I hope this helps :)
Here’s another one I don’t understand, please give me the answer and explain how you got it
1 answer:
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Answer:
6.78ft/sec
Step-by-step explanation:
From the question, dx/dt= 3.9 ft/sec
We are looking for Dy/dt
From geometry,vof this case the relationship between x and y is needed here, there is two similar triangle that exhibited by the man and the lamb
12/y= 5.1/(y-x)
Then ,cross multiply, we have
12(y-x)=5.1y
12y-12x=5.1y
12y-5.1y=12x
6.9y=12x
y=( 12/6.9)x
Differentiating implicitly the bother sides with respect to t, we have
Dy/dt= ( 12/6.9)dx/dt
But dx/dt= 3.9 ft/sec
Then Dy/dt= ( 12/6.9)× 3.9
Dy/dt=6.78ft/sec
Hence, the rate that the tip of the person's shadow moves away from the lamppost when the person is 9 ft away from the lampost is 6.78ft/sec
CHECK THE ATTACHMENT FOR THE FIQURE
The present value of an annuity of n periodic payments of P at r% where payment is made annually is given by:
![PV=P \left[\frac{1-(1+r)^{-n}}{r} \right]](https://tex.z-dn.net/?f=PV%3DP%20%5Cleft%5B%5Cfrac%7B1-%281%2Br%29%5E%7B-n%7D%7D%7Br%7D%20%5Cright%5D)
Given that <span>Estes Park Corp. pays a constant dividend of P = $6.95 on its stock. The company will maintain this dividend for the next n = 12 years and will then cease paying dividends forever. If the required return on this stock is r = 10 % = 0.1.
Thus, the current share price is given by:
![Current \ share \ price=6.95 \left[\frac{1-(1+0.1)^{-12}}{0.1} \right] \\ \\ =6.95\left[\frac{1-(1.1)^{-12}}{0.1} \right] =6.95\left(\frac{1-0.3186}{0.1} \right)=6.95\left(\frac{0.6814}{0.1} \right) \\ \\ =6.95(6.813)=\bold{\$47.36}](https://tex.z-dn.net/?f=Current%20%5C%20share%20%5C%20price%3D6.95%20%5Cleft%5B%5Cfrac%7B1-%281%2B0.1%29%5E%7B-12%7D%7D%7B0.1%7D%20%5Cright%5D%20%5C%5C%20%20%5C%5C%20%3D6.95%5Cleft%5B%5Cfrac%7B1-%281.1%29%5E%7B-12%7D%7D%7B0.1%7D%20%5Cright%5D%20%3D6.95%5Cleft%28%5Cfrac%7B1-0.3186%7D%7B0.1%7D%20%5Cright%29%3D6.95%5Cleft%28%5Cfrac%7B0.6814%7D%7B0.1%7D%20%5Cright%29%20%5C%5C%20%20%5C%5C%20%3D6.95%286.813%29%3D%5Cbold%7B%5C%2447.36%7D)
Therefore, the current share price is $47.36
</span>
Given that <span>Estes Park Corp. pays a constant dividend of P = $6.95 on its stock. The company will maintain this dividend for the next n = 12 years and will then cease paying dividends forever. If the required return on this stock is r = 10 % = 0.1.
Thus, the current share price is given by:
Therefore, the current share price is $47.36
</span>