# Integral rational trigonometric ​

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.)

## Related Questions

Jamal is comparing his transportation options for an upcoming trip. He’s considering a rental car and a taxi service. Based on his planned routes during his trip, he expects a taxi service would cost about $128. Jamal could also get a rental car for a daily rate and unlimited miles. If Jamal’s trip will last 4 days and he expects to pay about$24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?

Graph A

Step-by-step explanation:

Say that the car rental rate stands for c dollars ( $). We know that Jamal's trip lasts for 4 days, paying$ 24 in expenses for gas, and $128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality. ______ The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( \$ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,

24 + 4c < 128 - Subtract 24 from either side,

4c < 104 - Divide by 4 on either side, isolating c,

c < 26

The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.

______

The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.

A is the answer

Step-by-step explanation:

Complete parts ​(a) through ​(c) below. ​(a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the level of significance with degrees of freedom. ​(b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the level of significance based on a sample size of n. ​(c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the level of significance based on a sample size of n.

(a) The critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.

(b) The critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.

(c) The critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.

Step-by-step explanation:

We have to find the critical t values for each of the following levels of significance and sample sizes given below.

As we know that in the t table there are two columns. The horizontal column is represented by the symbol P which represents the level of significance and the vertical column is represented by the symbol '' which represents the degrees of freedom.

(a) A right-tailed test of a population mean at the α=0.01 level of significance with 15 degrees of freedom.

So, here the level of significance = 0.01

And the degrees of freedom = n - 1  = 15

Now, in the t table, the critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.

(b) A left-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 20.

So, here the level of significance = 0.05

And the degrees of freedom = n - 1

= 20 - 1 = 19

Now, in the t table, the critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.

(c) A two-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 13.

So, here the level of significance = = 0.025 {for the two-tailed test}

And the degrees of freedom = n - 1

= 13 - 1 = 12

Now, in the t table, the critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.

Simplify 3x/4 X 4y/2

3xy / 20

Aaaaaaaaaaaaaaaaaaaaaaa

the answer is   9.879

How are exponents related to taking the root of a number?

with exponents, you take a number and multiply it by itself.

Step-by-step explanation:

the root of a number is the number that can be multiplied a certain amount of times to get us that number.

therefore roots get you to the root of a number.

Hope it helps!

(even if its two weeks late.....)

A red die is tossed and then a green die is tossed. What is the possibility that the red die shows a six or the green die shows a six?