time in seconds. The record time decreases every year by 0.4 seconds).
You purchased a car for $30 000. It depreciates by 25% of its current value every year. a) Write a function that can be used to model the value of the car after x years. b) How much will the car be worth 3 years after it is purchased? c) How long would it take for the car to depreciate to a value of $20 000?
Q/ Find the rootof the Function by (Itretion methad). 2. Fex)= ê-x Xo accusooeet
if an astronaut weighs 130 pounds on the surface of the earth, then her weight when she is h miles above the earth is given by the function w(h)=130 (3960/3960+h)2 what is her weight when she is 100 miles above the earth?
A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft
What is the value of the constant "k" for this function?

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54. An 8 foot long ladder is leaned against the side of a two-story house. Let x be the distance between the bottom of the house and the bottom of the ladder. Write the formula for the function f(x) that gives the height (distance above the ground) at which the top of the ladder touches the houses