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DedPeter [7]
3 years ago
11

Please help me solving this problem.

Mathematics
1 answer:
Illusion [34]3 years ago
7 0

(a) The radius of the circle is the distance the wave travels since it first formed, so if <em>g(t)</em> is the radius of the circle at time <em>t</em>, then it changes at a rate according to

d<em>g</em>/d<em>t</em> = 60 cm/s

Integrate both sides with respect to <em>t</em> to solve for <em>g</em> :

∫ d<em>g</em>/d<em>t</em> d<em>t</em> = ∫ (60 cm/s) d<em>t</em>

<em>g(t)</em> = (60 cm/s) <em>t</em> + <em>C</em>

but <em>C</em> = 0 since the radius at <em>t</em> = 0 must be 0.

<em>g(t)</em> = (60 cm/s) <em>t</em>

<em />

(b) The area of any circle with radius <em>r</em> is <em>πr</em> ². So

<em>f(r)</em> = <em>πr</em> ²

(c) The composition of <em>f</em> with <em>g</em> represents the area of water encircled by the wave at time <em>t</em> :

<em>(f</em> o <em>g)(t)</em> = <em>f(g(t))</em> = <em>π</em> <em>g(t) </em>²

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