Answer:
15-9
Step-by-step explanation:
[ - 6 * x^2 * y^8 + 12* x * y^3 - 36 * x * y^2 ] / [6*x*y^2] =
[-6x^2 y^8 ] / [6xy^2] + [12x y^3] / [6xy^2] - [36xy^2] / [6xy^2] =
- xy^6 + 2y - 6
Answer: - xy^6 + 2y - 6
Answer:
25 can.
Step-by-step explanation:
Here is the complete question: You are making juice from concentrate. The directions on the packaging say to mix 1 can of juice with 3 cans of water to make orange juice. How many 12 fluid ounces cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
Given: Ratio to make juice with concentrate:water is 1:3.
As required we need to prepare 200 6 ounce serving of Orange juice.
∴ ![200\times 6= 1200\ ounce](https://tex.z-dn.net/?f=200%5Ctimes%206%3D%201200%5C%20ounce)
Let there be x ounce of concentrate and 3x ounce of water to make 1200 ounce of orange juice.
Now, ![x+3x= 1200](https://tex.z-dn.net/?f=x%2B3x%3D%201200)
∴ x= 300 ounce
Next, lets find out how many cans of 12 ounce is required.
![\frac{300}{12} = 25\ cans](https://tex.z-dn.net/?f=%5Cfrac%7B300%7D%7B12%7D%20%3D%2025%5C%20cans)
∴ 25 cans is required to make 1200 ounce of orange juice.
Answer:
![y=-\frac{1}{4}(x-2)^{2}+9](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%2B9)
Step-by-step explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at
.
Directrix of the parabola is
.
Let
be any point on the parabola. Then, from the definition of a parabola,
Distance of
from focus = Distance of
from directrix.
Therefore,
![\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2%29%5E%7B2%7D%2B%28y-8%29%5E%7B2%7D%7D%3D%7Cy-10%7C)
Squaring both sides, we get
![(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9](https://tex.z-dn.net/?f=%28x-2%29%5E%7B2%7D%2B%28y-8%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D-%28y-8%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%2By-8%29%28y-10-%28y-8%29%29...............%5B%5Cbecause%20a%5E%7B2%7D-b%5E%7B2%7D%3D%28a%2Bb%29%28a-b%29%5D%5C%5C%28x-2%29%5E%7B2%7D%3D%282y-18%29%28y-10-y%2B8%29%5C%5C%28x-2%29%5E%7B2%7D%3D2%28y-9%29%28-2%29%5C%5C%28x-2%29%5E%7B2%7D%3D-4%28y-9%29%5C%5Cy-9%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%5C%5Cy%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%2B9)
Hence, the equation of the parabola is
.