The equation is Oy = 3/6x
Answer:
(-1,5)
Step-by-step explanation:
When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:
The coordinates of x and y are:
![(x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%5Cleft%28%5Cdfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%20%5Cdfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5Cright%29)
Given:
![A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3](https://tex.z-dn.net/?f=A%28x_1%2Cy_1%29%3D%28-7%2C%204%29%5C%5CB%28x_2%2Cy_2%29%3D%288%2C%209%29%5C%5CAP%3APB%3Dm%3An%3D2%3A3)
The coordinates of P is:
![(x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%5Cleft%28%5Cdfrac%7B2%2A8%2B3%2A-7%7D%7B2%2B3%7D%2C%20%5Cdfrac%7B2%2A9%2B3%2A4%7D%7B2%2B3%7D%5Cright%29%5C%5C%3D%5Cleft%28%5Cdfrac%7B-5%7D%7B5%7D%2C%20%5Cdfrac%7B25%7D%7B5%7D%5Cright%29%5C%5C%5C%5C%3D%28-1%2C5%29)
Answer:
h = 1.34 inches
Step-by-step explanation:
Given that,
The volume of cone, V = 3.6 cubic inches
Let the radius of cone is, r = 1.6 inches
We need to find the height of the cone. The formula for the volume of a cone is given by :
![V=\dfrac{1}{3}\pi r^2 h\\\\h=\dfrac{3V}{\pi r^2}\\\\h=\dfrac{3\times 3.6}{\pi \times 1.6^2}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%5C%5C%5C%5Ch%3D%5Cdfrac%7B3V%7D%7B%5Cpi%20r%5E2%7D%5C%5C%5C%5Ch%3D%5Cdfrac%7B3%5Ctimes%203.6%7D%7B%5Cpi%20%5Ctimes%201.6%5E2%7D)
h = 1.34 inches
So, the height of the cone is equal to 1.34 inches.
Answer:
w = - 16.06 or w = 2.06
Step-by-step explanation:
Given
w² + 14w - 33 = 0 ( add 33 to both sides )
w² + 14w = 33
To complete the square
add ( half the coefficient of the w- term )² to both sides
w² + 2(7)w + 49 = 33 + 49, that is
(w + 7)² = 82 ( take the square root of both sides )
w + 7 = ±
( subtract 7 from both sides )
w = - 7 ±
, that is
w = - 7 -
≈ - 16.06 or w = - 7 +
≈ 2.06