SOLUTION: a right triangle has one vertex on the graph of y = x^2 at (x,y),another at the origin, and the third on the positive y- axis at (0,y). express the area A of the triangle as a func

Algebra ->  Sequences-and-series -> SOLUTION: a right triangle has one vertex on the graph of y = x^2 at (x,y),another at the origin, and the third on the positive y- axis at (0,y). express the area A of the triangle as a func      Log On


   

Question 194333: a right triangle has one vertex on the graph of y = x^2 at (x,y),another at the origin, and the third on the positive y- axis at (0,y). express the area A of the triangle as a function of x. for what value of x will be the area of the triangle be equal to 30 square units?
please help me to solve!!!!
please i really don't know how to solve!!!
please.....help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's draw a picture:




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:






But remember, we let y=x%5E2. So replace "y" with x%5E2 to get





Now focusing on just the triangle, we get the following




So the base is "x" and the height is x%5E2


Now recall (or look up), the area of any triangle is A=%28bh%29%2F2



A=%28bh%29%2F2 Start with the given formula


A=%28x%2Ax%5E2%29%2F2 Plug in b=x and h=x%5E2


A=x%5E3%2F2 Multiply



So the area is A=x%5E3%2F2




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


A=x%5E3%2F2 Start with the given equation.


30=x%5E3%2F2 Plug in A=30


30%2A2=x%5E3 Multiply both sides by 2.


60=x%5E3 Multiply


x%5E3=60 Rearrange the equation


x=root%283%2C60%29 Take the cube root of both sides.


Approximate the right side with a calculator.


So the answer is approximately