Yes that’s it son welp ok
Given that,
An equation : -9c² +2c +3 = 0
To find,
Find the value of x.
Solution,
We have, -9c² +2c +3 = 0
We can solve it using the formula as follows :
![x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here, a = -9, b = 2 and c =3
Put the values,
![c=\dfrac{-2\pm \sqrt{(2)^2-4(-9)(3)}}{2(-9)}\\\\c=\dfrac{-2+\sqrt{(2)^{2}-4(-9)(3)}}{2(-9)}, \dfrac{-2-\sqrt{(2)^{2}-4(-9)(3)}}{2(-9)}\\\\c=-0.47, 0.69](https://tex.z-dn.net/?f=c%3D%5Cdfrac%7B-2%5Cpm%20%5Csqrt%7B%282%29%5E2-4%28-9%29%283%29%7D%7D%7B2%28-9%29%7D%5C%5C%5C%5Cc%3D%5Cdfrac%7B-2%2B%5Csqrt%7B%282%29%5E%7B2%7D-4%28-9%29%283%29%7D%7D%7B2%28-9%29%7D%2C%20%5Cdfrac%7B-2-%5Csqrt%7B%282%29%5E%7B2%7D-4%28-9%29%283%29%7D%7D%7B2%28-9%29%7D%5C%5C%5C%5Cc%3D-0.47%2C%200.69)
So, the solution are -0.47 and 0.69.
34,590 because even if 0 engines are made, then 34,590 is still expected as a base price
You divide the area and the base
First notice that the triangle with sides
![x,y,a](https://tex.z-dn.net/?f=x%2Cy%2Ca)
and the triangle with sides
![z,a+b,x](https://tex.z-dn.net/?f=z%2Ca%2Bb%2Cx)
are similar. This is true because the angle between sides
![x,y](https://tex.z-dn.net/?f=x%2Cy)
in the smaller triangle is clearly
![30^\circ](https://tex.z-dn.net/?f=30%5E%5Ccirc)
, while the angle between sides
![y,z](https://tex.z-dn.net/?f=y%2Cz)
in the larger triangle is clearly
![60^\circ](https://tex.z-dn.net/?f=60%5E%5Ccirc)
. So the triangles are similar with sides
![x,y,a](https://tex.z-dn.net/?f=x%2Cy%2Ca)
corresponding to
![a+b,z,x](https://tex.z-dn.net/?f=a%2Bb%2Cz%2Cx)
, respectively.
Now both triangles are
![30^\circ-60^\circ-90^\circ](https://tex.z-dn.net/?f=30%5E%5Ccirc-60%5E%5Ccirc-90%5E%5Ccirc)
, which means there's a convenient ratio between its sides. If the length of the shortest leg is
![\ell_1](https://tex.z-dn.net/?f=%5Cell_1)
, then the length of the longer leg is
![\ell_2=\sqrt3\ell_1](https://tex.z-dn.net/?f=%5Cell_2%3D%5Csqrt3%5Cell_1)
and the hypotenuse has length
![\ell_3=\sqrt{{\ell_1}^2+{\ell_2}^2}=2\ell_1](https://tex.z-dn.net/?f=%5Cell_3%3D%5Csqrt%7B%7B%5Cell_1%7D%5E2%2B%7B%5Cell_2%7D%5E2%7D%3D2%5Cell_1)
.
Since
![x](https://tex.z-dn.net/?f=x)
is the shortest leg in the larger triangle, it follows that
![a+b=2x](https://tex.z-dn.net/?f=a%2Bb%3D2x)
, so