Answer to Question #4134 in Abstract Algebra for robin
A ﬂexible wire P QRS, of total length 12 metres, is bent into a three-edged
planar shape, and its ends P, S are placed against a disc of
radius 9 metres with centre O, as shown in the diagram below. (The arc
P S is not part of the wire.) The end-segments P Q and RS of the wire lie
along straight lines through O, while the arc QR forms part of a circle
with centre O and subtends an angle x (in radians) at O.
This question concerns the area A enclosed between the wire and the edge
of the disc, which is shown shaded below. This area can be expressed by
A = f(x), where
f(x)=9x(4 − 3x)(16 + 3x) / 2(2+x)^2
0 ≤ x ≤4/3
(a) (i) Plot the graph of the function f(x). Your graph should cover the
interval [0, 1.33] in the x-direction and [0, 20] in the y-direction.
(ii) By using the ‘Trace’ facility (and also, if you wish, the ‘Zoom’
facility), estimate to two decimal places the coordinates of the
point on this graph at which y = f(x) takes its maximum value.
(iii) On the same graph, plot the line y = 8. Using the ‘Trace’ facility,
estimate to two decimal places both solutions of the equation
f(x) = 8. (These solutions give the values of x for which the
shaded area is 8 m2
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Question #4134 from robin:
I would be interested to see the answer supplied to Robin for this question as I would like to see for my own benefit how the solution is extracted is this possible please.
Kind Regards, Michael Dickinson