Answer:
(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.
(b) 
Step-by-step explanation:
Given
![f(x) = e^{-4x};\ [0,2]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20e%5E%7B-4x%7D%3B%5C%20%5B0%2C2%5D)
Solving (a); Does the function satisfy M.V.T on the given interval
We have:
![f(x) = e^{-4x};\ [0,2]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20e%5E%7B-4x%7D%3B%5C%20%5B0%2C2%5D)
The above function is an exponential function, and it is differentiable and continuous everywhere
Solving (b): The value of c
To do this, we use:

In this case:
![[a,b] = [0,2]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B0%2C2%5D)
So, we have:


Calculate f(2) and f(0)

So:


This gives:



Note that:


This implies that:

So, we have:


Divide both sides by -4


Take natural logarithm of both sides


Apply law of natural logarithm

So:

Solve for c

Answer:
4:3
Step-by-step explanation:
Given function:
Divide similar factor by each term:
Rewrite:
Therefore, the simplest ratio for 8 circles and 6 squares would be 4:3..
Answer:
A
Step-by-step explanation:
Given the 2 equations
x = 3 - y → (1)
5x - 12 = y → (2)
Substitute x = 3 - y into (2)
5(3 - y) - 12 = y ← distribute and simplify left side
15 - 5y - 12 = y
3 - 5y = y ( add 5y to both sides )
3 = 6y ( divide both sides by 6 )
= y, that is
y = 0.5 → A
Answer:
D
Step-by-step explanation:
D because the number of runs is consistent with the number of innings.
Answer:
The x in this question is 151 degrees