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3 years ago

Whether the following relation represents a function. Use pencil and paper.

Mathematics

2 answers:

Free_Kalibri [48]3 years ago

6 0

Answer: it’s yes because A function is a relationship between quantities

saveliy_v [14]3 years ago

5 0

The answer is O yes the relation does represent a function

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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.

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3 years ago

Imagine that city officials in your hometown expect a huge rise in population over the next few years. Which of the following pe

ioda

Answer:

C an urban planner

Step-by-step explanation:

8 0

3 years ago

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Plzzzzzzzz help this is math

elena-s [515]

The answer would be
m= -25

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3 years ago

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A car advertisement states that a certain car can accelerate from rest to 70 m/s in 7 seconds. Find the car's average accelerati

Contact [7]

Answer:

The average acceleration of the car will be 10 m/s.

Step-by-step explanation:

70 / 7 = 10 m/s.

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3 years ago

Suppose f(x)=x^3 find the graph of f(x+3)

hoa [83]

Replace x with x+3:

f(x+3) = (x+3)²

which is x² translated 3 units left

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3 years ago