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sweav901
09.07.2019 •
Mathematics
Apebble is dropped into a calm pond, causing ripples in the form of concentric circles. the radius (in feet) of the outermost ripple is given by r(t) = 0.6t, where t is time (in seconds) after the pebble strikes the water. the area of the circle is given by a(r) = πr2. find (a ∘ r)(t).
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Ответ:
Solution-
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.
The radius of the outer ripple is given by r(t)= 0.6t,
where t is the time in seconds after the pebble strikes the water.
The area of the circle is given by the function![a(r) = \pi r^2](/tpl/images/0070/2072/58ae1.png)
(a ◦ r)(t) = a(r(t)) ( ∵ Using function composition / plugging in the second function into the first function)
⇒![a(r(t))=a[0.6t]=(\pi)(0.6t)^2=0.36 \pi t^2](/tpl/images/0070/2072/49590.png)
∴ This is the expression for area of circle of outermost ripple, at time t after the pebble strikes the water.
Ответ:
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Step-by-step explanation:
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