5. (6 marks) use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100.
( take +100 into considersation since previous solution didnt )

Step-by-step explanation:

We will prove by mathematical induction that, for every natural ,  

We will prove our base case, when n=4, to be true.

Base case:

Inductive hypothesis:  

Given a natural ,  

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

With this we have proved our statement to be true for n+1.  

In conlusion, for every natural .

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.