Combine like terms first (so like the ones that have x with x and someone please help them bc I explained it bad
Answer:
![r=\frac{9\cos \theta}{\sin^2 \theta}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B9%5Ccos%20%5Ctheta%7D%7B%5Csin%5E2%20%5Ctheta%7D)
Step-by-step explanation:
The given equation in rectangular coordinates is;
![y^2=9x](https://tex.z-dn.net/?f=y%5E2%3D9x)
We use the relation;
![x=r\cos \theta](https://tex.z-dn.net/?f=x%3Dr%5Ccos%20%5Ctheta)
and
![y=r \sin \theta](https://tex.z-dn.net/?f=y%3Dr%20%5Csin%20%5Ctheta)
This implies that;
![(r \sin \theta)^2=9(r \cos \theta)](https://tex.z-dn.net/?f=%28r%20%5Csin%20%5Ctheta%29%5E2%3D9%28r%20%5Ccos%20%5Ctheta%29)
![r^2 \sin^2 \theta=9r \cos \theta](https://tex.z-dn.net/?f=r%5E2%20%5Csin%5E2%20%5Ctheta%3D9r%20%5Ccos%20%5Ctheta)
Divide through by r to get;
![r \sin^2 \theta=9\cos \theta](https://tex.z-dn.net/?f=r%20%5Csin%5E2%20%5Ctheta%3D9%5Ccos%20%5Ctheta)
Divide both sides by ![\sin^2 \theta](https://tex.z-dn.net/?f=%5Csin%5E2%20%5Ctheta)
![r=\frac{9\cos \theta}{\sin^2 \theta}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B9%5Ccos%20%5Ctheta%7D%7B%5Csin%5E2%20%5Ctheta%7D)
divide 2.49 by 5
2.49/5 = 0.498 rounded to nearest hundredth is 0.50 per pound
1$ = 100 cents, 1 hour = 60 minutes
$7.80/hour = (7.8*100) cents / (1*60)minutes
= 780 cents/60 minutes
= 13 cents/minute
<span>Option b.</span>
The volume of the rectangular prism can be found with the formula
v= length × width × height
V = 10×10×30 = 3000
the volume of the triangular prism can be found with
v = 1/2(base×width×height)
v=1/2×30×9×10 = 1/2×2700
v = 1350
Now add the two volumes together for the total volume...
3000+1350 = 4,350 in^3