Find a formula for the described function. A rectangle has area 49 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.)

Q: Write a formula for the function g(x) obtained when the graph of f(x) = x is shifted up 1 unit and…

A: fx=x It is shifted up by 1 unit, that is x+1 Now it is shifted to left side by 5 units, that is…

Q: Starting with the graph of f(x)=7x, write the formula for the function that results from (a)…

A: The given function is fx=7x. a)  Write the formula for the function that results from shifting fx 5…

Q: Write a formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 3 units…

A: We will use basic of plotting.

Q: The owner of a small restaurant can prepare a particular meal at a cost of 100 won. He estimates…

A:

Q: A closed box with a square base is to have a volume of 16, 000 cm?. The material for the top and…

A: a) Given that, the volume of the box is 16000. Let x be the length of square base box and h be the…

Q: The price​ p, in​ dollars, of a specific car that is x years old is modeled by the function below.…

A: The price​ p, in​ dollars, of a specific car that is x years old is modeled by the function below.…

Q: Sketch the graphs of the following function. f (x) = x3 + 3x + 1

A: The function given is fx=x3+3x+1. For x=0, f0=03+30+1.=1. For x=1, f1=13+31+1.=5. The table for the…

Q: Use the graph of f(x) above to estimate the value of f' (– 3) to one decimal place. f'(– 3) =

A: From the given graph, it is observed that the graph is changing from concave down to concave up at…

Q: Show if the following functions are even, odd, or neither. You must put in values that you chose to…

A: Consider the given information: The given function is, y=x3+2x2-3x-5 To show that the function is…

Q: Suppose you want to crop (remove) 3 inches from the width of a photo. After you have cropped…

A: NOTE: Refresh your page if you can't see any equations. . x=original width of the photo. you want to…

Q: Write a formula for the function g (x) obtained when the graph of f (x) = |x| is shifted down 8 unm…

A:

Q: Зх — 5 f (x) = х+2

A:

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

A: Given, Cardboard of size 12 cm  by 12 cm in which square corner of sides x cm is cut out. We have to…

Q: Given the function f (x) = 2ª, along with its graph below, complete the following: (a) Express the…

A: The given function is f(x)=2x. a) Express the function h(x)=82x in terms of the original function…

Q: write a formula for the function g(x) obtained when the graph of f(x)= 1/x is shifted down 4 units…

A: write a formula for the function g(x) obtained when the graph of f(x)= 1/x is shifted down 4 units…

Q: .Find the domain and range of the following functions:

A: Given data: The given function is y=(9-x2)1/2. The domain is the value of x for which the given…

Q: Write a formula for the function g(x) obtained when the graph of fx) = Vx shifted up 1 unit and to…

A:

Q: Use the below table values to approximate f' (3) using the Three - point end point formula with h= -…

A:

Q: Determine the open intervals on which the graph of the function is concave upward or concave…

A:

Q: Simplify the difference quotients f(x+h)-f(x)/h and f(x)-f(a)/(x-a) for the following function by…

A: Here, we find f(x+h)  by replacing x by x+h  ,substitute the values of f(x+h) and f(x) and then by…

Q: Consider the function h : N → N given by h(n) = n + (-1)*+l.

A:

Q: Sketch the graph of each of the following functions from your knowledge of the graph of the square…

A: a) Domain   Range b) DOMAIN RANGE

Q: The number of dogs, N, in a neighborhood t years after 1995 is given by N= dogs. Express this…

A: Explanation of the answer is as follows

Q: Write a formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 5 units…

A: When graph shift down and up change will happen in y and when graph shift right and left change will…

Q: Display the graph of the function f (n) = 2n + 1 from the set of integers to the set of integers.

A: Consider the provided function,

Q: find the domain of the following function, and give your answer in interval notation: h(x)=…

A:

Q: find a function that satisfies the following conditions: f'=3x^2+6x+4, f(2)=13

A: Given :  f'=x2+6x+4,  f(2)=13

Q: Determine the formula for the the function f below. p(x) 1 1 - 1 12 1 3 72 1 4 432 2.

A: when x=1 p(x)=12=3·16 when x=2 p(x)=112=3136=3162 when x=3 p(x)=172=31216=3163 when x=4…

Q: Determine the intervals where the graph of the given function is concave up and concave down. f(x) =…

A:

Q: The population P of Buffalo, New York, from 1980 to 2018 can be approximated by the function P(t)=…

A: Solution:- P(t)= 356,656(0.991)t

Q: In reference to the following function: f(x) = x^2 + 7x + 13 / x + 4 What is the domain and…

A: Sol

Q: A 12-inch tall sunflower is planted in a garden and the height of the sunflower increases by 8% per…

A:

Q: The function f(x)=5* +x? is one-to-one. Find the value of (f-l)'(1). Round your answer to the…

A: The rule for differentiating the inverse function in this context can be written in Leibniz notation…

Q: Refer to the function below, and find z when h (a) = 18. h (x) = 4x+2 %3D

A:

Q: Find the length of the graphs of the following function, show all the work.

A:

Q: Suppose you want to crop (remove) 4 inches from the width of a photo. After you have cropped…

A: original width = x  you have cropped (reduced) the width of the photo by 4 inches. So, new width =…

Q: Consider the function f(x) below. Over what interval is the function concave down? Give your answer…

A: Consider the function: fx=4x3−6x2−x+10Differentiate w.r.t. "x",f'x=12x2−12x−1Again differentiate…

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

A: A square card board is of 18cm by 18cm side of a card board is 18cm find the volume of the box

Q: Write a formula for the function g(x) obtained when the graph of f(x)=|x| is shifted down 10 units…

A: Solution :-  f(x) = xf is shifted 10 units down∴ f(x) = x-10Now, h(x) shifted 12 units right∴g(x) =…

Q: Write a formula for a function g whose graph is similar to f(x) but shifted to the left 9 units and…

A:

Q: Evaluate the following function at the indicated values. 2t - ()* R(t)

A:

Q: Find the interval in which the following function is positive: 3. -1 1 2 3 6 -1 -2 -3 4)

A:

Q: If a rock is dropped from a height of 186 ft, its poistion t seconds after it is dropped until it…

A:

Q: For the given function, where is it concave up and concave down? Give your answers in interval…

A: Concavity of the function using second derivativetest

Q: For the given function, where is it concave up and concave down? Give your answers in interval…

A: h'(x)=2(e^(-3x) -3xe^(-3x)) h"(x)=2(-6e^(-3x) +9xe^(-3x)) h"(x)=0 2(-6e^(-3x)+9xe^(-3x))=0 -6+9x=0…

Q: The time in seconds, t, it takes for a specific object being dropped from a particular height in…

A:

Q: Suppose you want to crop (remove) 4 inches from the width of a photo. After you have cropped…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: H(x)=2.75x+71.48 can be used to estimate the​ height,

A:

Q: Write a formula for the function g(x) obtained when the graph of fx) = Vx is shifted up 1 unit and…

A: Given function is fx=x. Here the given function have to shift 1 unit up and then to left for 4…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.