Answer: She started with $160.
It will take 6 weeks before she has less than half of what she originally invested.
Step-by-step explanation:
If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the investment after t weeks.
t represents the number of weeks.
P represents the initial value of the investment.
r represents rate of depreciation.
From the information given,
A = $142.40
r = 11% = 11/100 = 0.11
t = 1
Therefore
142.40 = P(1 - 0.11)^1
142.40 = P(0.89)
P = 142.4/0.89
P = 160
For her to have half of what she invested originally, then
80 = 160(0.89)^t
80/160 = (0.89)^t
0.5 = (0.89)^t
Taking log of both sides to base 10
Log 0.5 = log0.89^t = tlog0.89
- 0.3010 = - 0.051t
t = - 0.3010/- 0.051
t = 5.9
Approximately 6 weeks
What makes me happy irl is nothing really, I only exist to make others happy
6 times
6 * 1/4 is 6/4
6/4 is 1 2/4 which is 1 1/2
The formula for the volume of a cone is (1/3)*area of the base * height.
The base is a circle, whose area is pi times radius^2. Here this is pi *
(r^2) = 3.14*(72 / 2 yd)^2 = 4069.44 yd^2. And so the volume is (1/3) *
4069.44 yd^2 * 24yd = 32,555.52 yd^3. I recommend that you find the
most common formulas of the geometrical figures and make a flashcard
that you can use at any moment.
Answer:
Step-by-step explanation:
![volume = \frac{4}{3} \pi {r}^{3} \\ \\ 288\pi = \frac{4}{3} \pi {r}^{3} \\ \\ 3(288\pi) = 4\pi {r}^{3} \\ \\ \frac{3(288\pi)}{4\pi} = {r}^{3} \\ \\ 216 = {r}^{3} \\ \\ r = \sqrt[3]{216} \\ r = 6](https://tex.z-dn.net/?f=volume%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20288%5Cpi%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%203%28288%5Cpi%29%20%3D%204%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B3%28288%5Cpi%29%7D%7B4%5Cpi%7D%20%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20216%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20r%20%3D%20%20%5Csqrt%5B3%5D%7B216%7D%20%20%5C%5C%20r%20%3D%206)
