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IrinaK [193]
3 years ago
15

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.​

Mathematics
1 answer:
bija089 [108]3 years ago
3 0

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.

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