Let the square base of the container be of side s inches and the height of the container be h inches, then
Surface are of the container, A = s^2 + 4sh
For minimum surface area, dA / ds + dA / dh = 0
i.e. 2s + 4h + 4s = 0
6s + 4h = 0
s = -2/3 h
But, volume of container = 62.5 in cubed
i.e. s^2 x h = 62.5
(-2/3 h)^2 x h = 62.5
4/9 h^2 x h = 62.5
4/9 h^3 = 62.5
h^3 = 62.5 x 9/4 = 140.625
h = cube root of (140.625) = 5.2 inches
s = 2/3 h = 3.47
Therefore, the dimensions of the square base of the container is 3.47 inches and the height is 5.2 inches.
The minimum surface area = s^2 + 4sh = (3.47)^2 + 4(3.47)(5.2) = 12.02 + 72.11 = 84.13 square inches.
The cheap answer is, you simply "grab the denominator of one and multiply it times the other's top and bottom", so let's do so,
Answer:
-n + 373
Step-by-step explanation:
just add the numbers as the variable as no like variables (n)
Step-by-step explanation:
Let
f
(
x
)
=
x
3
−
6
x
2
+
k
x
+
10
If
(
x
+
2
)
is a factor
Then,
f
(
−
2
)
=
0
f
(
−
2
)
=
−
8
−
24
−
2
k
+
10
=
0
2
k
=
−
22
k
=
−
11
