Question

A drainage canal has a cross section in the shape of a parabola. Suppose that the canal is 10 feet deep and 20 feet wide at the top. If the water depth in the ditch is 5 feet, how wide is the surface of the water in the ditch?

Answer 1

The answer is "
`\bold{10√(2)}`".

Explanation:

Equation of the parabola:

`\to y=ax^2 \ \ \ \ \ \ \ \ \ _(where), (x,y) _(are) (10,10) \\\\\`

`\to 10=a(10)^2\\\\\to 10=100a\\\\\to a=(10)/(100)\\\\\to a= (1)/(10)\\`

if the value of a=
`(1)/(10)` then put the value into the equation:

`\to y=(x^2)/(10)\\\\`

when depth of water y=5

`\to 5=(x^2)/(10)\\\\\to x^2=50\\\\\to x=\pm√(50)\\\\`

So, width:

`\to 2√(50)=2√(25 * 2)\\`

`=2 √(5^2* 2)\\\\=2* 5 √(2)\\\\=10√(2)`