What is 8 times as many as 3 is
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#8 you do 360= 112+136+x... then you solve for x. X=112. Now you divide this by two since it is an inscribed angle. For #9 I have this very simplified work in the picture. Sorry I did not do #10
ΔABC is a 45 - 45 - 90 triangle. The pattern of its sides is as follows:
Each leg = 1 unit (and both legs are that way, since the triangle is isosceles - so two sides are the same)
Hypotenuse = √2 units.
So if we know either leg, we multiply by √2 to get the hypotenuse. In reverse, we divide by √2 if we know the hypotenuse to get the measurement of a leg.
Our problem tells us that the hypotenuse AC is 10 units. We divide 10 by √2 to get the measurement of leg AB. Since it's a 45 -45 - 90 triangle, AB = BC.
to rationalize the radical
Thus, each leg is 5\sqrt{2} [/tex].
The formula of the present value of annuity due:
![PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)](https://tex.z-dn.net/?f=PV%3DC%2A%5B%5Cfrac%7B1-%281%2Bi%29%5E%7B-n%7D%7D%7Bi%7D%5D%2A%281%2Bi%29)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
![PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=](https://tex.z-dn.net/?f=PV%3D3000%2A%5B%5Cfrac%7B1-%281%2B0.12%29%5E%7B-6%7D%7D%7B0.12%7D%5D%2A%281%2B0.12%29%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D)
![=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32](https://tex.z-dn.net/?f=%3D3000%2A%5B%5Cfrac%7B1-0.5066%7D%7B0.12%7D%5D%2A1.12%3D3000%2A4.1114%2A1.12%3D13814.32)
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is: