A box with a square base and open top must have a volume of 442368 cm3. 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(x)=

Next, find the derivative, A'(x).

A'(x)=

Now, calculate when the derivative equals zero, that is, when A'(x)=0. [Hint: multiply both sides by x2.]

A'(x)=0 when x=

We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x).

A"(x)=

Evaluate A"(x) at the x-value you gave above.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5

if i put something wrong your not gonna like it so rather not say nothing.

idk wbu

step-by-step explanation: