Variation equation calculator - If X Proportion Y and X=4,Y=2 then Find Y when X=18. calculator

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Solution

Solution provided by AtoZmath.com

Here `x^2` = x^2 = x2 and 2x = 2*x

1. Find value of variation
You can enter the input like ...(use '?' for finding value of variation)

1. `x prop y` and `x=4` when `y=2`. Find `y` when `x=18`

2. `x prop 1/y^3` and `x=16` when `y=12`. Find `y` when `x=54`

3. `x prop y^3/z` and `x=8` when `y=4, z=3`. Find `x` when `y=6, z=4`

4. `x prop yz` and `x=8` when `y=4, z=3`. Find `x` when `y=6, z=4`

5. `x prop y^3z` and `x=8` when `y=4, z=3`. Find `x` when `y=6, z=4`

2. Prove results for given variation

1. If `x prop y` then prove that `x^3 + y^3 prop x^2y - xy^2`

2. If `x prop y` then prove that `x^2 + y^2 + xy prop x^2 - y^2`

3. If `x prop y`, `y prop z` then prove that `x^3 + y^3 + z^3 prop xyz`

4. If `5x - 7y prop 6x + 3y` then prove that `x prop y`

5. If `5x + 2y prop 3x - 7y` then prove that `x prop y`

6. If `9x - 3y prop 4x + 5y` then prove that `x prop y`

7. If `2x^2 - 3y^2 prop 4x^2 + 5y^2` then prove that `x prop y`

8. If `4x^3 + 5y^3 prop 2x^3 - 9y^3` then prove that `x prop y`

9. If `x^2 + 9y^2 prop xy` then prove that `x prop y`

10. If `4x^2 + 9y^2 prop xy` then prove that `x^2 + y^2 prop xy`

Example

1. `x prop y and x=4,y=2.` Find `x=18,y=?`

Solution:
`x prop y`

`=>x=K*y`

Now, `x=4,y=2`

`=>4 = K * 2`

`=> K = (4)/(2)`

`=> K = 2`

Hence, `x=2*y`

`x=18,y=?`

`=>18=2 * y`

`=> (18)/(2) = y`

`=>y=9`