SOLUTION: A rectangle is inscribed in a circle of radius 6 (see the figure). Let P=(x,y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.
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-> SOLUTION: A rectangle is inscribed in a circle of radius 6 (see the figure). Let P=(x,y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.
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Question 1146559: A rectangle is inscribed in a circle of radius 6 (see the figure). Let P=(x,y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.
Answer the following questions.
(a) Express the area A of the rectangle as a function of x.
i got the answer 4x(squareroot(36-x^2)
b. Express the perimeter p of the rectangle as a function of x.
i got the answer 4(x+squareroot(36-x^2)
c. Graph A equalsA(x). For what value of x is A largest?
how do i graph it so i can get the answer.
Take your value for part (a) which is
We could take the derivative of that and set that derivative equal
to 0. However that would be very time-consuming. It would be much
easier to square both sides and find the value of x that maximizes
the value of the SQUARE of the area A, because if A² is the largest
it can be, then A is also the largest it can b.
We find the y value when x=3√3:
So the area is greatest when the inscribed rectangle is a square, when
the upper right hand corner is the point P(3√2, 3√2).
(The 0 value is when the area is least, when the rectangle degenerates
into just a line segment, whose area is 0 because its width is 0)
I think this is the graph your teacher wants. But if he/she wants
the graph of
,
then it is the graph below whose maximum point is (3√2, 72). To
plot it, you can only substitute values x=0 through 6.
Edwin
