If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. answer to the nearest cubic centimeter without commas. for example, if the answer is 2,000 write 2000.

The maximum volume of the box is:

              1000 cm³

Let x be the length of the square base

and h be the height(h) of the box.

As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)

As we know that the surface area of box is given by:

We are given surface area of box=600 cm²

Hence,

The volume of box is given by:

Hence,

Now, for maxima or minima we have derivative equal to zero.

Now,

Now, as we know if for a given x

then that x is a point of maxima.

Hence, when we put x=10 we get:  

Hence, x=10 is a point of maxima

Also, the value of V at x=10 is:

       Hence, the maximum volume of the box is:

                     1000 cm³

answer: jasmine will bake 4/3 or 1 1/3 cookies in an hour

step-by-step explanation:

if u add 1/3 every 15 minutes after an hour u will have 4/3 or 1 1/3

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.