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3 years ago

Solve the equation check your solution What is -z/4=-3/4

Mathematics

1 answer:

KatRina [158]3 years ago

3 0

The answer is z= 3.

Hope this helps.

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Find the area of a circle with a circumference of 30 pie meters

vesna_86 [32]

Step-by-step explanation:

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3 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.

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3 years ago

You schedule production of communications chips. After the chips are produced, they go to the QC department, where each chip mus

Irina-Kira [14]

The best batch size is 1053.

Since 5% have failed, this means 95% have passed the test.

95% = 95/100 = 0.95

We can set up an equation to answer this:
0.95x = 1000

Divide both sides by 0.95:
0.95x/0.95 = 1000/0.95
x = 1052.6 ≈ 1053

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3 years ago

How. do i find the line of symmetry

kkurt [141]

The line of symmetry is at zero because the coordinates are X= -2 , X= 2

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3 years ago