1. exercise 18, section 5.4. compute 90, 91, 92, 93, 94 and 95. make a conjecture about the units digit of 9n where n is a positive integer. use strong mathematical induction to prove your conjecture.

n is a positive integer and here 90, 91, 92, 93, 94 and 95 is 9⁰ = 1

9¹ = 9

9² = 81

9³ = 729

9⁴ = 6561

9⁵ = 59049

so mathematical induction is prove given below.

Step-by-step explanation:

9⁰ = 1

9¹ = 9

9² = 81

9³ = 729

9⁴ = 6561

9⁵ = 59049

lets us consider by P (n) for the base case n = 0 then 9⁰ = 1  So P (1) is true

k ≥ 1so consider all integers

1≤l≤ k

There is a need to prove P (k+1)

if k is odd

=.9.

is 9 so

= 9 +10m

then

= 9 ( 9 + 10m)

       =81 + 10 (9m)

so digit is 1 and k +1 is even

if you use photomath right away it will give you the answer not like this app that you have to wait for people.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.