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zzz [600]
3 years ago
14

For two weeks, Mark recorded the color of the traffic light at the intersection of Acorn Street and Fifth Avenue as his bus appr

oached the intersection. He created this frequency table. How many times was the traffic light red?
Red: ?
Green: 6
Yellow: 2
Total: 15
Mathematics
1 answer:
rewona [7]3 years ago
6 0
Hey there!

If the total amount of times Mark recorded the color of the traffic light is 15, then the number of red lights he recorded would be 15 minus the amount of green and yellow lights. 

15 – 6 – 2 = 7

There was a total of 7 red lights recorded by Mark. 

Hope this helped you out! :-)
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Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

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b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles                    

First, we need to find b:    

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b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})

2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:  

0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}

\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h  

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

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