Question 194333
First, let's draw a picture:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/step1-2.png">



Now since the point (x,y) is "x" units to the right and "y" units up, this means that the base of the triangle is "x" units long and the height is "y" units high. Now let's label the drawing:



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/step2-2.png">




But remember, we let {{{y=x^2}}}. So replace "y" with {{{x^2}}} to get



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/step3-1.png">



Now focusing on just the triangle, we get the following


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/step4.png">



So the base is "x" and the height is {{{x^2}}}



Now recall (or look up), the area of any triangle is {{{A=(bh)/2}}}




{{{A=(bh)/2}}} Start with the given formula 



{{{A=(x*x^2)/2}}} Plug in {{{b=x}}} and {{{h=x^2}}}



{{{A=x^3/2}}} Multiply




So the area is {{{A=x^3/2}}}





"for what value of x will be the area of the triangle be equal to 30 square units?"



{{{A=x^3/2}}} Start with the given equation.



{{{30=x^3/2}}} Plug in {{{A=30}}}



{{{30*2=x^3}}} Multiply both sides by 2.



{{{60=x^3}}} Multiply



{{{x^3=60}}} Rearrange the equation



{{{x=root(3,60)}}} Take the cube root of both sides.



*[Tex \LARGE x \approx 3.91487] Approximate the right side with a calculator.



So the answer is approximately *[Tex \LARGE x \approx 3.91487]