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CALC BC #1

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There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

Create your own at Storyboard That

There are many vehicles coming into the toll plaza..

They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.

They made a bet to see how many cars would come through the toll per hour.

Then he proved that he was not a moron, but then Raj asked another question...

Rambo clarifies his misunderstanding, but then Raj notices something...

Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.

I think there will be about 376 cars per hour

Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))


What are we gonna do?!!

The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).

I think you're a moron

Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.

I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?

No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing

Oh! I missed that. OMG there is a line forming where at any time "t", there arecars in the line. What will the max amount of cars be?

Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.

Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!

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Storyboard Text

  • Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))What are we gonna do?!!
  • The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).
  • I think you're a moron
  • I think there will be about 376 cars per hour
  • There are many vehicles coming into the toll plaza..
  • Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.
  • I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?
  • They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.
  • No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing
  • Oh! I missed that. OMG there is a line forming where at any time t, there arecars in the line. What will the max amount of cars be?
  • They made a bet to see how many cars would come through the toll per hour.
  • Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.
  • Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!
  • Then he proved that he was not a moron, but then Raj asked another question...
  • Rambo clarifies his misunderstanding, but then Raj notices something...
  • Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.
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