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3 years ago

1 - Um cilindro com êmbolo móvel contém um gás à pressão de 4,0.104N/m2. Quando é fornecido 6 kJ de

Mathematics

1 answer:

Lerok [7]3 years ago

4 0

I would want to answer but I do not understand that language sorry:)

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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

Solve the compound inequality and write the solution in interval notation: 34x−3≤3 or 25(x+10)≥0.

kirza4 [7]

Answer

x≤3/17 or x≥-10

Step-by-step explanation:

3 0

3 years ago

Simplify ( 1/2A + 1/2B )^2

zysi [14]

Notice that both A and B are multiplied by (1/2).

Thus, the given expression can be re-written as [(1/2)(A+B)]^2.

Square the (1/2) and the (A+B) separately, and then multiply together the resulting squares:

(1/4)(A^2 + 2AB + B^2)

4 0

3 years ago

Read 2 more answers

These box plots show the basketball scores for two teams.

Arisa [49]

The most appropriate statement is the interquartile range for the Wolverines, 30 is less than the IQR for the panthers, 40.

<h3>What is the correct statement?</h3>

The box plot is used to show the distribution of data. The box plot can be used to determine the range, interquartile range and median of the data set.

The range is the difference between the two ends of the whiskers.

Range for the Wolverines = 96 - 35 = 61

Range for the Panthers = 107 - 33 = 74

The interquartile range is the difference between the first and third lines on the box

IQR for the Wolverines = 85 - 55 = 30

Range for the Panthers = 90 - 50 = 40

To learn more about box plots, please check: brainly.com/question/1523909

#SPJ1

6 0

2 years ago

The slope of a line is 0, and the y-Intercept Is 6. What is the equation of the line written in slope-intercept form?

sdas [7]

Answer:

y=6

Step-by-step explanation:

if a slope is 0 than its just y=b. I hope u have a good day

6 0

2 years ago

1 - Um cilindro com êmbolo móvel contém um gás à pressão de 4,0.10*4N/m*2. Quando é fornecido 6 kJ de

1 - Um cilindro com êmbolo móvel contém um gás à pressão de 4,0.104N/m2. Quando é fornecido 6 kJ de