Question

The hypotenuse of a right triangle has one end at the origin and one end on the curve
y = 10^1/10

Picture:
http://www.webassign.net/userimages/Models006.JPG?db=v4net&id=155909

Express the area of the triangle as a function of x.

A(x)=?

I'm not exactly sure how to proceed with this question. Any help is appreciated!

Answer 1

y = 10^1/10 ?

Answer 2

That should probably be a function of x, huh?

Answer 3

first of all lets write a point P on the graph where the triangle intersect curve
\[P(x,y)\rightarrow P(x,f(x))\]
now thee area
\[A(x)=b*h\]
base =x and the height is y or f(x)
\[A(x)=x.f(x)\]
but \[f(x)=10^{1/10}=\sqrt[10 ]{10}\]
so\[A(x)=xf(x)=x(10^{1/10})\]