The exterior angle is equal to the sum of the other 2 interior angles
so ACD=19+121=140 degrees
Answer:
780
Step-by-step explanation:
779.7 rounds up to 780 because the decimal is above .5
The answer to this question is 20 seconds because there are 480 seconds in 8 minutes
(a)The amount of people that went on the escalator is given by the integral
![\displaystyle \int_0^{300} r(t)\, dt =270](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cint_0%5E%7B300%7D%20r%28t%29%5C%2C%20dt%20%3D270)
270 people enter the elevator <span>during the time interval 0 ≤ t ≤ 300
</span>You can save time by just writing that and getting an answer from your calculator. You are not expected to write out the entire integrand. Since this is for 0 ≤ t ≤ 300, you would be typing this integral into your calculator
![\displaystyle\int_0^{300} 44 \left( \frac{t}{100} \right)^3 \left(1 - \frac{t}{300} \right)^7](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B300%7D%2044%20%5Cleft%28%20%5Cfrac%7Bt%7D%7B100%7D%20%5Cright%29%5E3%20%5Cleft%281%20-%20%5Cfrac%7Bt%7D%7B300%7D%20%5Cright%29%5E7)
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(b)
![\displaystyle 20 + \int_0^{300} \big[ r(t) - 0.7\big] dt = 80](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A20%20%2B%20%5Cint_0%5E%7B300%7D%20%5Cbig%5B%20r%28t%29%20-%200.7%5Cbig%5D%20dt%20%3D%2080)
There are 80 people at time t = 300
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(c)Since there are 80 people at time t = 300 and r(t) = 0 for t > 300, the rate of people in line is only determined constant exiting rate of <span>0.7 person per second. The amount of people in line is linear for t > 300.
![80 + \int_0^t (0.7) \,dx = 0 \\ 80 + 0.7t = 0 \\ t \approx 114.286](https://tex.z-dn.net/?f=80%20%2B%20%5Cint_0%5Et%20%280.7%29%20%5C%2Cdx%20%3D%200%20%5C%5C%0A80%20%2B%200.7t%20%3D%200%20%5C%5C%0At%20%5Capprox%20114.286)
This is for t > 300, so
The first time t is approximately t = </span><span>414.286</span>
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(d)The absolute minimum will occur at a critical point where r(t) - 0.7 = 0 or at an endpoint.
By graphing calculator,
![r(t) - 0.7 = 0 \implies t \approx 33.013, 166.575](https://tex.z-dn.net/?f=r%28t%29%20-%200.7%20%3D%200%20%5Cimplies%20t%20%5Capprox%2033.013%2C%20166.575)
If
![P(t) = 20 + \int_0^t \left[ r(x) - 0.7 \right] dx](https://tex.z-dn.net/?f=%20P%28t%29%20%3D%2020%20%2B%20%5Cint_0%5Et%20%5Cleft%5B%20r%28x%29%20-%200.7%20%5Cright%5D%20dx)
represents the amount of people in line for 0 ≤ t ≤ 300, then
P(0) = 20 people (given)
P(33.013) ≈ 3.803
P(166.575) ≈ 166.575
P(300) = 80
Therefore, at t = 33.013, the number of people in line is a minimum with 4 people.