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3 years ago

Find the product of (p−10q)(p+10q)

Mathematics

1 answer:

Sonja [21]3 years ago

6 0

Answer:

p²-100q²

Step-by-step explanation:

p(p+10q)-10q(p+10q)

p·p+p(10q)-10q(p+10q)

p·p+p(10q)-10qp-10q(10q)

p·p+10pq-10pq-10q(10q)

p·p+0-10q(10q)

p·p-10q(10q)

p²-100q²

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Please, I need help in this ??

nignag [31]

Answer:

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

Step-by-step explanation:

$\int\frac{x^{4}}{x^{4} -1}dx$

Adding and Subtracting 1 to the Numerator

$\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx$

Dividing Numerator seperately by $x^{4} - 1$

$\int 1 + \frac{1}{x^{4}-1 }\, dx$

Here integral of 1 is x +c1 (where c1 is constant of integration

$x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx$ ----------------------------------(1)

We apply method of partial fractions to perform the integral

$\frac{1}{(x-1)(x+1)(x^{2}+1)}$ = $\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}$ ------------------------------------------(2)

$\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}$

1 = $A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)$ -------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = $\frac{1}{4}$

1 = B(-1-1)(1+1)

B = $-\frac{1}{4}$

1 = C(i-1)(i+1)

C = $-\frac{1}{2}$

Substituting A, B, C in equation (2)

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }$

On integration

Here $\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx$

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\frac{1}{4} ln(x-1)$ - $\frac{1}{4} ln(x+1)$ - $\frac{1}{2} arctanx$ + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

$x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2$

Here c1 + c2 can be added to another and written as c

Therefore,

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

4 0

3 years ago

In AWXY, the measure of ZY=90°, XW = 25, YX = 24, and WY = 7. What is the value

Lemur [1.5K]

Answer: 0.28

Step-by-step explanation:

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3 years ago

The ratio of small dogs to big dogs at the park is 1:3. Which does not represent this ratio?

Karolina [17]

Answer:

C.2:4

Step-by-step explanation:

1*2=2

3*2=6

2:6=2:4

not true so it is C.

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2 years ago

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Phil has $6.00 he wants to buy creepy erasers that cost $1.05 each .if he buys 5 more they are 0.79 each does he have enough mon

Scrat [10]

Answer:

No, he doesn't it would be 5 cents over the amount of money he has.

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3 years ago

Write 0.8 as a percentage

VikaD [51]

Is answer is 80% because you move the decimal to the right 2 times

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