The figure shows an open box with a square base. The box is to have a volume of 10 cubic feet. Express the amount of material needed to construct the box, A, as a function of the length of a side of its square base, x.

Q: Differentiate the function. G(x) = {/,? + 2x G'(x) = D

A: The given function is Gx=x7+2x4. Obtain the derivative of Gx=x7+2x4 as follows.

Q: Find the relative extremum of f

A: Given: f(x)5x5-3x3

Q: You have 600 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Let the length of the rectangular area=x and the width=ySo, perimeter=2(x+y)=600or, x+y=300or,…

Q: landscaping

A: We will find a linear equation.

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

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

Q: A rectangular building lot is three times as long as it is wide. Find a function that models its…

A: A rectangular building lot is three times as long as it is wide. Let w be the width of the…

Q: Write the height h of the rectangle as a function of x.

A: In two-dimension cartesian-coordinate system, the value of a function at a point represented by the…

Q: The function

A: Given, the function f : ℂ→ℂ defined by                   f(z)=ez+e-zhas

Q: A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls…

A:

Q: Graph the function Why is ƒ(x) called the integer part of x?

A:

Q: What is the domain of the function? Vx+2

A: Solution: The objective is to find the domain of the given function

Q: The rectangle shown below has a perimeter of 100 m. Express the area A of the rectangle as a…

A: We need to Express the area A of the rectangle as a function of x.

Q: The projected population of the United States for the years 2025 through 2055 can be modeled by  P…

A: States for the years 2025 through 2055 can be modeled by  P = 307.58e0.0052t,  where P is the…

Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: in this first we will find side of the box and then  Volume of the box = length × breath× height

Q: It costs $3 per hour to park in a parking lot, with a maximum cost of $12. Explain why the amount of…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question.Please…

Q: Is the function g(x) = x2 one-to-one?

A: Take x=2. g(2)=22=4. Take x=-2. g(-2)=(-2)2=4

Q: You have 800 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A:

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

A:

Q: Use the form to create a cubic function that (a) passes through the point and rises to the right and…

A:

Q: Graph the function using translations. f(x) 3*+1 4

A: Given, y= 3x+1 Let y=0, 3x+1=0 Therefore, x-intercept doesn't exist.   Let x=0, y= 31+0=31 y= 3…

Q: The manager of a furniture factory finds that it costs $2600 to manufacture 70 chairs in one day and…

A:

Q: Assume a box has a square base and the length of a side of the base is equal to twice the height of…

A: Volume of cuboid= lbh  surface Area=2(lb+bh+hl)

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A:

Q: A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure, the…

A: We know that the aluminum sheets are rectangular in shape. The cross sectional area of the gutter is…

Q: Express the gross salary G of Jackie, who earns $15 per hour, as a function of the number of hours…

A: topic - functions

Q: The height of a ball in feet, x seconds after it is thrown into the air is modeled by the function…

A: GivenThe height of ball in feet , x seconds after it is thrown into air is modelledby the function…

Q: A shipping crate has a square base with sides of length x feet, and it is half as tall as it is…

A: Square base, with sides of length x feet, and it is half as tall as its wide.

Q: 19

A:

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the…

A:

Q: The total attendance at a contemporary art museum is modeled by the function f(x) = 18,933(1.047)'.…

A: The total attendance of the contemporary art museum is modeled by the function ; f(x)=18,933(1.047)x…

Q: A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure…

A: Width of aluminium sheet is 20 inches The edges are turned from both sides by x inches. The cross…

Q: The monthly profit, in dollars, of a company that sells a t-shirts is given by the function P(x) = 1…

A: The given question as belonging to the calculus in which application of derivative so we have to…

Q: You have 600 yards of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Since the length of fencing of a rectangular field is 600 yards, which means that the perimeter of…

Q: An open-top box with a square base is to be constructed by taking a 36 by 36 square piece of…

A: The dimension of the square base is 36 by 36. Since a square of side length x in is cut out from…

Q: Differentiate the function.

A: Given R(a)=3a+12

Q: Graph the function f(x)=2sin(30)

A: Topic- function

Q: Rick's lumberyard has 380 yd of fencing with which to enclose a rectangular area. If the enclosed…

A: The lumberyard is having 380 yd of fencing which means the perimeter of lumberyard is 380 yd. Length…

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

A: Please refer the attached image for complete solution.

Q: The usual boat fare rate from Boracay to Private Island (which is a 4-km ride) is USD 6.0 So, if a…

A:

Q: What is the area A of a circle expressed as a function of its circumference C?

A: Our Aim is to express the area A of a circle as a function of its circumference C=?

Q: Rick's lumberyard has 240 yd of fencing with which to enclose a rectangular area. If the enclosed…

A:

Q: From a 6-cm by 6-cm piece of cardboard, square IX corners are cut out so that the sides can be…

A:

Q: -20 in.- 14 in.

A: Question is solved.

Q: What is meant by linear function in reference to algebra?

A:

Q: How does the function f(x)=1/2(x+2)2-3 compare to the parent function? Is it stretched, compressed,…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: An open-top box is made by cutting equal squares of side x out of the corners of a piece of carboard…

A: Given that an open top box is made by cutting equal squares of side x out of the corners of a piece…

Q: Express the area A of a circle as a function of its radius, r. Determine the area of a circle whose…

A:

Q: find the total cost C(x)C(x) in dollars of renting a van for a day and driving xx miles?

A:

Q: The figure shows a package whose front is a square. The length plus girth of the package is 108…

A: Given figure is,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.