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2 years ago

Please open attachment. 29 points

Mathematics

1 answer:

elixir [45]2 years ago

3 0

3) 1/1 2/0 -2/0 good luck i hope this helped

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You have $55 and spend x dollars. How much money do you have left?

andreyandreev [35.5K]

Well how much is x worth lol

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2 years ago

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Using the "Part4Series.txt" time series

vekshin1

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Step-by-step explanation:

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2 years ago

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

How many gallons of a 70% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 60% a

Flura [38]

We have 60 gallons of 20% antifreeze.

How much 70% antifreeze do we add to get 60% antifreeze?

We'll make "x" the gallons of 70% we must add.

.20 * 60 + .70 x = .60 * (60 + x)

12 + .70x = 36 + .60x

.10x = 24

x = 240 gallons of 70% antifreeze.

Source

1728.com/mixture.htm (see example B)

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2 years ago

How many half metres together measure 4 1-2m

telo118 [61]

Make it an improper fraction with two as the denominator, and you'll get 9/2. There are 9 halves in 4 1/2 meters

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3 years ago