Tommy’s class rank dropped 10 %
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
Noelle goes east at N mph.
Karina travels west at N + 9
then their velocity between them is (N + N + 9)
After 8 hours they travel 8(2N + 9) = 232
(2N + 9) = 29
2N = 20
N = 10 mph for Noelle
N+9=19 mph for Karina
Answer:
The position of particle at 1 second is 4 feet.
Step-by-step explanation:
We are given the following in the question:
where s is a position function and measure in feet and t is measured in seconds.
We have to evaluate the position at 1 second.
Putting t = 1 in the position function, we get.
Thus, the position of particle at 1 second is 4 feet.
