Use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100. (it is 5 to power of n and 2 to the power of 2n+1)

Step-by-step explanation:

The statement to be proved using mathematical induction is:

We will begin the proof showing that the base case is satisfied (n=4).

.

Then, 1 is true for n=4.

Now we will assume that the statement holds for some arbitrary natural number and prove that then, the statement holds for n+1. Observe that

With this the inductive step has been proven and then, our statement is true,

For every ,

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

x = 3 ± √(5+y)