Answer:
The doubling time of this investment would be 9.9 years.
Step-by-step explanation:
The appropriate equation for this compound interest is
A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.
If P doubles, then A = 2P
Thus, 2P = Pe^(0.07t)
Dividing both sides by P results in 2 = e^(0.07t)
Take the natural log of both sides: ln 2 = 0.07t.
Then t = elapsed time = ln 2
--------- = 0.69315/0.07 = 9.9
0.07
The doubling time of this investment would be 9.9 years.
Answer: A
Suppose that the last dollar that Victoria receives as income
brings her a marginal utility of 10 utils while the last dollar that
Fredrick receives as income brings him a marginal utility of
15 utils. If our goal is to maximize the combined total utility of
Victoria and Fredrick, we should
a. Redistribute income from Victoria to Frederick
b. Redistribute income from Fredrick to Victoria
c. Not engage in any redistribution because the current situation already maximizes total utility
d. None of the above
Step-by-step explanation:
Marginal utility is the added satisfaction derived from consuming an additional unit of a good or service. In the above question, Fredrick derives more satisfaction from his last dollar than Victoria, and will therefore achieve a higher marginal utility with additional income than Victoria does with her current income. If we want to maximize the combined utility, we should redistribute income from Victoria to Fredrick.
The logic behind this is the diminishing marginal utility. The first unit of a good consumed gives the highest level of satisfaction, marginal utility reduces with additional units consumed. In the same way, when we spend our income, we purchase the things that give us the maximum satisfaction first.
.
Answer:
8 - 2π square units.
π/16 - 1/8 square units.
6π - 9√3 square units.
Step-by-step explanation:
The area of the square = 2√2 * 2√2
= 2*2*2
= 8.
The area of the circle = πr^2
= π * [ ( 2√2)/ 2) ]^2
= π (√2)^2
= 2π.
Second Question:
The area of the circle = π(1/2)^2 = π/4.
Finding the area of the square:
1^2 = 2x^2
x^2 = 1/2
So the area of the square = 1/2
So the area of the red part = 1/4 ( π/4 - 1/2).
= π/16 - 1/8.
Third question
Area of the circle = 6^2 * π = 36π.
Now 60 degrees is 1/6 of 360 degrees so the are of the sector is 6π.
The area of the segment = 6π - 0.5 * 6^2 sin 60
= 6π - 18√3/2
= 6π - 9√3 square units.
Answer:
8k+11
Step-by-step explanation:
Combine like terms
9k-k
7+4
9k-k=8k
7+4=11
8k+11
