Answer:
350mlliliters = 0.35liters
9liters = 9000milliliters
Answer:
$30, $75, $45
Step-by-step explanation:
We can set up an equation, where x is an unknown value:
2x+5x+3x=150
10x = 150
x=15
Now that we know what x is, we can plug x in to solve for 2x, 5x, and 3x:
2x=2*15=30
5x=5*15=75
3x=3*15=45
Therefore, the answer is $30, $75, $45
The matrix
![A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bbmatrix%7D%5Ccos%5Ctheta%26-%5Csin%5Ctheta%5C%5C%5Csin%5Ctheta%26%5Ccos%5Ctheta%5Cend%7Bbmatrix%7D)
has eigenvalues
such that
![\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0](https://tex.z-dn.net/?f=%5Cdet%28A-%5Clambda%20I%29%3D%5Cbegin%7Bvmatrix%7D%5Ccos%5Ctheta-%5Clambda%26-%5Csin%5Ctheta%5C%5C%5Csin%5Ctheta%26%5Ccos%5Ctheta-%5Clambda%5Cend%7Bvmatrix%7D%3D0)
![(\cos\theta-\lambda)^2+\sin^2\theta=0](https://tex.z-dn.net/?f=%28%5Ccos%5Ctheta-%5Clambda%29%5E2%2B%5Csin%5E2%5Ctheta%3D0)
![(\cos\theta-\lambda)^2=-\sin^2\theta](https://tex.z-dn.net/?f=%28%5Ccos%5Ctheta-%5Clambda%29%5E2%3D-%5Csin%5E2%5Ctheta)
![\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}](https://tex.z-dn.net/?f=%5Ccos%5Ctheta-%5Clambda%3D%5Cpm%5Csqrt%7B-%5Csin%5E2%5Ctheta%7D)
![\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}](https://tex.z-dn.net/?f=%5Clambda%3D%5Ccos%5Ctheta%5Cpm%5Csqrt%7B-%5Csin%5E2%5Ctheta%7D)
for all values of
, so we need to have
in order for
to be real-valued. This happens for
![\sin\theta=0\implies\theta=n\pi](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D0%5Cimplies%5Ctheta%3Dn%5Cpi)
where
is any integer, and over the given interval we have
and
.
Answer:
$1,050 because 150x7=1,050
Step-by-step explanation: