Answer:
√6
Step-by-step explanation:
The short leg is half the hypotenuse, so √8÷2=√2
The base is √3 times the short leg, so √2·√3=√6
Answer:
96
Step-by-step explanation:
The loan duration is for 8 years, a total of 12·8 = 96 monthly payments. The 96th payment is the balloon payment.
Prove:
Using mathemetical induction:
P(n) = 
for n=1
P(n) =
= 6
It is divisible by 2 and 3
Now, for n=k, 
P(k) = 
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) = 
P(k+1) = 
P(k+1) = 
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) =
is divisible by 2 and 3 for all positive integer n.