ANSWER

EXPLANATION
The given equation is

Take antilogarithm of both sides to base e.

This will simplify to

Group like terms to obtain,


Take square root of both sides to get,
Answer:
Step-by-step explanation:
Let's start with the equation of the volume of a cylinder:

Where:
- r is the radius of the cylinder (r=D/2=24/2=12 cm)
- h is the high of the cylinder (h = 60 cm)
We can us partial derivatives to find the differential of this volume. So we will have:
(1)
Now:


dr is a differential of the radius, so in our case it is 0.1 cm and dh, differential of the high, is 0.1*2 cm. We multiply by 2 because we need to consider the top and the bottom of the cylinder.
Now we just need to put all of this definitions in the equation (1).
I hope it helps you!
Plan A = 50 + 0.05(x-500)
Plan b = 20 + 0.06 (x-200)
set A equal to B
50 + 0.05 (x-500) = 20 + 0.06(x-200)
50 + 0.05x - 25 = 20 + 0.06x -12
rearrange like terms on one side.
50 - 25 -20 +12 =0.06x -0.05x
17 = 0.01x
x = 1700 minutes.
Given:
The two functions are:


To find:
The type of transformation from f(x) to g(x) in the problem above and including its distance moved.
Solution:
The transformation is defined as
.... (i)
Where, a is horizontal shift and b is vertical shift.
- If a>0, then the graph shifts a units left.
- If a<0, then the graph shifts a units right.
- If b>0, then the graph shifts b units up.
- If b<0, then the graph shifts b units down.
We have,


The function g(x) can be written as
...(ii)
On comparing (i) and (ii), we get

Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).