Answer:
t=√d-12/4 and t=√-d-12/4, d≥12
Step-by-step explanation:
Hope this helps.
68+70=180
=138=180
=180-138
=42 degrees (using angle sum property of triangles
Hope this helps you
Answer:
1/2 cup per friend
Step-by-step explanation:
He has 1 gallon of fruit sorbet to serve to 32 friends
Note that:
1 US gallon of water (gal) = 16.00 US cups of water (cup)
16 cups/1 gallon x 1 gallon/32 friends
1/2 cup per friend
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
