Answer:
2710 is the answer
Step-by-step explanation:
1800+130(7)
angles formed by these tosses are
and
degrees to the nearest hundredth.
<u>Step-by-step explanation:</u>
Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.
The Law of Cosines (also called the Cosine Rule) says:
![c^2 = a^2 + b^2 - 2ab (cosx)](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-%202ab%20%28cosx%29)
Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:
⇒ ![c^2 = a^2 + b^2 - 2ab (cosx)](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-%202ab%20%28cosx%29)
⇒ ![c^2 -a^2 - b^2 = -2ab (cosx)](https://tex.z-dn.net/?f=c%5E2%20-a%5E2%20-%20b%5E2%20%3D%20-2ab%20%28cosx%29)
⇒ ![(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}](https://tex.z-dn.net/?f=%28cosx%29%20%3D%5Cfrac%7B%20c%5E2%20-a%5E2%20-%20b%5E2%7D%7B%20-2ab%7D)
⇒ ![(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}](https://tex.z-dn.net/?f=%28cosx%29%20%3D%5Cfrac%7B%288.6%5E2%20-%205.8%5E2%20-%207.5%5E2%29%7D%7B%20%28%20-2%285.8%297.5%29%7D)
⇒ ![(cosx) =0.18310](https://tex.z-dn.net/?f=%28cosx%29%20%3D0.18310)
⇒ ![cos^{-1}(cosx) = cos^{-1}(0.18310)](https://tex.z-dn.net/?f=cos%5E%7B-1%7D%28cosx%29%20%3D%20cos%5E%7B-1%7D%280.18310%29)
⇒ ![x = 79.45](https://tex.z-dn.net/?f=x%20%3D%2079.45)
The Law of Sines (or Sine Rule) is very useful for solving triangles:
![\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%20A%7D%20%3D%20%5Cfrac%7B%20b%7D%7Bsin%20B%7D%20%3D%20%20%5Cfrac%7Bc%7D%7Bsin%20C%7D)
We can now find another angle using the sine rule:
⇒![\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}](https://tex.z-dn.net/?f=%5Cfrac%7B%208.6%20%7D%7B%20sin%2079.45%7D%20%3D%20%5Cfrac%7B7.5%7D%7B%20sin%20Y%7D)
⇒![sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}](https://tex.z-dn.net/?f=sin%20Y%20%3D%20%5Cfrac%7B%287.5%20%28sin%2079.45%29%29%7D%7B%20%208.6%7D)
⇒![Y = 59.02 degrees](https://tex.z-dn.net/?f=Y%20%3D%2059.02%20degrees)
So, the third angle =![180 - 79.45 - 59.02 = 41.53 degrees.](https://tex.z-dn.net/?f=180%20-%2079.45%20-%2059.02%20%3D%2041.53%20degrees.)
Therefore, angles formed by these tosses are
and
degrees to the nearest hundredth.
First, determine the effective interests given both interest rates.
(1) ieff = (1 + 0.068/12)^12 - 1 = 0.07016
(2) ieff = (1 + 0.078/12)^12 - 1 = 0.08085
Calculating the interests will entail us to use the equation,
I = P ((1 + i)^n - 1)
Substituting the known values,
(1) I = ($5125)((1 + 0.07016)^1/2 - 1)
I = $176.737
(2) I = ($5125)(1 + 0.08085)^1/2 - 1)
I = $203.15
a. Hence, the greater interest will be that of the second loan.
b. The difference between the interests,
d = $203.15 - $176.737
$26.413
a simple way to do away with denominators, is we can simply multiply both sides by the LCD, in this case the LCD is 3, so let's multiply both sides by 3.
![\bf 3\left( \cfrac{1}{3}x+y \right)=3(4)\implies x+3y=12\implies 3y=12-x \\\\\\ y=\cfrac{12-x}{3}\implies \stackrel{\textit{distributing the denominator}}{y=\cfrac{12}{3}-\cfrac{x}{3}}\implies y=4-\cfrac{1}{3}x](https://tex.z-dn.net/?f=%5Cbf%203%5Cleft%28%20%5Ccfrac%7B1%7D%7B3%7Dx%2By%20%5Cright%29%3D3%284%29%5Cimplies%20x%2B3y%3D12%5Cimplies%203y%3D12-x%0A%5C%5C%5C%5C%5C%5C%0Ay%3D%5Ccfrac%7B12-x%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bdistributing%20the%20denominator%7D%7D%7By%3D%5Ccfrac%7B12%7D%7B3%7D-%5Ccfrac%7Bx%7D%7B3%7D%7D%5Cimplies%20y%3D4-%5Ccfrac%7B1%7D%7B3%7Dx)