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2 years ago

True or False. (1, – 7) is a solution to the following systems of equations.

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

6 0

Answer:

False

Step-by-step explanation:

Hope it helps

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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

2 years ago

What is the degree measure of an arc 4 pie ft long in a circle of radius 10 ft

Bess [88]

Answer:

ow do you find arc length without the radius?

To calculate arc length without radius, you need the central angle and the sector area:

Multiply the area by 2 and divide the result by the central angle in radians.

Find the square root of this division.

Multiply this root by the central angle again to get the arc length.

The units will be the square root of the sector area angle.

Check your result with Omni Calculator.

Or the central angle and the chord length:

Divide the central angle in radians by 2 and perform the sin function on it.

Divide the chord length by double the result of step 1. This gives you the radius.

Multiply the radius by the central angle to get the arc length.

Check your result with Omni Calculator

Step-by-step explanation:

7 0

2 years ago

Which word describes the slope of the line? positive negative zero undefined

Sophie [7]

Answer:

Negative slope

Step-by-step explanation:

It is negative.

8 0

1 year ago

What is the answer to the following -1+8=

GenaCL600 [577]

Answer:

Step-by-step explanation:

-1+8=7

8 0

2 years ago

Read 2 more answers

Do the following lengths form a right triangle?

Dmitry_Shevchenko [17]

Answer:

yes, this forms a right angle

5 0

2 years ago