As suggested, let's use polar coordinates:
![\begin{cases}x=\rho\cos(\theta)\\y=\rho\sin(\theta)\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3D%5Crho%5Ccos%28%5Ctheta%29%5C%5Cy%3D%5Crho%5Csin%28%5Ctheta%29%5Cend%7Bcases%7D)
To get
![f(x,y)=\dfrac{x^3-xy^2}{x^2+y^2}\mapsto \dfrac{\rho^3\cos^3(\theta)-\rho^3\cos(\theta)\sin^2(\theta)}{\rho^2}](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D%5Cdfrac%7Bx%5E3-xy%5E2%7D%7Bx%5E2%2By%5E2%7D%5Cmapsto%20%5Cdfrac%7B%5Crho%5E3%5Ccos%5E3%28%5Ctheta%29-%5Crho%5E3%5Ccos%28%5Ctheta%29%5Csin%5E2%28%5Ctheta%29%7D%7B%5Crho%5E2%7D)
We can simplify the expression to
![\dfrac{\rho^3\cos^3(\theta)-\rho^3\cos(\theta)\sin^2(\theta)}{\rho^2}=\dfrac{\rho^3\cos(\theta)(\cos^2(\theta)-\sin^2(\theta))}{\rho^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Crho%5E3%5Ccos%5E3%28%5Ctheta%29-%5Crho%5E3%5Ccos%28%5Ctheta%29%5Csin%5E2%28%5Ctheta%29%7D%7B%5Crho%5E2%7D%3D%5Cdfrac%7B%5Crho%5E3%5Ccos%28%5Ctheta%29%28%5Ccos%5E2%28%5Ctheta%29-%5Csin%5E2%28%5Ctheta%29%29%7D%7B%5Crho%5E2%7D)
And simplify
to get
![\rho\cos(\theta)(\cos^2(\theta)-\sin^2(\theta))](https://tex.z-dn.net/?f=%5Crho%5Ccos%28%5Ctheta%29%28%5Ccos%5E2%28%5Ctheta%29-%5Csin%5E2%28%5Ctheta%29%29)
So, as
,
as well.
Answer:
16.2
Step-by-step explanation:
use Pythagorean theorem
a^2 + b^2 = c^2
15^2 + 6^
225 + 36 = 261
take the sq root of 261
Well to start off, we must first establish that line JP and line HP are equal because of the red ticks in the corner. So once we figured that out, then 3x-6 = x+2
»Next we add 6 to both side to make 3x = x+8
»Then we subtract x from both sides to equal 2x = 8
»Then we divide both sides by 2 which equals x=4
»So the final answer would be C. 4
Answer: There are 18 students in a van and 24 students in a bus.
Step-by-step explanation:
Let the number of students in the van be 'x' and the number of students in bus be 'y'.
Then, According to the question, we have the following system
![\text{[High School A ]}\ x+10y=258........................(1)\\\\\text{[High School B ]}\ 8x+5y=264........................................(2)\\](https://tex.z-dn.net/?f=%5Ctext%7B%5BHigh%20School%20A%20%5D%7D%5C%20x%2B10y%3D258........................%281%29%5C%5C%5C%5C%5Ctext%7B%5BHigh%20School%20B%20%5D%7D%5C%208x%2B5y%3D264........................................%282%29%5C%5C)
Multiply 2 to both the sides of equation (2), we get
![16x+10y=528.......................(3)](https://tex.z-dn.net/?f=16x%2B10y%3D528.......................%283%29)
Subtract equation (1) from equation (3), we get
![15x=270\\\Rightarrow\ x=\frac{270}{15}\\\Rightarrow\ x=18](https://tex.z-dn.net/?f=15x%3D270%5C%5C%5CRightarrow%5C%20x%3D%5Cfrac%7B270%7D%7B15%7D%5C%5C%5CRightarrow%5C%20x%3D18)
Substitute value of x in (1), we get
![18+10y=258\\\Rightarrow\ 10y=240\\\Rightarrow\ y=24](https://tex.z-dn.net/?f=18%2B10y%3D258%5C%5C%5CRightarrow%5C%2010y%3D240%5C%5C%5CRightarrow%5C%20y%3D24)
Hence, there are 18 students in a van and 24 students in a bus.
Answer:
![x=-\frac{3}{2}\textrm{ or }x=5](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B3%7D%7B2%7D%5Ctextrm%7B%20or%20%7Dx%3D5)
Step-by-step explanation:
Assuming you want to solve
,
![2x^2-7x-15=0\\(2x+3)(x-5)=0\\x=-\frac{3}{2}\textrm{ or }x=5](https://tex.z-dn.net/?f=2x%5E2-7x-15%3D0%5C%5C%282x%2B3%29%28x-5%29%3D0%5C%5Cx%3D-%5Cfrac%7B3%7D%7B2%7D%5Ctextrm%7B%20or%20%7Dx%3D5)