An umbrella has 12 evenly spaced ribs. If viewed as a flat circle of radius 11 units,
1 answer:
Answer:
Area = 121pi/12
~= 31.66 sq units
Step-by-step explanation:
They are talking about looking at an umbrella like its a circle. The radius is 11 units. That is from the center to the edge.
Consecutive means "in a row" or "next to each other" The 12 "ribs" are the like skeleton structure in the umbrella. But they cut the umbrella into 12 areas. They are asking for the area of one "slice". It is 1/12 of the area of the whole circle.
Area of a circle is
A = pi × r^2
Area of one slice is 1/12 of the whole.
A(1 slice)
= 1/12× pi × r^2
See image.
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then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,
(b) The velocity after 3 seconds is
(c) The particle is at rest when its velocity is zero:
(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:
In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,
By definition of absolute value, we have
In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as
and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to