Trans Formula Help!

[yohanson77]

Hello,
Got this, just need a hand transposing it. I'm finding it hard with the two H's.

Q. The radius 'R', chord length 'W' and height 'H' of a circular arch is given by:

R= W^2/8H+ H/2

Determine the values for the height 'H' of arch with a radius R=12m and width W=8m.

In advance thank you

Yohanson

 

[morson]

Put R = 12, and W = 8:

\(\displaystyle 12 = \frac{8^2}{8H}\ + \frac{H}{2}\\)

\(\displaystyle 12 = \frac{8}{H}\ + \frac{H}{2}\\)

Now, multiplying both sides by 2H:

\(\displaystyle 24H = 16 + H^2\)

So you have a quadratic equation to solve. Use the quadratic formula.

 

[yohanson77]

Quadratic

Hi morson,

Thank you for your help.

Am I right that to say the quadratic will be:

H^2 - 24H + 16 = 0

I just thought they all had to have values? what value would H^2 have?

Thank you

 

[morson]

Re: Quadratic

Am I right that to say the quadratic will be:

H^2 - 24H + 16 = 0

Absolutely. Now, what value of H makes the left side of that equation 0? In fact, there are two values of H which satisfy that equation (which is why the question gives the plural 'values')

The solution to \(\displaystyle ax^2 + bx + c = 0\) is given by \(\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\) so long as a is not zero. In your case, you have a = 1, b = -24, c = 16.