Pablo has  360 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length x (in meters). (a) Find a function that gives the area A(x) of the garden (in square meters) in terms of x A(x)= (b) What side length x  gives the maximum area that the garden can have? Side length x = ? meters (c) What is the maximum area that the garden can have? Maximum area: ? square meters

Q: The path of a diver is modeled by f(x)= -4/9x2 + 24/9x + 9 where f(x) is the height (in feet) and x…

A: Since, we have been given the path of driver by :-f(X)=Y=-49X2+249X +9 -(i)Our aim is to find the…

Q: A firm can produce 300 units per week. If its total cost function is C = 800 + 1400x dollars and its…

A:

Q: Find the domain and range of the quadratic function whose g 3) The maximum is -5 at x = -1

A: Explanation of the answer is as follows

Q: Determine whether the statement, "The maximum value of y for the quadratic function f(x) = -x2 + x +…

A:

Q: An apple orchard produces a profit of $40 per tree when planted with 3200 trees. Owing to…

A: Let number of tree is x Profit peer tree is equal to 40-0.04x-3200 Hence, total profit Px is…

Q: The daily profit in dollars of a specialty cake shop is described by the function…

A: Given:

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x)= 30x…

A:

Q: Find a formula for the quadratic function whose graph has its vertex at (5,2) and its y-intercept at…

A: Find a formula for the quadratic function whose graph has its vertex at (5,2) and its y-intercept at…

Q: A firm can produce 300 units per week. If its total cost function is C = 800 + 1100x dollars and its…

A:

Q: Mr. Camu wants to enclose his vegetable garden at the back of his estate with a fence on 3 sides. He…

A: Since Mr. Camu has 30m of fencing. As he wants to enclose his vegetable garden with a fence on 3…

Q: A firm can produce 100 units per week. If its total cost function is C = 600 + 1200x dollars and its…

A: Profit = Revenue - Cost  P(x)=(1300x-x^2)-(600+1200x) P(x)=-x^2+100x-600

Q: Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

A:

Q: Suppose a parabolic archway has a width of 280 cm and a height of 216 cm at its highest point above…

A: Given that, a parabolic archway has a width of 280 cm and a height of 216 cm at its highest point…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: topic - linear equation in one variable

Q: A firm can produce 500 units per week. If its total cost function is C = 400 + 1400x dollars and its…

A:

Q: A firm can produce 400 units per week. If its total cost function is C = 700 + 1500x dollars and its…

A: Given  total cost function is C = 700 + 1500x dollars total revenue function  R = 1900x − x2 dollars…

Q: A firm can produce 100 units per week. If its total cost function is C = 200 + 1400xdollars and its…

A: In this question given that c(x) = 200 + 1400x. And R(x) = 1500x - x2 . And we find maximum profit.…

Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the…

A:

Q: The quadratic function that best models this population as a function of the number of years after…

A:

Q: A piece of cardboard measuring 13 inches by 12 inches is formed into an open-top box by cutting…

A:

Q: What is the minimum value of 3x 4x +1 and for what value of x does it occur?

A: We have to find the minimum value of 3x2-4x+1 and for what value of x does it occur.

Q: If total costs for a commodity are given by C(x) = 750 + 20x and total revenues are given by R(x) =…

A: Total costs, C(x)=750+20xTotal Revenue, R(x)=140x-x2

Q: An appliance company determined that in order to sell X dishwashers, the price per dishwasher must…

A:

Q: Suppose that y = nx2 - 15x - 2 has a maximum at x = -3. Determine the value of n. %3D

A: If a function y=f(x) has a maximum at some value x=c, then the derivative of the function at x=c is…

Q: The annual revenue and cost functions for a manufacturer of zip drives are approximately…

A:

Q: The area of a rectangle is represented by 12x - x² where x is a side of the rectangle. For what…

A:

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by  P(x)=…

A: First of all, consider the given function P (x) which shows relation between the profit of a tour…

Q: If total costs for a commodity are given by  C(x) = 850 + 30x   and total revenues are given by…

A: Given Total cost C(x) = 850 + 30x and Total revenue R(x) = 140x − x2

Q: Find the maximum area of a rectangle inscribed under f(x)=16-x2 and the x axis

A:

Q: The weekly revenue (in dollars) earned from selling x porcelain vases is given by the function R(x)=…

A:

Q: Discuss the possibilties for the number of times the graphs of two different quadratic functions…

A: We need to find possibilities for two graph of quadratic function intersection.

Q: In a nutrient medium, the rate of increase in the surface area of a cell culture can be modelled by…

A:

Q: Suppose a company has a total costs of 0.1x² + 35x + 15000, where x is the total number of units…

A: We will find out the required values.

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: Given relation:P(x)=50x-0.25x2Where,P(x)=Profitx-number of tickets Differentiate P(x) with respect…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: Given equation is :   P(x)=45*x-0.25*x2 We know , for a parabola  f(x)=a*x2+b*x+c , the coordinates…

Q: A firm can produce 100 units per week. If its total cost function is C = 600 + 1400x dollars and…

A:

Q: Find the point on the graphf(x)=4-x^2 that is closest to the point (0,1)

A: To find the point on the graph f(x)=4-x2 that is closest to the point (0,1)

Q: Find the value of x that results in a maximum value of y if -2=x^2+y^2-4x+4y?

A: The given equation is -2=x2+y2-4x+4y. To find the value of x that results in a maximum value of y,…

Q: A firm can produce 300 units per week. If its total cost function is  C = 400 + 1400x  dollars and…

A: P(x) = R(x) - C(x) = 1700x - x² - 400 - 1400x = -x² + 300x - 400   Now take the derivative of the…

Q: If the total revenue in ABC company has given by R=-x^3+285x^2=45000x, where R is the measure in…

A: Topic:- Application of Derivative

Q: A firm can produce only 2900 units per month. The monthly total cost is given by  C(x) = 500 + 200x…

A: Since, A firm can produce only 2900 units per month. where, the monthly total cost is given by  C(x)…

Q: The profit of a cell phone manufacturer is found by the function y= -2x2+108x+75, where x is the…

A: Solution of question as follows

Q: Suppose a baby food company has determined that its total revenue R for its food is given by R = - x…

A: R=-x3+45x2+525x To find: Production level that will yield maximum revenue.

Q: A firm can produce 500 units per week. If its total cost function is  C = 200 + 1000x  dollars and…

A: Given:

Q: A piece of cardboard measuring 14 inches by 12 inches is formed into an open-top box by cutting…

A: To calculate the formula for the volume of the box in terms of x. Also to find the value of x that…

Q: if you vertically stretch the quadratic parent function, F(x)=x2, by multiplying by 7, what is the…

A: Explanation of the solution is given below...

Q: The owner of a video store has determined that the profits P of the store are approximately modeled…

A: Profit function, P(x) = -x2 + 30x + 76

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by…

A:

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

Q: What is the maximum value of the function y = -x² + 6x – 7?

A: 3 To find the maximum value of the given function y = -x2 +6x -7