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3 years ago

7 times a number is 8 less than the square of that number. Find the negative solution.

Mathematics

1 answer:

charle [14.2K]3 years ago

7 0

Answer:

-1

Step-by-step explanation:

The required relation is ...

7n = n^2 -8

0 = n^2 -7n -8 . . . . put in standard form

0 = (n -8)(n +1) . . . . factor

Solutions are n=8 and n=-1.

The negative solution is -1.

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5. (6 marks) Use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100.

Tju [1.3M]

Step-by-step explanation:

We will prove by mathematical induction that, for every natural $n\geq 4$ ,

$5^n\geq 2^{2n+1}+100$

We will prove our base case, when n=4, to be true.

Base case:

$5^4=625\geq 612=2^{2*4+1}+100$

Inductive hypothesis:

Given a natural $n\geq 4$ ,

$5^n\geq 2^{2n+1}+100$

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

$2^{2(n+1)+1}+100=2^{2n+1+2}+100=\\=4*2^{2n+1}+100\leq 4(2^{2n+1}+100)\leq 4*5^n$

With this we have proved our statement to be true for n+1.

In conlusion, for every natural $n\geq4$ .

$5^n\geq 2^{2n+1}+100$

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3 years ago

-x is greater than or equal to 0.5

Degger [83]

Answer:

you need to add more

Step-by-step explanation:

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Eric had $15.00 to spend on paints, which sold for $1.14 each. How many jars of paint can he buy?

Ahat [919]

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Eric can buy 13 jars of paint.
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Answer:

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Vanilla essence = 20 ml

Sugar = 1kg

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Step-by-step explanation:

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Deffense [45]

The Exact Square Root Is: 4.58257569496

Estimate Is: 5

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