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2 years ago

Help plz I have 6 minutes

Mathematics

1 answer:

ivanzaharov [21]2 years ago

7 0

Answer:

x = 105

Step-by-step explanation:

Sum of n-sided polygon = (n - 2)*180

The polygon given is a 7-sided polygon, therefore substitute n = 7 into (n - 2)*180

Sum of the polygon = (7 - 2)*180 = 900°

Thus:

x + 102 + 165 + 123 + x + 11 + 128 + 161 = 900

Add like terms

2x + 690 = 900

2x = 900 - 690

2x = 210

x = 210/2

x = 105

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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 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump for women was 70.0 in

sveta [45]

Answer: year 2194

Explanation:

1) Model the jump of the women:

i) initial jump = 70.0 in

ii) increase rate = 0.48% per year

iii) equation: h = 70.0(1 +0.0048)ⁿ

2) Model the jump of the men:

i) initial jump 86.5 inches.

ii) increase rate, 0.4%.

iii) equation: h = 86.5 (1 + 0.004)ⁿ

3) Equal the two equations (h = h) to find when the jumps will be equal:

i) 70.0(1 +0.0048)ⁿ = 86.5 (1 + 0.004)ⁿ

ii) 70.0(1.0048)ⁿ = 86.5 (1.004)ⁿ

ii) [1.0048ⁿ / 1.004ⁿ] = 86.5/70.0

iii) [1.0048/ 1.0040]ⁿ = 86.5/70.0

iv) n log (1.0048 / 1.0040) = log ( 86.5/70)

v) n = log (86.5/70) / log (1.0048/1.0040) ≈ 266

3) year = 1928 + 266 = 2194

That is in the year 2194

8 0

2 years ago

Read 2 more answers

Somebody pls help I’m doin a exam!!!!

ra1l [238]

Answer:

Step-by-step explanation:

12x+2y=36

2y=36-12x

5x+36-12x=22

7x=14

x=2

2y=36-12(2)

2y=12

y=6

btw,next time, please do not include words like(failing ,exam,test,etc) in your question,otherwise, the question might be deleted.

5 0

2 years ago

The area of a circle is 2464cm2.calculate it's diameter to 2 significant figures<br>

tigry1 [53]

Answer:

Step-by-step explanation:

Answer:

The diameter of the circle is 56 cm.

Step-by-step explanation:

Given : The area of the circle is 2464 cm square.

To find : The diameter of the circle?

Solution :

The area of the circle is defined as

Where, A=2464 cm² is the area,

r is the radius

Substituting the values,

Radius of the circle is 28 cm.

The diameter of the circle is

Therefore, The diameter of the circle is 56 cm.

3 0

3 years ago

PLEASE HELP!!!!!!! A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a

Marianna [84]

Answer:

The answer to your question is car 1 = 30 gal and car 1 = 20 gal

Step-by-step explanation:

car 1 = a

car 2 = b

Efficiency of car 1 = 35 mi/gal

Efficiency for car 2 = 20 mi/gal

Total distance = 1450

Total gas consumption = 50 gal

Equations

35a + 20b = 1450 ------- (I)

a + b = 50 ------- (II)

Solve by elimination

Multiply equation II by -35

35a + 20b = 1450

-35a - 35b = -1750

Simplify

0 - 15b = -300

Solve for b

b = -300/-15

Result

b = 20

Substitute b in equation II to find a

a + 20 = 50

Solve for a

a = 50 -20

Result

a = 30

4 0

3 years ago