1.5p+3p+2.5p= total amount
There some cube root if you need those
Answer: It would equal 359.
Step-by-step explanation:
1. Set up your division table
2. start by deviding 57 by 16
3. subtract the total amount of times it goes into 57
4. pull down the next number and add zeros if you need too
5. repeat until you get your complete number which in this case would be 359
(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.
Answer:
130 grams
Step-by-step explanation:
1:13
10:130