Answer:
b=7.5
Step-by-step explanation:
The equation that could be used to represent this relationship is... c = 20f
If 50 people attended, Hanks cost would be... $1000... because...
- c = 20 x 50
- 1000 = 20 x 50
So, it will be $1000 for the party, if 50 people come to the party.
______________________________________________________________
I had this question before on FLVS, so I know that these are the correct answers
<h2>
1. FIRST QUESTION.</h2>
M is directly proportional to ![r^3](https://tex.z-dn.net/?f=r%5E3)
Suppose you have two variables, say,
. We say that
varies directly as
or, in other words,
is directly proportional to
if and only if:
Where
is a nonzero constant called the constant of proportionality.
Knowing this, we can solve this problem. Here
is directly proportional to
. So:
![M=kr^{3}](https://tex.z-dn.net/?f=M%3Dkr%5E%7B3%7D)
We know that when
, hence the constant of proportionality can be found as follows:
![M=kr^{3} \\ \\ 160=k(4^3) \\ \\ 160=k(64) \\ \\ Solving \ for \ k: \\ \\ k=\frac{160}{64} \therefore k=\frac{5}{2}](https://tex.z-dn.net/?f=M%3Dkr%5E%7B3%7D%20%5C%5C%20%5C%5C%20160%3Dk%284%5E3%29%20%5C%5C%20%5C%5C%20160%3Dk%2864%29%20%5C%5C%20%5C%5C%20Solving%20%5C%20for%20%5C%20k%3A%20%5C%5C%20%5C%5C%20k%3D%5Cfrac%7B160%7D%7B64%7D%20%5Ctherefore%20k%3D%5Cfrac%7B5%7D%7B2%7D)
So:
![M=\frac{5}{2}r^3](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B5%7D%7B2%7Dr%5E3)
<h3>PART A)</h3>
When
, then:
![M=\frac{5}{2}(2^3) \\ \\ M=\frac{5}{2}(8) \\ \\ \boxed{M=20}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B5%7D%7B2%7D%282%5E3%29%20%5C%5C%20%5C%5C%20M%3D%5Cfrac%7B5%7D%7B2%7D%288%29%20%5C%5C%20%5C%5C%20%5Cboxed%7BM%3D20%7D)
<h3>PART B)</h3>
When
, then:
![540=\frac{5}{2}(r^3) \\ \\ r^3=\frac{2(540)}{5} \\ \\ r^3=216 \\ \\ r=\sqrt[3]{216} \\ \\ \boxed{r=6}](https://tex.z-dn.net/?f=540%3D%5Cfrac%7B5%7D%7B2%7D%28r%5E3%29%20%5C%5C%20%5C%5C%20r%5E3%3D%5Cfrac%7B2%28540%29%7D%7B5%7D%20%5C%5C%20%5C%5C%20r%5E3%3D216%20%5C%5C%20%5C%5C%20r%3D%5Csqrt%5B3%5D%7B216%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7Br%3D6%7D)
<h2>2. SECOND QUESTION.</h2>
M is directly proportional to ![r^2](https://tex.z-dn.net/?f=r%5E2)
We know that when
, hence the constant of proportionality is:
![M=kr^{2} \\ \\ 14=k(2^2) \\ \\ 14=k(4) \\ \\ Solving \ for \ k: \\ \\ k=\frac{14}{4} \therefore k=\frac{7}{2}](https://tex.z-dn.net/?f=M%3Dkr%5E%7B2%7D%20%5C%5C%20%5C%5C%2014%3Dk%282%5E2%29%20%5C%5C%20%5C%5C%2014%3Dk%284%29%20%5C%5C%20%5C%5C%20Solving%20%5C%20for%20%5C%20k%3A%20%5C%5C%20%5C%5C%20k%3D%5Cfrac%7B14%7D%7B4%7D%20%5Ctherefore%20k%3D%5Cfrac%7B7%7D%7B2%7D)
So:
![M=\frac{7}{2}r^2](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B7%7D%7B2%7Dr%5E2)
<h3>PART A)</h3>
When
, then:
![M=\frac{7}{2}(12^2) \\ \\ M=\frac{7}{2}(144) \\ \\ \boxed{M=504}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B7%7D%7B2%7D%2812%5E2%29%20%5C%5C%20%5C%5C%20M%3D%5Cfrac%7B7%7D%7B2%7D%28144%29%20%5C%5C%20%5C%5C%20%5Cboxed%7BM%3D504%7D)
<h3>PART B)</h3>
When
, then:
![224=\frac{7}{2}(r^2) \\ \\ r^2=\frac{224(2)}{7} \\ \\ r^2=64 \\ \\ r=\sqrt{64} \\ \\ \boxed{r=8}](https://tex.z-dn.net/?f=224%3D%5Cfrac%7B7%7D%7B2%7D%28r%5E2%29%20%5C%5C%20%5C%5C%20r%5E2%3D%5Cfrac%7B224%282%29%7D%7B7%7D%20%5C%5C%20%5C%5C%20r%5E2%3D64%20%5C%5C%20%5C%5C%20r%3D%5Csqrt%7B64%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7Br%3D8%7D)