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Elza [17]
3 years ago
13

Does #1 look correct?

Mathematics
1 answer:
ipn [44]3 years ago
4 0

Answer:

Yes

Step-by-step explanation:

If we need to find the distance between two points on a number line, we subtract one of the points from the other. We then take the absoulte value of the difference. You done this right.

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Integrate cosx/sqrt(1+cosx)dx
Step2247 [10]
<span>Take the integral: integral (cos(x))/sqrt(cos(x)+1) dx
For the integrand (cos(x))/sqrt(1+cos(x)), substitute u = 1+cos(x) and du = -sin(x) dx: = integral (u-1)/(sqrt(2-u) u) du
For the integrand (-1+u)/(sqrt(2-u) u), substitute s = sqrt(2-u) and ds = -1/(2 sqrt(2-u)) du: = integral -(2 (1-s^2))/(2-s^2) ds
Factor out constants: = -2 integral (1-s^2)/(2-s^2) ds
For the integrand (1-s^2)/(2-s^2), cancel common terms in the numerator and denominator: = -2 integral (s^2-1)/(s^2-2) ds
For the integrand (-1+s^2)/(-2+s^2), do long division: = -2 integral (1/(s^2-2)+1) ds
Integrate the sum term by term: = -2 integral 1/(s^2-2) ds-2 integral 1 ds
Factor -2 from the denominator: = -2 integral -1/(2 (1-s^2/2)) ds-2 integral 1 ds
Factor out constants: = integral 1/(1-s^2/2) ds-2 integral 1 ds
For the integrand 1/(1-s^2/2), substitute p = s/sqrt(2) and dp = 1/sqrt(2) ds: = sqrt(2) integral 1/(1-p^2) dp-2 integral 1 ds
The integral of 1/(1-p^2) is tanh^(-1)(p): = sqrt(2) tanh^(-1)(p)-2 integral 1 ds
The integral of 1 is s: = sqrt(2) tanh^(-1)(p)-2 s+constant
Substitute back for p = s/sqrt(2): = sqrt(2) tanh^(-1)(s/sqrt(2))-2 s+constant
Substitute back for s = sqrt(2-u): = sqrt(2) tanh^(-1)(sqrt(1-u/2))-2 sqrt(2-u)+constant
Substitute back for u = 1+cos(x): = sqrt(2) tanh^(-1)(sqrt(sin^2(x/2)))-2 sqrt(1-cos(x))+constant
Factor the answer a different way: = sqrt(1-cos(x)) (csc(x/2) tanh^(-1)(sin(x/2))-2)+constant
Which is equivalent for restricted x values to:
Answer: | | = (2 cos(x/2) (2 sin(x/2)+log(cos(x/4)-sin(x/4))-log(sin(x/4)+cos(x/4))))/sqrt(cos(x)+1)+constant</span>
3 0
3 years ago
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 18 N acts on
inysia [295]

Answer: F=15N


Step-by-step explanation:

1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:

F=ka

Where F is the force acting on the object, a is the object's acceleration and k is the constant of proportionality.

2. Keeping this on mind, you can calculate the constant of proportionality by substituting F=18 and a=6 into the equation and solving for k:

18=k6\\k=\frac{18}{6}\\k=3

3. Now, you can calculate the force when the acceleration of the object becomes 5 m/s², as following:

F=3(5)\\F=15

3. The result is:

F=15N

7 0
3 years ago
A bag contains 3 red marbles 4 blue marbles and 7 Green marbles if two marbles are drawn out of the bag what is the probability
mr_godi [17]

Answer:

0.368

Step-by-step explanation:

Number of red marbles= 3

Number of blue marbles= 4

Number of green marbles= 7

Total number of marbles= 3+4+7= 14

Let the first ball is taken out to be red

P(R)=\frac{3}{14}

than again a second ball is drawn, number of balls left= 14-1=13

Number of red= 2

P(R)=\frac{2}{13}

Total probability=\frac{3}{14}+\frac{2}{13}

Total probability= 0.368

Hence, the correct answer is 0.368

3 0
3 years ago
C) 40.3, 32.7, 40.29, 43.43,<br>32.23 In Decreasing order please ​
iogann1982 [59]

Answer:

32.7, 40.29, 40.3, 43.43

Step-by-step explanation:

Hope this helps =)

Correct me if I am wrong

5 0
3 years ago
3
Dimas [21]

Answer:

the line perpendicular: x=-3

Step-by-step explanation:

8 0
2 years ago
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