PLEASE EXPLAIN 1a.) A right triangle has one vertex on the graph of y = 7 - x2,

Question

PLEASE EXPLAIN

1a.) A right triangle has one vertex on the graph of y = 7 - x2, x > 0, at (x, y), another at the origin, and the third on the positive x-axis at (x, 0). Express the area A of the triangle as a function of x.

A(x)=

1b.)Two cars leave an intersection at the same time. One is headed south at a constant speed of 24 miles per hour, the other is headed west at a constant speed of 70 miles per hour. Express the distance d between the cars as a function of the time t. (Hint: At t = 0 the cars leave the intersection.)

D(t)=

Explanation / Answer

We know that the point (x,y) is on the line y = 9 - x^2, but we want everything in terms of x so replace y with 9 - x2 so the point now becomes (x, 7 - x^2). This point lies directly over the point (x, 0) and the distance between them represents the height of the triangle. Therefore the height of the triangle is 7 - x^2. The length of the base is the distance from the origin (0, 0) to the point (x, 0) and this distance is x.

So we know:

height = - x2
base = x

Area of triangle = 1/2*b*h

So the answer would be:

1/2(x)(7 - x2)

If you want in quadratic form multiply through the x

(7/2)x - x^2

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.