Answer: 57 in³
Step-by-step explanation:
1. You know that the volume (V) of gas a balloon can hold varies directly as the cube of its radius (r). Then, you can write the following expression:
![V=kr^{3}](https://tex.z-dn.net/?f=V%3Dkr%5E%7B3%7D)
Where k is the constant of proportionality.
2. You can calculate k as following:
![k=\frac{V_1}{r^{3}}\\k=\frac{81in^{3}}{(3in)^{3}}\\k=3](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BV_1%7D%7Br%5E%7B3%7D%7D%5C%5Ck%3D%5Cfrac%7B81in%5E%7B3%7D%7D%7B%283in%29%5E%7B3%7D%7D%5C%5Ck%3D3)
3. Then, to calculate the cubic inches that must be released to reduce the radius down to 2 inches:
- Solve for the volume as following:
![V_2=3(2in)^{3}=24in^{3}](https://tex.z-dn.net/?f=V_2%3D3%282in%29%5E%7B3%7D%3D24in%5E%7B3%7D)
- Make the subtraction of the two volumes shown above. Then, the result is:
![V_3=81in^{3}-24in^{3}=57in^{3}](https://tex.z-dn.net/?f=V_3%3D81in%5E%7B3%7D-24in%5E%7B3%7D%3D57in%5E%7B3%7D)
Yes those are. It the correct order good job
Answer:
x = - ![\frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D)
Step-by-step explanation:
Given
9x² + 30x + 25 = 0 ← left side is a perfect square
(3x + 5)² = 0, thus
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - ![\frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D)
solution is x = -
with multiplicity 2