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2 years ago

Hunter placed 2 red, 3 blue, 1 yellow, 8 black, and 7 white straws into a bag.

1 answer:

8 0

7/21 or 1/3rd, it's just a ratio of white to all, there's 7 white straws and 21 in all, then you can simplify it down to 1/3rd.

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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

Each marble bag sold by hans marble company contains 7 yellow marbles for every 5 blue marbles. if a bag has 35 blue marbles, ho

Pavlova-9 [17]

The answer is 49 because since she multiplied 5 by 7 you have to do the same to yellow marbles so 7×7 = 49

5 0

3 years ago

In Biology class, Ji-yoon is viewing cells with a microscope. Cell F

ryzh [129]

Answer:bananas T^T

Step-by-step explanation:

5 0

2 years ago

Do you think this Scatter plot is linear or no? I really can't tell.

MrRa [10]

Answer:

I would say no because the dots are all over the place.

Step-by-step explanation:

It keeps going up then down back up and down again?

4 0

2 years ago

LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5, find the value of x

Sidana [21]

<span>LMNO is a parallelogram
so NM = OL
x + 15 = 3x + 5
solve for x
x - 3x = 5 - 15
-2x = -10
x = 5

Answer
x = 5</span>

5 0

3 years ago

Read 2 more answers