Let the shorter leg = a.
The longer leg, b = a + 4.
The hypotenuse, c = a + 8
a^2 + b^2 = c^2
a^2 + (a + 4)^2 = (a + 8)^2
a^2 + a^2 + 8a + 16 = a^2 + 16a + 64
a^2 - 8a - 48 = 0
(a - 12)(a + 4) = 0
a - 12 = 0 or a + 4 = 0
a = 12 or a = -4
a = -4 is discarded because it is negative.
a = 12
b = 16
c = 20
The lengths are 12 m, 16 m, and 20 m.
Think about a really long, flat 3-dimensional object. This has a certain volume, and a certain (big) surface area because of its length. Now, make the 3-dimensional object fat and maintain the volume. Notice how you have minimized surface area but maintained volume. This is how I would go about solving it.
ANSWER
The correct answer is D.
EXPLANATION
The given function is
According to the rational roots theorem, the possible rational roots of f(x) are all factors of 9 expressed over all the factors of 3,
The correct answer is D.
Remark
Not many per square mile. Sounds like an ideal place to live.
Step One
Find the number of Square Miles.
Area = Height * Width
Area = 380 * 200
Area = 76,000 square miles.
Step Two
Find the Density
<u>Formula</u>
Density = Population / Square Miles
Population = 814,000 people
Square miles = 76000
Solve
Density = 814000/76000 = 10.7 people per square mile.
Remark
Isn't that incredible. It means if all the Area of South Dakota were given to the people living there, each family of 4 would get roughly 1/2 a square mile.
Missing question: How many executives should be surveyed?
Solution:
Mean = 13 hours
SD = 3 hours
Confidence level = 95%
Mean viewing time within a quarter of an hour = 0.25 = 1.96*3/sqrt (N)
Where N = Sample population
N = {(1.96*3)/0.25}^2 = 553.19 ≈ 554
Therefore, 554 executives should be surveyed to yield such results.
