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ollegr [7]
3 years ago
9

An angle whose measure is -120 is in standard position. In which quadrant does the terminal side of the angle fall

Mathematics
1 answer:
My name is Ann [436]3 years ago
5 0
I believe it falls in the 3rd quadrant
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<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%20%5Cinfty%20%20%5Cfrac%7B%20%5Csqrt%5B%20%20%5Cscriptsize%5Cphi%
Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx

Replace x \to x^{\frac1\phi} = x^{\phi-1} :

I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx

Split the integral at x = 1. For the integral over [1, ∞), substitute x \to \frac1x :

\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx

The integrals involving tan⁻¹ disappear, and we're left with

I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}

8 0
2 years ago
Choose the correct sum of the polynomials (4x3 − 2x − 9) (2x3 5x 3). 6x3 − 3x − 6 2x3 − 7x − 12 6x3 3x − 6 2x3 3x − 3.
dimaraw [331]

The correct sum of the polynomial is \rm 6x^3 + 3x - 6.

We have to determine

The correct sum of the polynomials.

<h3>Sum of the polynomials</h3>

Sum of the polynomials is just a matter of combining like terms, with some order of operations.

Then,

The correct sum of the polynomial is;

\rm (4x^3 - 2x - 9) + (2x^3 + 5x + 3) \\\\ 4x^3 - 2x - 9 + 2x^3 + 5x + 3\\\\ 6x^3 + 3x - 6

Hence, the correct sum of the polynomial is \rm 6x^3 + 3x - 6.

To know more about the sum of the polynomial click the link is given below.

brainly.com/question/9465649

5 0
2 years ago
What is 70/3? *Please do not put the answer as a run-on decimal, thanks!*
VladimirAG [237]

Answer:

the answer is 23 1/3 or 23 and 1/3 or 23.3 with repeating decimal

Step-by-step explanation:

first find the number that 3 multiplied by a number equals closest to say 70 so 69 leaving 1 amd you use your denominator you divided by and you would have 1/3

6 0
2 years ago
Read 2 more answers
I need help showing my work for the answer.
user100 [1]

Answer: ong

Step-by-step explanation: im straight

4 0
3 years ago
Help me please?!!!!!!!!!
Basile [38]
I think it’s the last one but I’m not sure
4 0
3 years ago
Read 2 more answers
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