Question

( PARTA) Find the dimensions (both base and height ) of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola below. y = 8 − x

(PARTB) A box with a square base and open top must have a volume
of 62,500 cm^{3}. Find the dimensions( sides of base and
the height) of the box that minimize the amount of material
used.

Answer #1

1- An open box with a square base is to have a volume of 10
ft3.
(a) Find a function that models the surface area A of
the box in terms of the length of one side of the base
x.
(b) Find the box dimensions that minimize the amount of material
used. (Round your answers to two decimal places.)
2- Find the dimensions that give the largest area for the
rectangle. Its base is on the x-axis and its...

A box with a square base and open top must have a volume of
202612 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

A box with a square base and open top must have a volume of
296352 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

A company plans to manufacture a rectangular box with a square
base, an open top, and a volume of 404 cm3. The cost of the
material for the base is 0.5 cents per square centimeter, and the
cost of the material for the sides is 0.1 cents per square
centimeter. Determine the dimensions of the box that will minimize
the cost of manufacturing it. What is the minimum cost?

Find the area of the largest rectangle with one corner at the
origin, the opposite corner in the first quadrant on the graph of
the parabola f(x)=600−8x2, and sides
parallel to the axes. The maximum possible area is ___.
Find the area of the largest rectangle with one corner at the
origin, the opposite corner in the first quadrant on the graph of
the line f(x)=12−2x, and sides parallel
to the axes. The maximum possible area is ___

A
rectangle has two of its vertices on the X axis and the other two
above the X axis on the graph of the parabola y = 16-x ^ 2. Of all
possible rectangles, find the dimensions of the one with the
largest area.

A box with an open top has a square base and four sides of equal
height. The volume of the box is 225 ft cubed. The height is 4 ft
greater than both the length and the width. If the surface area is
205 ft squared. what are the dimensions of the box?
What is the width of the box?.
What is the length of the box?

ASAP
A company plans to manufacture a rectangular container with a
square base, an open top, and a volume of 320 cm3. The cost of the
material for the base is 0.8 cents per square centimeter, and the
cost of the material for the sides is 0.2 cents per square
centimeter. Determine the dimensions of the container that will
minimize the cost of manufacturing it. What is the minimum
cost?

A box with a square base and open top must have a volume of
108000 cm^3. 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.
[Hint: use the volume formula to express the height of the box in
terms of x.]
Simplify your formula as much as possible....

A rectangle is inscribed with its base on the x-axis and its
upper corners on the parabola y= 1x^2. What are the dimensions of
such a rectangle with the greatest possible area?

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