Abox (with no top) will be made by cutting squares of equal size out of the corners of a 2626 inch by 4343 inch rectangular piece of cardboard, then folding the side flaps up. find the maximum volume of such a box.

If x represents the side length of the square cut from each corner, then the dimensions of the base of the box are 26-2x by 43-2x. The volume of the box is

... V = x(26-2x)(43-2x)

where x is restricted to the domain 0 ≤ x ≤ 13.

Plotting this equation using a graphing calculator shows the maximum volume to be 2644.7 in³.

_____

The analytical solution can be found by setting the derivative of V to zero.

... V = 4x³ - 138x² +1118x

... dV/dx = 0 = 12x² -276x +1118

This has solutions given by the quadratic formula, where a=12, b=-276, c=1118:

... x = (-b±√(b²-4ac))/(2a)

The plus sign will give a solution that is not in the allowed domain of x, so the only viable solution is the one where the radical is subtracted.

... x = (276 - √(76176--53664))/24 = (23/2) - √(469/12) ≈ 5.2483 . . . inches

Then the corresponding maximum volume is found from the equation for V.

... V ≈ (5.2483)(26 - 2·5.2483)(43 - 2·5.2483) ≈ 2644.6877 in³ . . . . as above

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.

answer: 40392

step-by-step explanation:

10098 x 4 = 40392