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
Substitute y = -x into the first equation:
-8x - 7(-x) = -5
-8x + 7x = -5
-x = -5
x = 5
Substitute x = 5 into y = -x
y = -(5)
y = -5
Answer: x = 5, y = -5
Answer:
<em>The correct option is: D) S(a) = 2.00a + 100.00; shift 50 units up</em>
Step-by-step explanation:
The rent for an apartment is represented by 
Now, the rent increases by $50.00 when the apartment is furnished. So, the rent of a furnished apartment will be: 
Thus the new function will be: 
<u>As the output of the original function is increased by 50.00, so the graph of the original function will shift 50 units upward</u>.
Answer:
-5
Step-by-step explanation:
When you subtract a negative you end up adding it instead
