1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LuckyWell [14K]
3 years ago
8

Integral rational trigonometric ​

Mathematics
1 answer:
abruzzese [7]3 years ago
8 0

Substitute <em>x</em> = 3 - 2 cos(<em>θ</em>) and d<em>x</em> = 2 sin(<em>θ</em>) d<em>θ</em> (where "sin" = "sen"). So we have

∫ sin(<em>θ</em>) / (3 - 2 cos(<em>θ</em>)) d<em>θ</em> = 1/2 ∫ 1/<em>x</em> d<em>x</em>

= 1/2 ln|<em>x</em>| + <em>C</em>

= 1/2 ln(3 - 2 cos(<em>θ</em>)) + <em>C</em>

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

You might be interested in
Each block in Ton’s neighborhood is 2/3 mile long if he walk 4 1/2 blocks how far does he walk?
nataly862011 [7]

if each block is 2/3 miles long, and he walks 4 1/2 blocks, we can simply multiply to two. It looks like this:

(2/3)(4 1/2)

to multiply, make 4 1/2 into an improper fraction and multiply normally

(2/3)(9/4)

Ton walks 3 miles total.

3 0
3 years ago
Determine whether the bolded numerical value is a parameter or a statistic. Explain your reasoning.The average annual salary of
sergey [27]

Answer:  F. Statistic​, because the data set of salaries of 50 employees is a sample.

Step-by-step explanation:

A parameter gives measure of a characteristic for the entire population where as a statistic gives measure of a characteristic for the subset of population (sample).

Given : The average annual salary of 50 of a company's 800 employees is $54,000.

It means the sample size = 50 and the sample mean salary= $54,000.

i.e $54,000 is giving the measure for mean salary for the sampled 50 employees.

It means $54,000 is a statistic .

Hence, the correct answer is option (F).

7 0
4 years ago
Which quadratic function shows a y-intercept of 4 and a maximum value of 5
Elena L [17]

Answer:

The 4th graph

Step-by-step explanation:

To have a maximum value, your parabola would have to open downwards. So the first 2 are wrong. Since your y-intercept is positive 4, your graph would have to touch the y axis at 4. The 3rd graph is wrong since it touches the y-axis at a negative point. The correct answer would be the 4th answer choice.

8 0
3 years ago
PLEASE HELP Alice's freezer can be set to a range of temperatures, from
VMariaS [17]
I think it is B, but I'm not fully sure.

7 0
4 years ago
Simplify -5xy+6xy-3y+4y+x^2​
Nutka1998 [239]
Answer is x^2+xy+y if the answer is correct then give me a thank
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of x? Teach me
    5·1 answer
  • 20 POINTS!!! NEED HELP ASAP!!!
    13·2 answers
  • I need help solving these problems​
    8·1 answer
  • Convert 25% to a decimal.
    14·2 answers
  • PLEASE HELP PLEASE PLEASE
    14·1 answer
  • Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 End
    15·1 answer
  • After a 2 1/2 hour rainstorm, there are 5 inches of water in a bucket outside. What is the rate per inch?
    14·1 answer
  • the diameter of your bicycle wheel is 25 inched. how far will you move in two truns your wheel use 3 for pie
    12·1 answer
  • Helpppppppppppppppppppppppppppppppppppppppppp
    10·2 answers
  • Help Please.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!