Answer:
![y = 7e^{-3t}](https://tex.z-dn.net/?f=y%20%3D%207e%5E%7B-3t%7D)
Step-by-step explanation:
![y = C_1e^{3t} + C_2e^{-3t}](https://tex.z-dn.net/?f=y%20%3D%20C_1e%5E%7B3t%7D%20%2B%20C_2e%5E%7B-3t%7D)
implies that when
,
.
![7 = C_1e^{3\times0) + C_2e^{-3\times0}](https://tex.z-dn.net/?f=7%20%3D%20C_1e%5E%7B3%5Ctimes0%29%20%2B%20C_2e%5E%7B-3%5Ctimes0%7D)
![7 = C_1+C_2](https://tex.z-dn.net/?f=7%20%3D%20C_1%2BC_2)
For the condition
, as
,
.
In the expression for
, as
, the term containing
vanishes. Hence,
![0 = C_1e^{3t}](https://tex.z-dn.net/?f=0%20%3D%20C_1e%5E%7B3t%7D)
![C_1 = 0](https://tex.z-dn.net/?f=C_1%20%3D%200)
Since ![7 = C_1+C_2](https://tex.z-dn.net/?f=7%20%3D%20C_1%2BC_2)
![7 = 0+C_2](https://tex.z-dn.net/?f=7%20%3D%200%2BC_2)
![C_2 = 7](https://tex.z-dn.net/?f=C_2%20%3D%207)
Substituting for
and
in
,
![y = 7e^{-3t}](https://tex.z-dn.net/?f=y%20%3D%207e%5E%7B-3t%7D)
Answer:
2500 Minutes
Step-by-step explanation:
If you get 2 points every 5 minutes, how long will it take it to get 1000 points? It's simple
Divide the Number of Points by the Number Of Points you get every 5 minutes then times it by the number of minutes you get 2 points making 2,500 Minutes
I hope it helped ya!
Since the triangles are similar, then 32 = x+7 those two angles are too
solve for "x"
now using proportions
![\bf \cfrac{\textit{small triangle}}{\textit{large triangle}}\qquad \cfrac{JK}{18}=\cfrac{12}{12+10}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Ctextit%7Bsmall%20triangle%7D%7D%7B%5Ctextit%7Blarge%20triangle%7D%7D%5Cqquad%20%5Ccfrac%7BJK%7D%7B18%7D%3D%5Ccfrac%7B12%7D%7B12%2B10%7D)
solve for JK
![\bf \cfrac{\textit{small triangle}}{\textit{large triangle}}\qquad \cfrac{12}{12+10}=\cfrac{9}{9+KG}\implies 12(9+KG)=(22)9 \\\\\\ 108+9KG=198](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Ctextit%7Bsmall%20triangle%7D%7D%7B%5Ctextit%7Blarge%20triangle%7D%7D%5Cqquad%20%5Ccfrac%7B12%7D%7B12%2B10%7D%3D%5Ccfrac%7B9%7D%7B9%2BKG%7D%5Cimplies%2012%289%2BKG%29%3D%2822%299%0A%5C%5C%5C%5C%5C%5C%0A108%2B9KG%3D198)
solve for KG
the scale factor of the perimeter of both triangles is just the same as the ratio of the sides, or
Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%
<h3>What is the overall profit?</h3>
Assume that the buying price was $1 each.
The amount earned from 60% of them is:
= 60% x 100,000 x 1
= $60,000
The profit from selling 50% of the remaining is:
= (50% x 40,000) x 1.60
= $32,000
The loss from selling the other 50%:
= (50% x 40,000) x 0.90
= $22,222.22
Total selling price:
= 60,000 + 32,000 + 22,222.22
= $114,222.22
Total profit:
= (114,222.22 - 100,000) / 100,000
= 14.2%
Find out more on sales profit at brainly.com/question/19104371
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Answer:
Step-by-step explanation: