A box with a square base and closed top is required to have a volume of 27,000 cm3
. Find the dimensions of the box that minimize the amount of material used.

h=30cm

Base sides, x=30cm

Step-by-step explanation:

Let x be the dimension of the sides and h the dimension of height;

#Material used is directly proportional to surface area. Minimizing surface area will minimize the amount of material used.

Find area as a function of x:

To minimize Area, we find the first derivative of Area:

#find the second derivative to verify the minimum:

Substitute x in the volume equation to find h:

Hence, the dimensions of the box that minimize the amount of material used h=30cm and x=30cm

a

step-by-step explanation:

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180