Answer:
![\displaystyle y=\frac{16-9x^3}{2x^3 - 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B16-9x%5E3%7D%7B2x%5E3%20-%203%7D)
![\displaystyle y=-\frac{56}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B56%7D%7B13%7D)
Step-by-step explanation:
<u>Equation Solving</u>
We are given the equation:
![\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D%7D)
i)
To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.
We have to make it in steps like follows.
Cube both sides:
![\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%3D%5Cleft%28%5Csqrt%5B3%5D%7B%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D%7D%5Cright%29%5E3)
Simplify the radical with the cube:
![\displaystyle x^3=\frac{3y+16}{2y+9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%3D%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D)
Multiply by 2y+9
![\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%282y%2B9%29%3D%5Cfrac%7B3y%2B16%7D%7B2y%2B9%7D%282y%2B9%29)
Simplify:
![\displaystyle x^3(2y+9)=3y+16](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%282y%2B9%29%3D3y%2B16)
Operate the parentheses:
![\displaystyle x^3(2y)+x^3(9)=3y+16](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E3%282y%29%2Bx%5E3%289%29%3D3y%2B16)
![\displaystyle 2x^3y+9x^3=3y+16](https://tex.z-dn.net/?f=%5Cdisplaystyle%202x%5E3y%2B9x%5E3%3D3y%2B16)
Subtract 3y and
:
![\displaystyle 2x^3y - 3y=16-9x^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%202x%5E3y%20-%203y%3D16-9x%5E3)
Factor y out of the left side:
![\displaystyle y(2x^3 - 3)=16-9x^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%282x%5E3%20-%203%29%3D16-9x%5E3)
Divide by
:
![\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdisplaystyle%20y%3D%5Cfrac%7B16-9x%5E3%7D%7B2x%5E3%20-%203%7D%7D)
ii) To find y when x=2, substitute:
![\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B16-9%5Ccdot%202%5E3%7D%7B2%5Ccdot%202%5E3%20-%203%7D)
![\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B16-9%5Ccdot%208%7D%7B2%5Ccdot%208%20-%203%7D)
![\displaystyle y=\frac{16-72}{16- 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B16-72%7D%7B16-%203%7D)
![\displaystyle y=\frac{-56}{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B-56%7D%7B13%7D)
![\mathbf{\displaystyle y=-\frac{56}{13}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdisplaystyle%20y%3D-%5Cfrac%7B56%7D%7B13%7D%7D)
Hey there, again! :D
Since the angle measuring 38 degrees is adjacent to m<1, it will equal 180 degrees.
180-38= 142
m<1= 142 degrees
I hope this helps!
~kaikers
True… irrational numbers focus more around square roots that cant be simplified into a single number, or symbols like pi. while not all rational numbers are whole, an irrational number can never be whole.
Answer:
ans is 16°,40°and64°
let ratio be 2x,5xand 8x
Step-by-step explanation:
their sum=120°
2x+5x+8x=120
15x=120
x=120/15=8°
2x=2×8=16°
5x=5×8=40°
8x=8×8=64°