Answer:
1, 3, 5, 7
Step-by-step explanation:
You can use the identity ...
![2\cos{(a)}\cos{(b)}=\cos{(a+b)}+\cos{(a-b)}](https://tex.z-dn.net/?f=2%5Ccos%7B%28a%29%7D%5Ccos%7B%28b%29%7D%3D%5Ccos%7B%28a%2Bb%29%7D%2B%5Ccos%7B%28a-b%29%7D)
Then ...
![4\cos{(x)}\cos{(2x)}\cos{(4x)}=2\cos{(x)}(\cos{(4x+2x)}+\cos{(4x-2x)})\\\\=\cos{(6x+x)}+\cos{(6x-x)}+\cos{(2x+x)}+\cos{(2x-x)}\\\\=\cos{(x)}+\cos{(3x)}+\cos{(5x)}+\cos{(7x)}](https://tex.z-dn.net/?f=4%5Ccos%7B%28x%29%7D%5Ccos%7B%282x%29%7D%5Ccos%7B%284x%29%7D%3D2%5Ccos%7B%28x%29%7D%28%5Ccos%7B%284x%2B2x%29%7D%2B%5Ccos%7B%284x-2x%29%7D%29%5C%5C%5C%5C%3D%5Ccos%7B%286x%2Bx%29%7D%2B%5Ccos%7B%286x-x%29%7D%2B%5Ccos%7B%282x%2Bx%29%7D%2B%5Ccos%7B%282x-x%29%7D%5C%5C%5C%5C%3D%5Ccos%7B%28x%29%7D%2B%5Ccos%7B%283x%29%7D%2B%5Ccos%7B%285x%29%7D%2B%5Ccos%7B%287x%29%7D)
So, {a, b, c, d} = {1, 3, 5, 7}.
Step-by-step explanation:
The lateral area is formula for a cylinder is
![2\pi \times r \times h](https://tex.z-dn.net/?f=2%5Cpi%20%5Ctimes%20r%20%5Ctimes%20h)
where r is radius and h is height.
![2\pi \times 8 \times 3 = 48\pi](https://tex.z-dn.net/?f=2%5Cpi%20%5Ctimes%208%20%5Ctimes%203%20%3D%2048%5Cpi)
The surface area of cylinder is
![2\pi \times {r}^{2} + 2\pi \times r \times h](https://tex.z-dn.net/?f=2%5Cpi%20%5Ctimes%20%20%7Br%7D%5E%7B2%7D%20%20%2B%202%5Cpi%20%5Ctimes%20r%20%5Ctimes%20h)
![2\pi(64) + 2\pi(24)](https://tex.z-dn.net/?f=2%5Cpi%2864%29%20%2B%202%5Cpi%2824%29)
![128\pi + 48\pi](https://tex.z-dn.net/?f=128%5Cpi%20%2B%2048%5Cpi)
![176\pi](https://tex.z-dn.net/?f=176%5Cpi)
Volume of cylinder is
![\pi \times {r}^{2} \times h](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%20%20%7Br%7D%5E%7B2%7D%20%20%5Ctimes%20h)
![\pi \times 64 \times 3](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%2064%20%5Ctimes%203)
![192\pi](https://tex.z-dn.net/?f=192%5Cpi)
Answer:
y = -2x + 3
Step-by-step explanation:
y = mx + b
slope = m
m = y2 - y1/x2 - x1
-3 - 3/3 - 0 = -6/3
m = -2
y = -2x + b
b = y-intercept
b = 3
y = -2x + 3
Answer:
I think it's 687.5
Step-by-step explanation:
(125 × 11) ÷ 2
<h3>Angles sum up to:</h3><h3>( n - 2 ) × 180 = ( 5 - 2 ) × 180 = 3 × 180 = 540</h3>
![x + 4x + 4x + 135 + 135 = 540](https://tex.z-dn.net/?f=x%20%2B%204x%20%2B%204x%20%2B%20135%20%2B%20135%20%3D%20540)
![9x + 270 = 540](https://tex.z-dn.net/?f=9x%20%2B%20270%20%3D%20540)
![9x = 540 - 270 \\ 9x = 270](https://tex.z-dn.net/?f=9x%20%3D%20540%20-%20270%20%5C%5C%209x%20%3D%20270)
![x = \frac{270}{9} = 30](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B270%7D%7B9%7D%20%20%3D%2030)