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3 years ago

Use the Pythagorean Theorem to determine if a

Mathematics

1 answer:

MakcuM [25]3 years ago

6 0

Answer:

how can it be triangle with 0ft length

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

Question : Find if the coordinates given lie on the circles below: (a) Does (4,2) lie on the circle with equation

lorasvet [3.4K]

Answer: No

Explanation

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3 years ago

Edith plants a daffodil bulb.

WINSTONCH [101]

Answer:

Step-by-step explanation:

Njhhh

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3 years ago

If breadth of a rectangle is 19m and perimeter is 80m, find the length of the rectangle.

soldi70 [24.7K]

Answer: 21

Step-by-step explanation:

since 19 is the breadth and the perimeter is 80m, so 19*2=38 and 80-38= 42 so 42/2=21. The answer is 21

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3 years ago

The apple pie baked from 8:25 P.M. until 8:55 P.M. How much time did it take the pie to bake?

maw [93]

Answer:

30 minutes.

Step-by-step explanation:

8:55 - 8:25 is 30 minutes.

If you add 30 to 8:25, you would get 8:55.

Therefore, it's 30 minutes.

8 0

3 years ago

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