Answer 1:
It is given that the positive 2 digit number is 'x' with tens digit 't' and units digit 'u'.
So the two digit number x is expressed as,
[tex]x=(10 \times t)+(1 \times u)[/tex]
[tex]x=10t+u[/tex]
The two digit number 'y' is obtained by reversing the digits of x.
So, [tex]y=(10 \times u)+(1 \times t)[/tex]
[tex]y=10u+t[/tex]
Now, the value of x-y is expressed as:
[tex]x-y=(10t+u)-(10u+t)[/tex]
[tex]x-y=10t+u-10u-t[/tex]
[tex]x-y=9t-9u[/tex]
[tex]x-y=9(t-u)[/tex]
So, [tex]9(t-u)[/tex] is equivalent to (x-y).
Answer 2:
It is given that the sum of infinite geometric series with first term 'a' and common ratio r<1 = [tex]\frac{a}{1-r}[/tex]
Since, the sum of the given infinite geometric series = 200
Therefore,[tex]\frac{a}{1-r}=200[/tex]
Since, r=0.15 (given)
[tex]\frac{a}{1-0.15}=200[/tex]
[tex]\frac{a}{0.85}=200[/tex]
[tex]a=0.85 \times 200[/tex]
a=170
The nth term of geometric series is given by [tex]ar^{n-1}[/tex].
So, second term of the series = [tex]ar^{2-1}[/tex] = ar
Second term = [tex]170 \times 0.15[/tex]
= 25.5
So, the second term of the geometric series is 25.5
Step-by-step explanation:
