2.6 Question 9

[Eigenvalue]

Precalculus
Michael Sullivan
Edition 4
Chapter 2, Section 2.6

A rectangle is inscribed in a circle with radius 2. Let P= (x,y) be the point in quadrant I that is the vertex of the rectangle and is on the circle.

a) Express the area A of the rectangle as a function of x

b) Express the perimeter p of the rectangle as a function of x

c) Graph A=A(x); for what value of x is A the largest

d) Graph p=p(x); for what value of x is p the largest

See attachment

[Guest]

Hi its Bob

With P = (x, y) in quadrant I on the circle of radius 2, [tex]y = \sqrt{4 − x^2}[/tex]. The rectangle has width 2x and height 2y.

a [tex]A = (2x)(2y) = 4x \sqrt{4 − x^2}[/tex], for 0 < x < 2

b)[tex]P = 2(2x) + 2(2y) = 4x + 4 \sqrt{4 − x^2}[/tex]

[nycmath]

Precalculus
Michael Sullivan
Edition 4
Chapter 2, Section 2.6

A rectangle is inscribed in a circle with radius 2. Let P= (x,y) be the point in quadrant I that is the vertex of the rectangle and is on the circle.

a) Express the area A of the rectangle as a function of x

b) Express the perimeter p of the rectangle as a function of x

c) Graph A=A(x); for what value of x is A the largest

d) Graph p=p(x); for what value of x is p the largest

See attachment

NOTE:

MOVING FORWARD, PLEASE POST SULLIVAN'S HIGHLIGHTED QUESTIONS PER SECTION OR WE WILL NEVER COMPLETE THE COURSE.

[nycmath]

Hi its Bob

With P = (x, y) in quadrant I on the circle of radius 2, [tex]y = \sqrt{4 − x^2}[/tex]. The rectangle has width 2x and height 2y.

a [tex]A = (2x)(2y) = 4x \sqrt{4 − x^2}[/tex], for 0 < x < 2

b)[tex]P = 2(2x) + 2(2y) = 4x + 4 \sqrt{4 − x^2}[/tex]

Thank you for using LaTex.

[nycmath]

Part C

This is the graph of A(x) = 4x[tex]\sqrt{4-x^2}[/tex] on [0,2].
The graph is the located in Quadrant 1 from
x = 0 to x = 2. The largest x-value [tex]\approx[/tex] 1.41421.

[nycmath]

Part D

This is the graph for P(x) = 4x + 4[tex]\sqrt{4-x^2}[/tex].

The largest value of x [tex]\approx[/tex] 1.41421.