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P(-3, 0) Q(x, y) R(x, y) x dA 9-3x-2x² dx √√9-x²

P(-3, 0) Q(x, y) R(x, y) x dA 9-3x-2x² dx √√9-x²

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A circle whose equation is x2 + y2 = 9 has centre at (0,0) and radius equal to 3 . Triangle PQR is inscribed in circle; its vertices are at P (-3,0) , Q (x,y) and R (x,-y) , where Q and R are movable points located in first and fourth quadrants, respectively. All this information is represented in attached figure.
(a) For point Q, show that y = root(9 - x2)
(b) From the above, find an expression giving area of triangle PQR(A) as a function of x.
(c) Show that dA/dx = (refer to attached expression)

(d) From the above (or any alternative way), find y-coordinate of R such that A is MAXIMUM. 
 

P(-3, 0) Q(x, y) R(x, y) x
Transcribed Image Text:P(-3, 0) Q(x, y) R(x, y) x
dA 9-3x-2x² dx √√9-x²
Transcribed Image Text:dA 9-3x-2x² dx √√9-x²
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