Answer:
3000 cm^3.
Step-by-step explanation:
If the top number is 15 it's
15 * 20 * 10
= 3000 cm^3.
![9\cos(2t)=6\implies\cos(2t)=\dfrac23](https://tex.z-dn.net/?f=9%5Ccos%282t%29%3D6%5Cimplies%5Ccos%282t%29%3D%5Cdfrac23)
Using the fact that cos is 2π-periodic, we have
![\cos(2t)=\dfrac23\implies2t=\cos^{-1}\left(\dfrac23\right)+2n\pi](https://tex.z-dn.net/?f=%5Ccos%282t%29%3D%5Cdfrac23%5Cimplies2t%3D%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2B2n%5Cpi)
That is,
for any
and integer
.
![\implies t=\dfrac12\cos^{-1}\left(\dfrac23\right)+n\pi](https://tex.z-dn.net/?f=%5Cimplies%20t%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2Bn%5Cpi)
We get 2 solutions in the interval [0, 2π] for
and
,
![t=\dfrac12\cos^{-1}\left(\dfrac23\right)\text{ and }t=\dfrac12\cos^{-1}\left(\dfrac23\right)+\pi](https://tex.z-dn.net/?f=t%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%5Ctext%7B%20and%20%7Dt%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2B%5Cpi)
Answer:
![\huge\boxed{z=3}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bz%3D3%7D)
Step-by-step explanation:
If two polygons are similar, then corresponding sides are in proportion.
The corresponding sides:
4 → x
y → 15
3 → w
2 → 6
z → 9
therefore:
<em>cross multiply</em>
![(z)(6)=(9)(2)](https://tex.z-dn.net/?f=%28z%29%286%29%3D%289%29%282%29)
<em>divide both sides by 6</em>
![z=3](https://tex.z-dn.net/?f=z%3D3)
Answer:
x=-3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(x−6)+6=5x−6
(3)(x)+(3)(−6)+6=5x+−6(Distribute)
3x+−18+6=5x+−6
(3x)+(−18+6)=5x−6(Combine Like Terms)
3x+−12=5x−6
3x−12=5x−6
Step 2: Subtract 5x from both sides.
3x−12−5x=5x−6−5x
−2x−12=−6
Step 3: Add 12 to both sides.
−2x−12+12=−6+12
−2x=6
Step 4: Divide both sides by -2.
−2x
−2
=
6
−2
x=−3