MATHEMATICS COLLEGE

Integral rational trigonometric

Answers

Answer 1

Answer:

Substitute x = 3 - 2 cos(θ) and dx = 2 sin(θ) dθ (where "sin" = "sen"). So we have

∫ sin(θ) / (3 - 2 cos(θ)) dθ = 1/2 ∫ 1/x dx

= 1/2 ln|x| + C

= 1/2 ln(3 - 2 cos(θ)) + C

(We can remove the absolute value because -1 ≤ cos(θ) ≤ 1, so 1 ≤ 3 - 2 cos(θ) ≤ 5, and |x| = x when x ≥ 0.)

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Answers

Answer:

Its B

Step-by-step explanation:

Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fractions where needed.)

Answers

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

$a = 2i + j -3k$

$b = 3i - 2j -k$

Required

The angle between them

The cosine of the angle between them is:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

First, calculate a.b

$a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)$

Multiply the coefficients of like terms

$a \cdot b =2 * 3 - 1 * 2 - 3 * -1$

$a \cdot b =7$

Next, calculate |a| and |b|

$|a| = \sqrt{2^2 + 1^2 + (-3)^2$

$|a| = \sqrt{14$

$|b| = √(3^2 + (-2)^2 + (-1)^2)$

$|b| = √(14)$

Recall that:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

This gives:

$\cos(\theta) = (7)/(√(14) * √(14))$

$\cos(\theta) = (7)/(14)$

$\cos(\theta) = 0.5$

Take arccos of both sides

$\theta =\cos^(-1)(0.5)$

$\theta =60^o$

1. Which fraction has a value that's equal to 7/8

Answers

Answer:

to find the right answer multiple by 2

Step-by-step explanation:

and you get 14/16

The ratio of squirrels to chipmunks in the yard was 2:7. How many squirrels were in the yard if there were 49 chipmunks?Explain please.

Answers

Let the number of squirells be 2x and number of chipmunks be 7x ,

Given that number of chipmunks is 49, so

= > 7x = 49

= > x = 49 / 7

= > x = 7

So the number of squirells will be 2x = 2( 7 ) = 14

$\bold{There \: were \: 14 \: squirells \: in \: the \: yard}$

College Algebra Half Life ProblemRecently, while digging in Chaco Canyon, New Mexico, archaeologists found corn pollen that was 4000 years old. This was evidence that Native Americans had been cultivating crops in the Southwest centuries earlier than scientists had thought.

What percent of the carbon-14 had been lost from the pollen?

(half-life of carbon-14 = 5730)

Answers

I think the correct answer is 56%

A set X is said to be closed under multiplication if for every X1, X2 E X we have X1X2 E X. Let A be the union of all bounded subsets X CR that are closed under multiplication. Does inf(A) exist? If it does, find it.