The steepest line possible is a vertical line. Its slope is bigger than any
possible number you can think of, because it can change its height by
any amount in zero time. Its slope is 'undefined', meaning that there's
no number that can describe it. Some people would say it's 'infinity',
but that's not a number.
Yes, they are its just that the other one is smaller. Otherwise, they are the same
Answer:
x=14
Step-by-step explanation:
x-4=⅓(6x-54)
x-4=2x-18
x+14=2x
x=14
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
Answer: the correct is x=1,
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
x=1
