Answer:
x = 10
Step-by-step explanation:
Please, use " ^ " to denote exponentiation: g(x) = 4(x - 2)^2 - 4
The vertex is located at (2, -4) which numbers come directly from the '2' in (x - 2) and the "-4" at the end of the equation.
Where is the function f(x) that you mentioned?
The axis of symmetry here is the vertical line that passes through the vertex. Its equation is x = 10.
Answer:
64 : 343
Step-by-step explanation:
First use the radii to find the volume
1) Radius of first sphere is 4 (taken from 4:7 ratio)
Insert it into the equation for volume of a sphere: V=4
/3πr^3
V = (4/3)(π)(4^3)
V = (4/3)(π)(64)
V = 256/3 π
Volume of the first sphere = 256/3 π
2) Radius of the second sphere is 7 (also taken from 4:7 ratio)
Insert it into the equation for volume of a sphere: V=4
/3πr^3
V = (4/3)(π)(7^3)
V = (4/3)(π)(343)
V = 1372/3 π
Volume of the second sphere = 1372/3 π
Next, calculate the ratio by dividing the two numbers
256/3 π ÷ 1372/3 π
Answer should be 64 : 343
The simple way to do this problem is to just cube the numbers:
4:7 becomes 4^3 : 7^3 = 64 : 343
Either way works.
It's easy to show that 
is strictly increasing on ![x\in\left[0,\frac\pi8\right]](https://tex.z-dn.net/?f=x%5Cin%5Cleft%5B0%2C%5Cfrac%5Cpi8%5Cright%5D)
. This means
and
Then the integral is bounded by
