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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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3 years ago
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3 years ago
The school that Imani goes to is selling tickets to the annual dance competition. On the first day of the ticket sales the schoo
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Answer:

The adult and the child ticket are both 8 dollars

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x =adult ticket price

y = child ticket price

I will assume you forget to put that they sold 2 child tickets on the second day

7x+5y=96 and 3x+2y= 40

I will use elimination.  Multiply the first equation by 2 and the second equation by -5 to eliminate y

2(7x+5y)=96*2

14x + 10y = 192

The second equation

-5(3x+2y)= 40*-5

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14x + 10y = 192

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------------------------

-x = -8

Multiply by -1

x = 8

Now we need to find y

3x+2y= 40

3(8) +2y = 40

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8 0
3 years ago
consider the sequence 11; 5; -1; -7;.... determine the sequence of the nth term of the sequence! PLSSSS HELP​
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Answer:

Tn = 17-6n

Step-by-step explanation:

d = 5-11 = -6

Tn = a + (n-1)d = 11 + (n-1)×-6

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3 years ago
Probability of numbers divisible by 9 from numbers 1-100?
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Those numbers divisible by 9 are the multiple of 9; thus need to know how many multiples of 9 there are between 1 and 100:

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7 0
3 years ago
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