Given the function f(m)=20-0.25m to represent the amount of money f(m) she has left after talking m minutes, the zero of the equation can be gotten by setting f(m) to 0

f(m)=20-0.25m

0 =20-0.25m

-20 = -0.25m

m = -20/-0.25

m = 80

Hence Trudy will have talked for 80minutes if she has no money left

3 0

2 years ago

Prove 2^n > n for all n equal to or greater than 1. I mostly need help with how to solve the problem when it is greater than

noname [10]

If $n$ is an integer, you can use induction. First show the inequality holds for $n=1$ . You have $2^1=2>1$ , which is true.

Now assume this holds in general for $n=k$ , i.e. that $2^k>k$ . We want to prove the statement then must hold for $n=k+1$ .

Because $2^k>k$ , you have

$2^{k+1}=2\times2^k>2k$

and this must be greater than $k+1$ for the statement to be true, so we require

$2k>k+1$

for $k>1$ . Well this is obviously true, because solving the inequality gives $3k>1\implies k>\dfrac13$ . So you're done.

If you $n$ is any real number, you can use derivatives to show that $2^n$ increases monotonically and faster than $n$ .

7 0

2 years ago

Find the surface area of the prism

Natali5045456 [20]

<em><u>ANSWER</u></em>

My answer is in the photo above

6 0

2 years ago