Answer:
See pic below.
Step-by-step explanation:
Answer:
what I can help to you
Step-by-step explanation:
say something
Answer:
,
![(6, \frac{11\pi}{6} )](https://tex.z-dn.net/?f=%286%2C%20%5Cfrac%7B11%5Cpi%7D%7B6%7D%20%29)
Step-by-step explanation:
Note I'm using a, instead of theta to represent angles.
To convert rectangular to polar, apply these formulas
![r = \sqrt{ {x}^{2} + {y}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%20%7By%7D%5E%7B2%7D%20%20%7D%20)
![\alpha = \tan {}^{ - 1} ( \frac{y}{x} )](https://tex.z-dn.net/?f=%20%5Calpha%20%20%3D%20%20%5Ctan%20%7B%7D%5E%7B%20-%201%7D%20%28%20%5Cfrac%7By%7D%7Bx%7D%20%29%20)
Note : Rectangular coordinates are the coordinates you were learning since elementary school or middle school.
The first number is x, and the second is y.
So
![r = \sqrt{(3 \sqrt{3} ) {}^{2} + ( - 3) {}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B%283%20%5Csqrt%7B3%7D%20%29%20%7B%7D%5E%7B2%7D%20%2B%20%28%20-%203%29%20%7B%7D%5E%7B2%7D%20%20%7D%20)
![r = \sqrt{36}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B36%7D%20)
![r = 6](https://tex.z-dn.net/?f=r%20%3D%206)
![\alpha = \tan {}^{ - 1} ( \frac{ - 3}{3 \sqrt{3} } )](https://tex.z-dn.net/?f=%20%5Calpha%20%20%3D%20%20%5Ctan%20%7B%7D%5E%7B%20-%201%7D%20%28%20%5Cfrac%7B%20-%203%7D%7B3%20%5Csqrt%7B3%7D%20%7D%20%29%20)
Since our y coordinate is negative and x coordinate is Positve , on the unit circle, the angle must be in the fourth quadrant.
So the angle must be in between
![\frac{3\pi}{2} < \alpha < 2\pi](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%20%3C%20%20%5Calpha%20%20%3C%202%5Cpi)
![\alpha = \tan {}^{ - 1} ( \frac{ - 1}{ \sqrt{3} } )](https://tex.z-dn.net/?f=%20%5Calpha%20%20%3D%20%20%5Ctan%20%7B%7D%5E%7B%20-%201%7D%20%28%20%5Cfrac%7B%20-%201%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%29%20)
![\alpha = \frac{11\pi}{16}](https://tex.z-dn.net/?f=%20%5Calpha%20%20%3D%20%20%5Cfrac%7B11%5Cpi%7D%7B16%7D%20)
So our answer is
(6, 11pi/6).
The factors of given polynomial are:![(2x+9)(3x+7)](https://tex.z-dn.net/?f=%282x%2B9%29%283x%2B7%29)
Further explanation:
Factorization is either done by using quardatic formula or directly making factor.
For making factors, the constant term is multiplied with the coefficient of x^2 and pairs of factors are made such that their sum or difference is equal to the co-efficient of x.
Given
![6x^2+41x+63](https://tex.z-dn.net/?f=6x%5E2%2B41x%2B63)
63x6 gives us: 378
Factor pairs of 378 are:
182,2
126,3
54,7
42,9
14,27 => 41
So the pair we are going to use is 14,27
![6x^2+41x+63\\=6x^2+14x+27x+63\\=2x(3x+7)+9(3x+7)\\=(2x+9)(3x+7)\\](https://tex.z-dn.net/?f=6x%5E2%2B41x%2B63%5C%5C%3D6x%5E2%2B14x%2B27x%2B63%5C%5C%3D2x%283x%2B7%29%2B9%283x%2B7%29%5C%5C%3D%282x%2B9%29%283x%2B7%29%5C%5C)
So the factors of given polynomial are:![(2x+9)(3x+7)](https://tex.z-dn.net/?f=%282x%2B9%29%283x%2B7%29)
Keywords: Factorization, polynomials
Learn more about factorization at:
#LearnwithBrainly