Question

The sales $S$ (in thousands of units) of a seasonal product are given by the model $S=74.50+43.75 \sin \frac{\pi t}{6}$ where $t$ is the time in months, with $t=1$ corresponding to January. Find the average sales for each time period. (a) The first quarter $(0 \leq t \leq 3)$ (b) The second quarter $(3 \leq t \leq 6)$ (c) The entire year $(0 \leq t \leq 12)$ 

          The sales $S$ (in thousands of units) of a seasonal product are given by the model
$S=74.50+43.75 \sin \frac{\pi t}{6}$
where $t$ is the time in months, with $t=1$ corresponding to January. Find the average sales for each time period.
(a) The first quarter $(0 \leq t \leq 3)$
(b) The second quarter $(3 \leq t \leq 6)$
(c) The entire year $(0 \leq t \leq 12)$
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Added by Brandy C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The sales $S$ (in thousands of units) of a seasonal product are given by the model $S=74.50+43.75 \sin \frac{\pi t}{6}$ where $t$ is the time in months, with $t=1$ corresponding to January. Find the average sales for each time period. (a) The first quarter $(0 \leq t \leq 3)$ (b) The second quarter $(3 \leq t \leq 6)$ (c) The entire year $(0 \leq t \leq 12)$
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Transcript

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00:01 So we're given this sales model, and we want to find the average sales for each time period.
00:06 So the average value equation is given by 1 over b minus a times the integral from a to b of f of x, dx.
00:18 So in this case, for the first period, or for the first quarter, that's going to be 1 over 3 minus 0, since those are the b and a values respectively, times the integral from 0 to 3, of 3, of, of s of t d t and we're going to do this in calculator then for part b it's one over six minus three times the integral from three to six of s of t d t and lastly we're going to have one over 12 minus zero times the integral from zero to 12 of s of t d t so first we want to define what our s of t function is and that is 74 .50 plus 43 .75 times sine of pi t over 6 and make sure that you have this in radiance mode.
01:16 Then if we consider our integrals here, we have 1 over 3 times the integral from 0 to 3 of s of t...
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