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1024 14. Suppose the surface area of an open-top box with a square base and rectangular...
All boxes with a square base, an open top, and a volume of 200 ftº have...
All boxes with a square base, an open top, and a volume of 200 ftº have a surface area given by S(x)=x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). S'(x)=0 The absolute minimum value of the surface area function ist? (Round to three...
Y 240 All boxes with a square base, an open top, and a volume of 60...
Y 240 All boxes with a square base, an open top, and a volume of 60 ft have a surface area given by S(x)= x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). 240 S'(x) = 2x- The absolute minimum value of the surface...
A rectangular tank with a square base, an open top, and a volume of 884 ft is to be constructed o...
A rectangular tank with a square base, an open top, and a volume of 884 ft is to be constructed of sheet steel Find the dimensions of the tank that has the minimum surface area n& Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective tunction A- Type an expression.) The interval of interest of the objective function is tiond (Simplity your...
A rectangular tank with a square base, an open top, and a volume of 864 n...
A rectangular tank with a square base, an open top, and a volume of 864 n is to be constructed of sheet stoel. Find the dimensions of the tank that has the minimum surface area, Lets be the length of one of the sides of the square base and let A be the surface area of the tank. Write the primary equation in terms of A-O (Type an expression.) The domain of the primary equation is (Simplify your answer. Type...
A box with a square base and open top must have a volume of 2048 c m 3 . We wish to find the dimensions of the box that...
A box with a square base and open top must have a volume of 2048 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. The length of the base is x and the height is h. Since the base is a square, the surface area of just the base would be: Area = The surface area of just one side would be: Area = The surface area of all...
14. A cardboard box with volume 32 cubic inches, square base, and open top is to...
14. A cardboard box with volume 32 cubic inches, square base, and open top is to be constructed. Find the minimum area of cardboard needed, neglecting waste. Show all work and use the Second Derivative Test to verify you have found the minimum.
A box with a square base and open top must have a volume of 296352 cm....
A box with a square base and open top must have a volume of 296352 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. A(x) = Next, find the derivative, A'(x). A'(x) = The critical value is 3 = The function is decreasing ✓ until the critical...
A rectangular tank with a square base, an open top, and a volume of 6912 n°...
A rectangular tank with a square base, an open top, and a volume of 6912 n° is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The dimensions of the tank with minimum surface area aren. (Simplify your answer. Use a comma to separate answers.)
A box with an open top has a square base and four sides of equal height....
A box with an open top has a square base and four sides of equal height. The volume of the box is 972 ftcubed. The height is 3ft greater than both the length and the width. If the surface area is 513ft squared,what are the dimensions of the box
6. A rectangular box with an open top is being constructed so that its base is...
6. A rectangular box with an open top is being constructed so that its base is twice as long as it is wide. In addition, the base of the box cost $2 per square foot while the sides cost $1.50 per square foot. We only want to spend $16 on materials for the box. a. Draw a labeled diagram that represents the situation using relevant variables. b. Write a formula for the box's surface area, A, in terms of only...
All boxes with a square base, an open top, and a volume of 200 ftº have a surface area given by S(x)=x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). S'(x)=0 The absolute minimum value of the surface area function ist? (Round to three...
Y 240 All boxes with a square base, an open top, and a volume of 60 ft have a surface area given by S(x)= x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). 240 S'(x) = 2x- The absolute minimum value of the surface...
A rectangular tank with a square base, an open top, and a volume of 884 ft is to be constructed of sheet steel Find the dimensions of the tank that has the minimum surface area n& Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective tunction A- Type an expression.) The interval of interest of the objective function is tiond (Simplity your...
A rectangular tank with a square base, an open top, and a volume of 864 n is to be constructed of sheet stoel. Find the dimensions of the tank that has the minimum surface area, Lets be the length of one of the sides of the square base and let A be the surface area of the tank. Write the primary equation in terms of A-O (Type an expression.) The domain of the primary equation is (Simplify your answer. Type...
14. A cardboard box with volume 32 cubic inches, square base, and open top is to be constructed. Find the minimum area of cardboard needed, neglecting waste. Show all work and use the Second Derivative Test to verify you have found the minimum.
A box with a square base and open top must have a volume of 296352 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. A(x) = Next, find the derivative, A'(x). A'(x) = The critical value is 3 = The function is decreasing ✓ until the critical...
A rectangular tank with a square base, an open top, and a volume of 6912 n° is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The dimensions of the tank with minimum surface area aren. (Simplify your answer. Use a comma to separate answers.)
6. A rectangular box with an open top is being constructed so that its base is twice as long as it is wide. In addition, the base of the box cost $2 per square foot while the sides cost $1.50 per square foot. We only want to spend $16 on materials for the box. a. Draw a labeled diagram that represents the situation using relevant variables. b. Write a formula for the box's surface area, A, in terms of only...
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