1. Use strong induction to show that if you can run one mile or two miles, and if you can always run two more miles once you have run a specified number of miles, then you can run any number of miles.

Proof

Step-by-step explanation:

Given:

- If you run 1 or 2 miles

- You can always run 2 miles more after running specified number of miles

Find:

- Prove that you can run any number of miles

Solution:

- Let M ( n ) be " You can run the nth mile"

Basis step: n = 1 and n = 2

- M(1) and M(2) are True, because you can run one or two miles as given in statement.

Inductive Step:

- We assume that M(1) , M(2), , M( k ) are all true, thus you can run the first k miles.

- We then need to prove that M ( k+ 1 ) is also true.

- Since M ( k - 1 ) is true then M ( k + 1 ) is true. ( You can always run 2 miles more after running specified number of miles )

Conclusion:

- By the principle of strong induction, M ( n ) is true for all positive n integers.

i can't solve unless i know what the line is

step-by-step explanation:

welcome to/p>

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: