Answer:
answer in photo
hope this helps :)
Step-by-step explanation:
For this case we have the following functions:
We must find 
. By definition we have to:
So:
Finally, the composite function is:
Answer:
Answer:
0.47 and 11.53
Step-by-step explanation:
h = 60t − 5t²
27 = 60t − 5t²
5t² − 60t + 27 = 0
Quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
t = [ -(-60) ± √((-60)² − 4(5)(27)) ] / 2(5)
t = (60 ± √3060) / 10
t = 0.47 or 11.53
3x * 3x = 9x
9x + 6 - 2x + 5x - 4x^2 + 9
9x + 6 - 7x - 4x * 4x + 9
9x + 6 - 7x - 16x + 9
9x + -7x = 2x + 6 - 16x + 9
2x + 6 - 16x + 9
2x + (-3) - 16x
-14x + (-3) is the expression?
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
