Question

A right triangle has one vertex on the graph of y = x^8, x>0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x.​

Answer 1

Answer:

Area = $\frac{1}{2}x^{9}$

Step-by-step explanation:

From the graph attached,

Triangle given is a right triangle.

This triangle ha three vertices (0, y), (x, y) and (0, 0).

Therefore, measure of the base = x units

And measure of the height of the triangle = y units

Area of a triangle = $\frac{1}{2}(\text{Base})(\text{Height})$

                             = $\frac{1}{2}(x)(y)$

Since, y = $x^{8}$

Therefore, Area of the triangle = $\frac{1}{2}(x)(x)^8$

                                                   = $\frac{1}{2}x^{9}$  

Area of the given right triangle is $\frac{1}{2}x^{9}$ units².