Answer:
Step-by-step explanation:
The discriminant of ax^2+bx+c=0 is b^2-4ac, in this case
4^2-4(2)10
16-80
-64
Since -64<0 there are two imaginary (or ‘complex’) solutions.
Note: if d=0, there is one real solution. if d>0, there are two real solutions.
The answers will be as simple as writing the component solutions as components of a vector. For instance,
![\mathbf{Ax}=\mathbf 0](https://tex.z-dn.net/?f=%5Cmathbf%7BAx%7D%3D%5Cmathbf%200)
is solved by any vector belonging to the set
![\left\{\mathbf x\in\mathbb R^4~:~x_1=-3r+4s,x_2=r-s,x_3=r,x_4=s,(r,s)\in\mathbb R^2\right\}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cmathbf%20x%5Cin%5Cmathbb%20R%5E4~%3A~x_1%3D-3r%2B4s%2Cx_2%3Dr-s%2Cx_3%3Dr%2Cx_4%3Ds%2C%28r%2Cs%29%5Cin%5Cmathbb%20R%5E2%5Cright%5C%7D)
or simply as the vector
![\mathbf x=\begin{bmatrix}-3r+4s\\r-s\\r\\s\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathbf%20x%3D%5Cbegin%7Bbmatrix%7D-3r%2B4s%5C%5Cr-s%5C%5Cr%5C%5Cs%5Cend%7Bbmatrix%7D)
The general solution to
![\mathbf{Ax}=\mathbf b](https://tex.z-dn.net/?f=%5Cmathbf%7BAx%7D%3D%5Cmathbf%20b)
will be the particular solution plus any vector belonging to the nullspace, so that the general solution would take the form
![\mathbf x=\begin{bmatrix}-3r+4s\\r-s\\r\\s\end{bmatrix}+\begin{bmatrix}-1\\2\\4\\-3\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathbf%20x%3D%5Cbegin%7Bbmatrix%7D-3r%2B4s%5C%5Cr-s%5C%5Cr%5C%5Cs%5Cend%7Bbmatrix%7D%2B%5Cbegin%7Bbmatrix%7D-1%5C%5C2%5C%5C4%5C%5C-3%5Cend%7Bbmatrix%7D)
![\mathbf x=\begin{bmatrix}-1-3r+4s\\2+r-s\\4+r\\-3+s\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathbf%20x%3D%5Cbegin%7Bbmatrix%7D-1-3r%2B4s%5C%5C2%2Br-s%5C%5C4%2Br%5C%5C-3%2Bs%5Cend%7Bbmatrix%7D)
where
![r,s](https://tex.z-dn.net/?f=r%2Cs)
are any real numbers.
Answer:
-53
Step-by-step explanation:
6+(-8-4)x5+1
6-60+1
-53
Are we solving for something ??
We know that
step 1
find the volume of reservoir
[volume of reservoir]=15*20*10-----> 3000 ft³
step 2
find the volume of water in the reservoir
<span>if it is 56% full
</span>then
volume of water is------> .56*3000----> 1680 ft³
step 3
convert ft³ to gal
if 784 gal------------> 100 ft³
X--------------> 1680 ft³
X=1680*784/100-------> X=13.171.2 gal
the answer is
13171.2 gal