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natta225 [31]
3 years ago
15

Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Mathematics
1 answer:
Flura [38]3 years ago
3 0

Answer:

The inequality that you have is 5^{n}>2^{2n+1}+100,\,n>4. You can use mathematical induction as follows:

Step-by-step explanation:

For n=5 we have:

5^{5}=3125

2^{(2(5)+1)}+100=2148

Hence, we have that 5^{5}>2^{(2(5)+1)}+100.

Now suppose that the inequality holds for n=k and let's proof that the same holds for n=k+1. In fact,

5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.

Where the last inequality holds by the induction hypothesis.Then,

5^{k+1}>(2^{2k+1}+100)\cdot (4+1)

5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100

5^{k+1}>2^{2k+3}+100\cdot 4

5^{k+1}>2^{2(k+1)+1}+100

Then, the inequality is True whenever n>4.

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Let x = state b , then x + 2 = state a

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2x + 2 = 9090 subtract 2 from both sides
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that means x + 2 = 4546

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4 0
3 years ago
Mage has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can he buy?
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Answer:

x = 8 tickets

Step-by-step explanation:

Given that,

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Each movie ticket costs $4.50.

Let he bought x tickets. ATQ,

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So, he can buy 8 tickets.

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3 years ago
A box contains 17 balls numbered 1 through 17. Two balls are drawn in succession without replacement. If the second ball has the
Brilliant_brown [7]

Answer:

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Step-by-step explanation:

17 balls numbered 1 through 17

Picking without replacement :

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Numbers less Than = (3, 2, 1)

P(number less than second ball Given 4 is drawn for second ball) :

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2.)

(8/17 * 7/8) ÷ (8/17 * 7/8) + (9/17 * 1/17)

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3 years ago
Use I = PRT to solve.
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Answer:

Time T = 15 year

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Given:

Interest I = $270,000

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Rate R = 12% = 0.12

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Time T

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I = PRT

270,000 = (150,000)(0.12)(T)

270,000 = (18,000)(T)

Time T = 15 year

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8 0
3 years ago
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