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3 years ago

Please help and thank you

Mathematics

2 answers:

sesenic [268]3 years ago

7 0

The answer is B...

On the first day he spends 30 minutes training.. after that he is spending 10 minutes extra.. so on day two he would spend 40 minutes.. then day three.. 50 minutes.. day four.. 60 minutes and so on... The answer would be <em><u>B</u></em> though.

Lunna [17]3 years ago

4 0

Answer: B. 8th day: 100 minutes; 9th day: 110 minutes; 10th day: 120 minutes

Remember:

$a_{n}$ = $n$ th term

$n$ = number of terms

$a_{1}$ = first term

$d$ = common difference

Identify the given information.

$a_{1} = 30\\d = 10$

Choose which formula to use. In this case, you should use the explicit formula for arithmetic sequences.

$a_{n} = a_{1} + d(n - 1)$

Substitute in the given values and simplify.

$a_{n} = 30 + 10(n - 1)\\a_{n} = 30 + 10n - 10\\a_{n} = 10n + 20$

Substitute in 8, 9, and 10 for $n$ to find out how many days Rick would train on the 8th, 9th, and 10th day of training.

$a_{8} = 10(8) + 20 = 80 + 20 = 100\\a_{9} = 10(9) + 20 = 90 + 20 = 110\\a_{10} = 10(10) + 20 = 100 + 20 = 120$

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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

Find the equation of the plane that goes through three points:

frosja888 [35]

The equation of the plane that goes through these points is:

6x + 2y + z = 10.

<h3>How to find the equation of a plane given three points?</h3>

The equation of the plane is found replacing the points into the following equation:

ax + by + c = z.

For point A, we have that:

3b + c = 4.

For point B, we have that:

a + 2b + c = 0.

For point C, we have that:

-a + 6b + c = 4.

Hence the system is:

3b + c = 4.

a + 2b + c = 0.

-a + 6b + c = 4.

From the first equation, we have that:

c = 4 - 3b.

Replacing in the second, we have that:

a + 2b + 4 - 3b = 0

a - b = -4.

Replacing in the third, we have that:

-a + 6b + 4 - 3b = 4.

-a + 3b = 0.

a = 3b.

We have that a - b = -4, hence:

3b - b = -4

2b = -4

b = -2.

a = 3b, hence a = -6.

c = 4 - 3b -> c = 10.

Hence the equation is:

ax + by + c = z.

z = -6x - 2y + 10

6x + 2y + z = 10.

More can be learned about the equation of a plane at brainly.com/question/13854649

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1 year ago

Identify all the intercepts for the following function

Triss [41]

Where are the intercepts

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3 years ago

Calculate the value of y

Reika [66]

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4 0

3 years ago

Read 2 more answers

Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?

KatRina [158]

Answer:

They are perpendicular

Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept form of equation is y = mx+c

where m is slope of line and c is y intercept.

________________________________

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

m = -2 , c = 4

_________________________________________

equation 2 is y = one halfx + 4 ( one half is same as 1/2)

so equation is

y = x/2 +4

comparing it with y = mx + c

m = 1/2 , c = 4

_________________________________________

Now lets evaluate options

They are parallel. wrong option

For lines to be parallel slope should be same.

But here slope are different -2 and 1/2 .

Thus lines are not parallel.

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They are perpendicular. correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are perpendicular

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They are the same line. wrong option

For lines to be same both slope and y intercept should be same.

Y intercept is same but the slopes are different -2 and 1/2 .

Thus lines are not the same line.

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They are not related. wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

4 0

3 years ago