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marishachu [46]

3 years ago

9

A shark is swimming 25 feet below the surface of the water. It goes down another 12 feet. What is the new depth the shark is swi

mming at?

1 answer:

ivolga24 [154]3 years ago

7 0

Answer:

37

Step-by-step explanation:

You add them to see the new depth

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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

4 years ago

PLEASE HELP!!! 30+ POINTS

DedPeter [7]

Answer:

A measure of average is a value that is typical for a set of figures. Finding the average helps you to draw conclusions from data. The main types are mean, median and mode. Data is also often grouped.

Step-by-step explanation:

To find the mean add all the ages together and divide by the total number of children.

If you type all those ages into a calculator it is easy to make an error.

8 0

3 years ago

In the problem 4x + 10 list a term, factor, coefficient, and constant.

kifflom [539]

term- 4x and 10

This is because to be a term it has to be + or -

Factor- 4x+10

This is because that is what is happening in the problem

Coefficient- 4y

I don't know what the constant would be, But I hope that this helps you

6 0

3 years ago

Determine the measure of each numbered angle. Show work, provide a brief explanation.

monitta

Huhvgujvdthb friend gf t if y h iutzyreRx it’s g. Ttussuesru. G h

5 0

2 years ago

HELP !! The equations of three lines are given below.

Leviafan [203]

Answer:

1 neither

2 neither

3 neither

Step-by-step explanation:

6 0

4 years ago