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strojnjashka [21]
3 years ago
9

While training for an Ironman competition, Johnson swam 0.86 km, biked for 22.4 km, and ran 4.25 km. Johnson completed this rout

ine twice a week. How far did Johnson travel in one week while training, in meters?
Mathematics
1 answer:
igomit [66]3 years ago
3 0

Answer:

55020 metres

Step-by-step explanation:

Johnson swam 0.86 km, biked for 22.4 km, and ran 4.25 km. He did this twice a week.

To find the total distance traveled in one week in metres, we first add up the distances and multiply by 2 and then convert to metres.

The sum of the distances is:

0.86 + 22.4 + 4.25 = 27.51 km

Multiply by 2:

27.51 * 2 = 55.02 km

1 km = 1000 metres

55.02 km = 55.02 * 1000 = 55020 metres

He traveled 55020 metres while training.

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Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
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Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

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\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

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\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

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465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

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