Answer:
(2x +3 )(x-5)
one is the length and one is the width
Step-by-step explanation:
2x^2-7x-15
Factor
(2x )(x )
What are the factors of -15? -1*15 and -3*5, 3*-5 , 1*-15
We need 2* one factor ± the other factor = -7
2*-5 +3 = -7
That means the -5 is on the outside and the +3 is on the inside
(2x +3 )(x-5)
Answer:
The value is ![V(x) = 1706.7 \pi](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%201706.7%20%5Cpi)
Step-by-step explanation:
From the question we are told that
The first equation is ![y=16\sqrt{x}](https://tex.z-dn.net/?f=y%3D16%5Csqrt%7Bx%7D)
The second equation is ![y=4x](https://tex.z-dn.net/?f=y%3D4x)
Generally the first point of intersection of the first and second equation is x = 0
Generally the obtain the second point of intersection of the two equation we equate the two equations
So
=> ![16\sqrt{x} = 4x](https://tex.z-dn.net/?f=16%5Csqrt%7Bx%7D%20%3D%204x)
=> ![\sqrt{x} = \frac{4x}{16}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%20%5Cfrac%7B4x%7D%7B16%7D)
=> ![x = 4](https://tex.z-dn.net/?f=x%20%3D%204)
Generally the from washer method we have
![V(x) = \int\limits^4_0 {\pi [(H(x))^2 - (G(x))^2]} \, dx](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%20%5Cint%5Climits%5E4_0%20%7B%5Cpi%20%5B%28H%28x%29%29%5E2%20-%20%28G%28x%29%29%5E2%5D%7D%20%5C%2C%20dx)
So
![H(x) = 16\sqrt{x}](https://tex.z-dn.net/?f=H%28x%29%20%3D%20%2016%5Csqrt%7Bx%7D)
and
![G(x) = 4x](https://tex.z-dn.net/?f=G%28x%29%20%3D%20%204x)
So
![V(x) = \int\limits^4_0 {\pi [(16\sqrt{x})^2 - (4x)^2]} \, dx](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%20%5Cint%5Climits%5E4_0%20%7B%5Cpi%20%5B%2816%5Csqrt%7Bx%7D%29%5E2%20-%20%284x%29%5E2%5D%7D%20%5C%2C%20dx)
=> ![V(x) = \int\limits^4_0 {\pi [256x - 16x^2]} \, dx](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%20%5Cint%5Climits%5E4_0%20%7B%5Cpi%20%5B256x%20-%2016x%5E2%5D%7D%20%5C%2C%20dx)
=>![V(x) = \pi [256 \frac{x^2}{2} - 16 \frac{x^3}{3} ]|\left 4} \atop 0}} \right.](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%20%5Cpi%20%5B256%20%5Cfrac%7Bx%5E2%7D%7B2%7D%20-%2016%20%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5D%7C%5Cleft%204%7D%20%5Catop%200%7D%7D%20%5Cright.)
=> ![V(x) = \pi [256 * \frac{ 4^2}{2} - 16 * \frac{4^3}{3} ]](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%20%5Cpi%20%5B256%20%2A%20%5Cfrac%7B%204%5E2%7D%7B2%7D%20%20-%2016%20%2A%20%5Cfrac%7B4%5E3%7D%7B3%7D%20%5D)
=> ![V(x) = 1706.7 \pi](https://tex.z-dn.net/?f=V%28x%29%20%3D%20%201706.7%20%5Cpi)
Answer:
The common factors of 12 and 20 are 1, 2 and 4.
1. the combinations are 5 and 3 twice and 3 and 4 twice
5+3+5+3+3+4+3+4= 30 L
2. Trya can ride 12 , 18, 24,30 kilometres are the possible distance
3. lexi can put 4 ribbons and 2 photos on her bulletin that is 40 cm meters.
ribbons 4×4=16
bulletin 12×2=24
altogether 40 cm with nothing overlapping
4. don't know dollars and centd sorry I know pounds as I am British
Answer:
x = 12.52°
Step-by-step explanation:
The illustration forms a right angle triangle . The right angle triangle formed has a height of 200 ft and a base of 900 ft.
The opposite side of the triangle is 200 ft while the adjacent side of the triangle is 900 ft.
Using tangential ratio we can find the angle of depression. Therefore,
Let
x = angle of depression
tan x = opposite/adjacent
opposite = 200 ft
adjacent = 900 ft
tan x = 200/900
tan x = 2/9
x = tan⁻¹ 2/9
x = tan⁻¹ 0.222
x = 12.5166739144
x = 12.52°