A piece of cardboard measuring 13 inches by 8 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find a formula for the volume of the box in terms of x V(x) = Find the value for x that will maximize the volume of the box x =

Q: The cost of producing x units of a product is given by C(x) = 600 + 80x – 80 In(x), x > 1. Find the…

A: Extreme values of function –  Extreme values of a given function can be found using derivatives.…

Q: A 29-inch piece of wire is cut into two pieces, which are then bent into a square and a circle,…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the number x in the interval so that the difference of the number from thrice its cube is…

A: Solution is given below:

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=7−(6/7x) and the line…

A:

Q: Find the area of a triangle bounded by the y-axis, the line  f(x) = 6 − 6/7x  and the line…

A:

Q: What function should be used to maximize the volume of an open box whose surface area is equal to 20…

A:

Q: Find the number x in the interval-;,1| so that the difference of the number from thrice'its cube is…

A: How to find point where the function f(x)  is minimum: find f'(x) and solve f'(x) = 0 for x. after…

Q: Among the specifications of a company, which requires packing its product in boxes, it is found that…

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: According to question given thatC=0.001x3+9x+128We have to calculate the number of units that…

Q: A manufacturer estimates that she can sell a maximum of 105 thousand cell phones in a city. By…

A:

Q: A company finds that the marginal profit, in dollars per foot, from drilling a well that is x feet…

A:

Q: A rectangular billboard 9 feet in height stands in a field so that its bottom is 6 feet above the…

A: To maximize the function, we have to differentiate the function first and then equate with zero.

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

A:

Q: A soap factory estimates that the weekly profit (in dollars) from the production and sale of x cases…

A: Marginal profit is the profit earned by a firm or individual when one additional (marginal) unit is…

Q: A company finds that the total cost of manufacturing a units of a certain product is given by C(x)…

A: We will find the required information as shown below

Q: A piece of cardboard measuring 10 inches by 13 inches is formed into an open-top box by cutting…

A:

Q: The length / of a rectangle is increasing at a rate of 2 cm/s while the width w is decreasing at a…

A:

Q: A piece of cardboard measuring 12 inches by 9 inches is formed into an open-top box by cutting…

A: Given: Cardboard having length 12 inches. and width 9 inches. and cutting square with side length x…

Q: Find the critical points of the function f (x) = 2x³ – 9x² +12x+47. Show all your work.

A: Firstly we find the derivative of the function and then put it equal to zero and find the x values…

Q: A semi-circular pool with a diameter of 25ft and a depth of 7ft has a small leak at the bottom. The…

A: Ok, assume pool to be full with water initially,    So, initial water level = 7 ft. = 7*12 inches…

Q: I need some help with this optimization problem

A:

Q: Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces…

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: Given:

Q: A manufacturer estimates that she can sell a maximum of 165 thousand cell phones in a city. By…

A:

Q: y = 3 – 2x + x?

A: In this question, we need to find the critical points and test for maxima/minima of y=3-2x+x2.

Q: The total daily profit (in thousands of pesos)of a certain food company for the sale of ... x boxes…

A: Given:   Now, we need to find the value of x such that P(x) is the maximum. For simplicity, we plot…

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

A: A) Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: Given that  C = 0.001x3 + 3x + 432  To Find the number of units x that produces the minimum average…

Q: Find the rod of greatest length that can be inserted between y= square root of x and y=x^3…

A:

Q: Consider the production function:  Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output…

A: The given production function: y=0.75x+0.0042x2-0.000023x3  .......1 Differentiate both sides with…

Q: A manufacturer estimates that she can sell a maximum of 30 thousand cell phones in a city. By…

A:

Q: A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by cutting…

A: Given:- A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by…

Q: A local sandwich store has a fixed  weekly cost of 510.00 and variable cost for making a roast beef…

A: Given: A local sandwich store has a fixed weekly cost of $510.00 and variable cost for making a…

Q: The revenue function for a sound system is R(x) = 400x – x2 dollars %3D where x denotes the number…

A: R(x)=400x-x2 To find the marginal revenue we take derivative R'(x)=400-2x Expression for the…

Q: A boat on the ocean is 2 mi. from the nearest point on a straight shoreline; that point is 13 miles…

A: According to the question, x is the distance between the nearest point on a shoreline and the point…

Q: linear density of a rod of length 16 m is given by p(x)=25square root x+4 measured in kilograms per…

A: Explanation and solutions is given below....

Q: find all possible functions with the givenderivative. y' = cost/2

A: It is given that, y'=cost2We have to find all possible function.

Q: A tank containing chocolate milk initially contains a mixture of 460 gallons of milk and 40 gallons…

A: Let yt be the amount of chocolate syrup in the tank at time t.  The rate of change of the amount of…

Q: The marginal cost function for the manufacture of wireless headphones is given by: C0(x) = 20 −x200…

A:

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A:

Q: A manufacturer estimates that she can sell a maximum of 105 thousand cell phones in a city. By…

A: image is attached

Q: A golfer makes a successful chip shot to the green. Suppose that the path of the ball from the…

A: Please refer to the image below

Q: The marginal revenue from a product is given by r(x) = 50 – 3x – x2. Find the demand function for…

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: It is minimum average cost per unit problem.

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft³) and an initial pollutant…

A: Given: Volume of the reservoir is 8 billion cubic feet, V=8×109 ft3 Now initial polutant V is,…

Q: What function should be used to maximize the volume of a closed box whose surface area is equal to…

A: From the given figure, the volume of box is V=x2 h. Given that the surface area of the box is 16.…

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x…

A: Given: The total net shipments of aluminum (in billions of pounds) are approximated by…