Answer:
3x +84= 180,
x= 32
Step-by-step explanation:
m∠1 +m∠2= 180° (adj. ∠s on a str. line)
(x +84)° +(2x)°= 180°
x +84 +2x= 180
3x +84= 180
Solving the equation:
3x= 180 -84 <em>(</em><em>-84</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
3x= 96
x= 96 ÷3
x= 32
Answer:
4(2n+3)=12
Step-by-step explanation:
Answer:
![V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28%5Cpi%20%5Ccdot%2010%5E2%20%5Ccdot%2016%29%20%5C%5C%5C%5CV%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%281600%20%5Cpi%20%29%20%5C%5C%5C%5CV%20%3D%201675.52%20%5C%3A%20m%5E3)
The maximum amount of sand that can be stored in this structure is 1675.52 m³.
Step-by-step explanation:
The volume of a conical-shaped structure is given by
![V = \frac{1}{3} (\pi \cdot r^2 \cdot h)](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28%5Cpi%20%5Ccdot%20r%5E2%20%5Ccdot%20h%29)
Where r is the radius and h is the height of the structure.
We are given that
radius = 10m
height = 16m
Substituting the above values into the formula, we get
![V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28%5Cpi%20%5Ccdot%2010%5E2%20%5Ccdot%2016%29%20%5C%5C%5C%5CV%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%281600%20%5Cpi%20%29%20%5C%5C%5C%5CV%20%3D%201675.52%20%5C%3A%20m%5E3)
Therefore, the maximum amount of sand th can be stored in this structure is 1675.52 m³.
Since the function is even, its degree must be even (so it might be 2, 4, 6, ...)
In particular, all these numbers are one more than a perfect fourth power:
![(-3)^4=3^4=81 \implies f(-3)=f(3)=81+1=82](https://tex.z-dn.net/?f=%28-3%29%5E4%3D3%5E4%3D81%20%5Cimplies%20f%28-3%29%3Df%283%29%3D81%2B1%3D82)
![(-2)^4=2^4=16\implies f(-2)=f(2)=16+1=17](https://tex.z-dn.net/?f=%28-2%29%5E4%3D2%5E4%3D16%5Cimplies%20f%28-2%29%3Df%282%29%3D16%2B1%3D17)
![(-1)^4=1^4=81 \implies f(-1)=f(1)=1+1=2](https://tex.z-dn.net/?f=%28-1%29%5E4%3D1%5E4%3D81%20%5Cimplies%20f%28-1%29%3Df%281%29%3D1%2B1%3D2)
![0^4=0 \implies f(0)=0+1=1](https://tex.z-dn.net/?f=0%5E4%3D0%20%5Cimplies%20f%280%29%3D0%2B1%3D1)
So, the function is
![f(x)=x^4+1](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4%2B1)
and the degree is 4.