Answer:
see explanation
Step-by-step explanation:
The sum of the first 9 consecutive odd numbers is
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
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
Using an exponential function, it is found that the number 131.5 represents the initial value of the plane, in thousands of dollars.
<h3>Exponential function:</h3>
A decaying exponential function is modeled by:
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, the function for the value of the airplane after t years is given by:
Hence A(0) = 131.5, which means that the number 131.5 represents the initial value of the plane, in thousands of dollars.
To learn more about exponential functions, you can take a look at brainly.com/question/8935549
No. The sample size is too small to be reliable. If there were many bags of 500 candies that consistently showed a larger-than-marketed amount of green candy, that will be better proof.
