Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
Two strings are 15 inches and 7 inches long.
You could draw a diagram that has two rulers (that are longer than 12 inches).
Draw a piece of string that is exactly 15 inches on one ruler.
Draw another piece of string on the other ruler at exactly 7 inches.
Then you can find the total length of the two strings by adding 15 and 7 inches.
15 + 7 = 22
The total length of both the strings is 22 inches. You can draw a ruler and a piece of string on it at 22 inches.
Answer:
a. 1/2
b. 5/3
c. 0
d. undefined
Step-by-step explanation:
The answer is 1,230. All you have to do is add everything on the right side you don’t have to worry about anything on the left.
