Note that one side is 20 ft, and the other is 16.
This means that the side that is part of the triangle is 4 ft.
The measurement is still the same for the triangle's height.
Find the area of the rectangle:
24 x 16 = 384
Find the area of the triangle:
4 x 24 = 96
Add the two numbers together:
384 + 96 = 480
You're answer is (C)
hope this helps
Here are the calculations for Super Sport:
[12 ($72.50 x 0.8)] 1.065 = $741.24
Here is the math for Double Dribbles:
[12($54.75 x 1.09)] + (12 x $5.99) = $788.01
$788.01 - $741.24 = $46.77
The difference in price is $46.77.
10³ · x = 630
x = ?
10³ = 10 × 10 × 10 = 1,000
630 ÷ 1000 = x
630 ÷ 1000 = 0.63
x = 0.63
So we have:
10³ · 0.63 = 630
Answer:
║![DE,\\](https://tex.z-dn.net/?f=DE%2C%5C%5C)
![](https://tex.z-dn.net/?f=%3CABC%20%3D%20%3CADE%20and%20%3CACB%3D%3CAED%5C%5CTherefore%2C~ABC~%20and~%20ADE%20~are~%20similar~%20triangles.%5C%5CNow%2C%5C%5C%5C%5C%5Cfrac%7BAC%7D%7BAE%7D%20%3D%20%5Cfrac%7BAB%7D%7BAD%7D%5C%5C)
[Corresponding Sides of similar triangles are proportional.]
![or, \frac{y}{2y} = \frac{3}{3y} \\or, \frac{1}{2} = \frac{1}{y}\\or, y=2](https://tex.z-dn.net/?f=or%2C%20%5Cfrac%7By%7D%7B2y%7D%20%3D%20%5Cfrac%7B3%7D%7B3y%7D%20%5C%5Cor%2C%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7By%7D%5C%5Cor%2C%20y%3D2)
Answer:
![y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )](https://tex.z-dn.net/?f=y%3De%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29)
Step-by-step explanation:
A second order linear , homogeneous ordinary differential equation has form
.
Given: ![y''+y'+y=0](https://tex.z-dn.net/?f=y%27%27%2By%27%2By%3D0)
Let
be it's solution.
We get,
![\left ( r^2+r+1 \right )e^{rt}=0](https://tex.z-dn.net/?f=%5Cleft%20%28%20r%5E2%2Br%2B1%20%5Cright%20%29e%5E%7Brt%7D%3D0)
Since
, ![r^2+r+1=0](https://tex.z-dn.net/?f=r%5E2%2Br%2B1%3D0)
{ we know that for equation
, roots are of form
}
We get,
![y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%7D%7D%7B2%7D%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B3%7Di%7D%7B2%7D)
For two complex roots
, the general solution is of form ![y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )](https://tex.z-dn.net/?f=y%3De%5E%7B%5Calpha%20t%7D%5Cleft%20%28%20c_1%5Ccos%20%5Cbeta%20t%2Bc_2%5Csin%20%5Cbeta%20t%20%5Cright%20%29)
i.e ![y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )](https://tex.z-dn.net/?f=y%3De%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20c_1%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2Bc_2%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29)
Applying conditions y(0)=1 on
, ![c_1=1](https://tex.z-dn.net/?f=c_1%3D1)
So, equation becomes ![y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )](https://tex.z-dn.net/?f=y%3De%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2Bc_2%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29)
On differentiating with respect to t, we get
![y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7B-1%7D%7B2%7De%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2Bc_2%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29%2Be%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20%5Cfrac%7B-%5Csqrt%7B3%7D%7D%7B2%7D%20%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2Bc_2%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%5Cright%20%29)
Applying condition: y'(0)=0, we get ![0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}](https://tex.z-dn.net/?f=0%3D%5Cfrac%7B-1%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Dc_2%5CRightarrow%20c_2%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D)
Therefore,
![y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )](https://tex.z-dn.net/?f=y%3De%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5Cleft%20%28%20%5Ccos%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%2B%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5Csin%20%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B3%7Dt%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29)