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A closed box has a square base with side length / feet and heighth feet. Given...
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...
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...
I'm not sure about b,c,d. Is there anyone can help with this question? A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base...
I'm not sure about b,c,d. Is there anyone can help with this
question?
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0)4 metres. The volume of water is given by Vt)(t) Over time, the sides of the base are decreasing ata ateof0.05 m/s and the water is leaking from...
QR. The base of a triangular Prism has an area. of 42 square feet. The height...
QR. The base of a triangular Prism has an area. of 42 square feet. The height of the prism is 30 inches. What is the volume (in cubic feet) of the prisma
A rectangular box of height h metres with a square base with side x(t) metres, where initial leng...
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0) - 4 metres. The volume of water is given by V-(t)h(t) Over time, the sides of the base are decreasing at a rate of dt =-0.05 m/s and the water is leaking from a hole in the base of the...
An open box is to be constructed so that the length of the base is 4...
An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 2 dollars per square foot and the cost to construct the four sides is 1 dollars per square foot, determine the dimensions for a box to have volume = 27 cubic feet which would minimize the cost of construction. h 1 W The values for the dimension of...
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
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...
1024 14. Suppose the surface area of an open-top box with a square base and rectangular...
1024 14. Suppose the surface area of an open-top box with a square base and rectangular sides is modeled by the function S = x2+ where x is the measure (in inches) of each side of the base. Determine the value of x which yields the minimum surface area for the box. X
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...
I'm not sure about b,c,d. Is there anyone can help with this
question?
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0)4 metres. The volume of water is given by Vt)(t) Over time, the sides of the base are decreasing ata ateof0.05 m/s and the water is leaking from...
QR. The base of a triangular Prism has an area. of 42 square feet. The height of the prism is 30 inches. What is the volume (in cubic feet) of the prisma
A rectangular box of height h metres with a square base with side x(t) metres, where initial length of the side of the base is x(0) 2 metres. The box is initially filled with water to a height of h(0) - 4 metres. The volume of water is given by V-(t)h(t) Over time, the sides of the base are decreasing at a rate of dt =-0.05 m/s and the water is leaking from a hole in the base of the...
An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 2 dollars per square foot and the cost to construct the four sides is 1 dollars per square foot, determine the dimensions for a box to have volume = 27 cubic feet which would minimize the cost of construction. h 1 W The values for the dimension of...
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...
1024 14. Suppose the surface area of an open-top box with a square base and rectangular sides is modeled by the function S = x2+ where x is the measure (in inches) of each side of the base. Determine the value of x which yields the minimum surface area for the box. X
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