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4 years ago

How do I prove that 5^31-5^29 is divisible by 100 in the form of ___*100?

Mathematics

1 answer:

Nata [24]4 years ago

5 0

You can pull a common factor from both terms:

$5^{31}-5^{29}=5^{29+2}-5^{29}=5^{29}(5^2-1)=24\cdot5^{29}$

Next, pull a factor of 4 from 24, and 25 from the power of 5; since 100 = 25*4, we have

$5^{31}-5^{29}=\underbrace{5^{27}\cdot6}\cdot100$

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rosijanka [135]

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$

Notice that $x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1)$ . Decompose the integrand into partial fractions:

$\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}$
$=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}$

Integrating term-by-term, you get

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$

5 0

4 years ago

A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought

lesya [120]

A+c=100

3a+2c=275, from the first c=100-a making the 2nd equation become:

3a+2(100-a)=275 perform indicated multiplication on left side

3a+200-2a=275 combine like terms on left side

a+200=275, subtract 200 from both sides

a=75, and since c=100-a

c=100=75=25

So the answer is D. 25 children and 75 adults
Equation 1: a+c=100
Equation 2: 3a+2c=275

8 0

3 years ago

HELP PLEASE YOU'LL GET 25 POINTS

ollegr [7]

Answer:

Step-by-step explanation:

Im pretty sure

5 0

3 years ago

Read 2 more answers

Graph the given relation or equation and find the domain and range. Then

vredina [299]

X=1 Hopefully that helped

6 0

3 years ago

Review the table showing wind speed, y, in miles per hour, measured x hours after midnight.

hodyreva [135]

The trigonometric function that best models the data is determined as y = 1.87sin(–0.29x + 4.79) + 6.13.

<h3>Trigonometric function that models the data</h3>

The trigonometric function that best models the data is determined as follows;

y = 1.87sin(-0.29x + 4.79) + 6.13

Use the above equation to check if its gives you values in the table;

y = 1.87sin(-0.29 x 1 + 4.79) + 6.13

y = 1.87sin(4.5 rad) + 6.13

y = 4.3

y = 1.87sin(-0.29 x 2 + 4.79) + 6.13

y = 1.87sin(4.21 rad) + 6.13

y = 4.49

y = 1.87sin(-0.29 x 4 + 4.79) + 6.13

y = 1.87sin(3.63 rad) + 6.13

y = 5.2

y = 1.87sin(-0.29 x 7 + 4.79) + 6.13

y = 1.87sin(2.76 rad) + 6.13

y = 6.8

y = 1.87sin(-0.29 x 9 + 4.79) + 6.13

y = 1.87sin(2.18 rad) + 6.13

y =7.7

y = 1.87sin(-0.29 x 10 + 4.79) + 6.13

y = 1.87sin(1.89 rad) + 6.13

y = 7.9

y = 1.87sin(-0.29 x 13 + 4.79) + 6.13

y = 1.87sin(1.02 rad) + 6.13

y = 7.72

y = 1.87sin(-0.29 x 17 + 4.79) + 6.13

y = 1.87sin(-0.14 rad) + 6.13

y = 5.9

y = 1.87sin(-0.29 x 20 + 4.79) + 6.13

y = 1.87sin(-1.01 rad) + 6.13

y = 4.6

Thus, the trigonometric function that best models the data is determined as y = 1.87sin(–0.29x + 4.79) + 6.13.

Learn more about trigonometry functions here: brainly.com/question/1143565

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8 0

2 years ago