(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.
Draw 4 squares. The perimeter is 10 because the width is 4 and the length is 1. So 4 x 2 is 8 and 1 x 2 is 2. And 8 + 2 = 10.
Answer:
True
Step-by-step explanation:
we know that
The opposite sides of a parallelogram are parallel and the length of their sides is equal.
step 1
<em>Find the slope of each side</em>
we know that
If two lines are parallel then their slopes are the same
The formula to calculate the slope between two points is equal to
we have
<em>one side</em>
Substitute the values
<em>opposite side</em>
Substitute the values
compare
m1=m2
therefore
both lines are parallel
step 2
Find the distance
the formula to calculate the distance between two points is equal to
we have
<em>one side</em>
Substitute the values
<em>opposite side</em>
Substitute the values
Compare
d1=d2
Both sides have the same length
so
1) Both lines are parallel
2) Both sides have the same length
therefore
The statement is True
One correct answer would be 4 rows of 8 stamps each.
It sounds like you're doing arrays. If you weren't given any options to choose from and you have to create this yourself, then you can use the answer I helped you with.
With arrays there are different examples you can create. The only rule you have to follow is that you have everything shared equally with each row, meaning each row of what you choose can have no more and no less than any other row.
Ex: (given above) 2 rows of 16
4 rows of 8
8 rows of 4
16 rows of 2