Answer:
1) 64
2) 8
3) 2187
4) 5
5) 4
6) 12
7) 9
8) 
9) 27
10) 
11) 4b
12) 
Step-by-step explanation:
Step-by-step explanation:
the can is 5 inches tall, so its height is 5 inches, so 3 inches off 5 inches that'd be 3/5.
the can has a diameter of 0.8 inches, meaning it has a radius of half that, or 0.4 inches.
if say the volume of iced-tea is V, how much is 3/5 of V? well, is just their product.
![\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=0.4\\ h=5 \end{cases}\implies V=\pi (0.4)^2(5)\implies V=0.8\pi \\\\\\ \stackrel{\textit{and 3/5 of that will be}}{\cfrac{3}{5}\cdot 0.8\pi }\implies V\approx \stackrel{in^3}{1.51}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%5C%5C%5C%5C%20V%3D%5Cpi%20r%5E2%20h~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D0.4%5C%5C%20h%3D5%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Cpi%20%280.4%29%5E2%285%29%5Cimplies%20V%3D0.8%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Band%203%2F5%20of%20that%20will%20be%7D%7D%7B%5Ccfrac%7B3%7D%7B5%7D%5Ccdot%200.8%5Cpi%20%7D%5Cimplies%20V%5Capprox%20%5Cstackrel%7Bin%5E3%7D%7B1.51%7D)
Answer:
a = 3, b = -1, c = 2
Step-by-step explanation:
an^2 + bn + c
n = 1:
a + b + c = 4 Eq. 1
n = 2:
4a + 2b + c = 12 Eq. 2
n = 3:
9a + 3b + c = 26 Eq. 3
Eq. 2 minus Eq. 1
3a + b = 8 Eq. 4
Eq. 3 minus Eq. 2
5a + b = 14 Eq. 5
Eq. 5 minus Eq. 4
2a = 6
a = 3
Plug in a = 3 into Eq. 4
3(3) + b = 8
b = -1
Plug in a = 3 and b = -1 into Eq. 1.
3 - 1 + c = 4
c = 2
Answer: a = 3, b = -1, c = 2