Answer:
The answer to your question is 10 ft
Step-by-step explanation:
We can observe that all the sides have a length but the first to the left.
Also, we know the corners meet at right triangles, so to calculate the length of the missing side, we must add to sides.
But these sides must be the ones that are in front of it (6 ft and 4 ft)
Then ? = 6 + 4
10 ft
![r\approx0.139](https://tex.z-dn.net/?f=r%5Capprox0.139)
1) Since this is a Continuously Compounded operation in a 10 yrs period, then we can write out the following equation:
![\begin{gathered} A=Pe^{rt} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3DPe%5E%7Brt%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
2) Plugging into the equation the given data and since Otto is 20 yrs old and he plans to get $4,000 in ten years, we can write out:
![\begin{gathered} 4000=1000e^{\mleft\{10r\mright\}} \\ \frac{4000}{1000}=\frac{1000e^{10r}}{1000} \\ 4=e^{10r} \\ \ln (4)=\ln (e)^{10r} \\ 10r=\ln (4) \\ r=\frac{\ln (4)}{10} \\ r=0.1386 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%204000%3D1000e%5E%7B%5Cmleft%5C%7B10r%5Cmright%5C%7D%7D%20%5C%5C%20%5Cfrac%7B4000%7D%7B1000%7D%3D%5Cfrac%7B1000e%5E%7B10r%7D%7D%7B1000%7D%20%5C%5C%204%3De%5E%7B10r%7D%20%5C%5C%20%5Cln%20%284%29%3D%5Cln%20%28e%29%5E%7B10r%7D%20%5C%5C%2010r%3D%5Cln%20%284%29%20%5C%5C%20r%3D%5Cfrac%7B%5Cln%20%284%29%7D%7B10%7D%20%5C%5C%20r%3D0.1386%20%5Cend%7Bgathered%7D)
3) Thus the rate Otto needs is
![r=0.1386\approx0.139](https://tex.z-dn.net/?f=r%3D0.1386%5Capprox0.139)
Note that since the 0.1386 the six here is greater than 5 then we can round up to the next thousandth, in this case: 0.139. For the 0.1386 is closer to 0.139 (0.004) than to 0.138 (0.006).
Or 13.9%
<h2>Greetings!</h2>
A)
<h3>If you can see, every 4 minutes the amount of water is increasing at a constant rate. </h3>
197 - 153 = 44
285 - 241 = 44
<h3>This means that at 8 minutes, because there is 153 gallons already in, we can divide 8 by 4 to see how many groups of 4 minutes there were. </h3>
8 ÷ 4 = 2
So then we can subtract two lots of 44 from 153:
153 - (44 x 2) = 65
<h3>So the starting amount was 65.</h3>
B)
<h3>The answer to B is the second option, because it is true that the amount of water is increasing. This is by 44 gallons per 4 minutes.</h3>
The amount of gallons per minute can be found out by dividing the amount by 4:
44 ÷ 4 = 11
<h3>So it is 11 gallons per minute.</h3>
<h2>Hope this helps!</h2>
Answer:
4/7x - 5 ________________________________________