Answer:
The disposable income predicted to be $17 trillion in 2033.
Step-by-step explanation:
The disposable income, in billions, in t years after 2010 is given by the following function>
![D(t) = 10020e^{0.02292t}](https://tex.z-dn.net/?f=D%28t%29%20%3D%2010020e%5E%7B0.02292t%7D)
In what year is disposable income predicted to be $17 trillion (that is, $17,000 billion)?
This is t for which
. So
![D(t) = 10020e^{0.02292t}](https://tex.z-dn.net/?f=D%28t%29%20%3D%2010020e%5E%7B0.02292t%7D)
![17000 = 10020e^{0.02292t}](https://tex.z-dn.net/?f=17000%20%3D%2010020e%5E%7B0.02292t%7D)
![e^{0.02292t} = \frac{17000}{10020}](https://tex.z-dn.net/?f=e%5E%7B0.02292t%7D%20%3D%20%5Cfrac%7B17000%7D%7B10020%7D)
![\ln{e^{0.02292t}} = \ln{\frac{17000}{10020}}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B0.02292t%7D%7D%20%3D%20%5Cln%7B%5Cfrac%7B17000%7D%7B10020%7D%7D)
![0.02292t = \ln{\frac{17000}{10020}}](https://tex.z-dn.net/?f=0.02292t%20%3D%20%5Cln%7B%5Cfrac%7B17000%7D%7B10020%7D%7D)
![t = \frac{\ln{\frac{17000}{10020}}}{0.02292}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Cln%7B%5Cfrac%7B17000%7D%7B10020%7D%7D%7D%7B0.02292%7D)
![t = 23](https://tex.z-dn.net/?f=t%20%3D%2023)
2010 + 23 = 2033
The disposable income predicted to be $17 trillion in 2033.
Answer:
2 2/5
Step-by-step explanation:
4 x 3/5
12/5 = 2 2/5
Hope I helped!
The area of the new rug is
x² + 2x - 15
Since
A = l x w
The new rug is 3 in shorter than her old rug, so we divide the area by (x - 3)
(x² + 2x - 15) / (x - 3)
By factoring
(x - 3)(x + 5) / (x - 3)
Cancelling out terms
x + 5
The width is 5 inches wider
The required time is mathematically given as
t-150 minutes.
This is further explained below.
<h3>What is the time?</h3>
We know that the volume of the prism is given by.
Volume ![$=$ (Base Area $) \times$ Height](https://tex.z-dn.net/?f=%24%3D%24%20%28Base%20Area%20%24%29%20%5Ctimes%24%20Height)
Base Area ![$=\frac{1}{2} \times(1.4+0.6) \times 2$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%281.4%2B0.6%29%20%5Ctimes%202%24)
Base Area ![$=2 \mathrm{~m}^2$](https://tex.z-dn.net/?f=%24%3D2%20%5Cmathrm%7B~m%7D%5E2%24)
Now,
![Volume $=2 \times 1=2 \mathrm{~m}^3$](https://tex.z-dn.net/?f=Volume%20%24%3D2%20%5Ctimes%201%3D2%20%5Cmathrm%7B~m%7D%5E3%24)
Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.
Because of this, the volume increases.
![Volume $=2 \times 0.8=1.6 \mathrm{~m}^3](https://tex.z-dn.net/?f=Volume%20%24%3D2%20%5Ctimes%200.8%3D1.6%20%5Cmathrm%7B~m%7D%5E3)
Now, the rate of emptying the tank is,
![=\frac{2-1.6}{30}=\frac{1}{75} \mathrm{~m}^3 / \mathrm{min}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2-1.6%7D%7B30%7D%3D%5Cfrac%7B1%7D%7B75%7D%20%5Cmathrm%7B~m%7D%5E3%20%2F%20%5Cmathrm%7Bmin%7D)
In conclusion, We also know that,
$$
![\begin{aligned}&\text { time }=\frac{\text { volume }}{\text { rate }} \\&\text { time }=\frac{2}{\frac{1}{75}}-150 \mathrm{~min}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Ctext%20%7B%20time%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20volume%20%7D%7D%7B%5Ctext%20%7B%20rate%20%7D%7D%20%5C%5C%26%5Ctext%20%7B%20time%20%7D%3D%5Cfrac%7B2%7D%7B%5Cfrac%7B1%7D%7B75%7D%7D-150%20%5Cmathrm%7B~min%7D%5Cend%7Baligned%7D)
Therefore, Colin must wait for the pond to drain for a total of 150 minutes.
Read more about the time
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Answer:
2 + x
2 + (x)
x + (2)
Step-by-step explanation:
Switch them around.