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Related Rates Project

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by

Megan Makela

on 26 October 2012

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Transcript of Related Rates Project

Related Rates...
with a Whovian. A New Companion? Problem Number One has been cleverly disguised with an explosion, except not really. Let's make this look a bit more like math... Here's Problem Number Two, which has no explosions. Gross. Math. Not really, but still. Look! Katelyn and Megan did math. And I think it may even be correct. I hope so, actually. After the departure and death of Amy and Rory Pond, (Well, Williams. But that's for a different discussion.) The Doctor has been in need of a new companion. Luckily, he has found a lovely calculus teacher, Thetford. Convinced her students are moving successfully through the lesson on related rates, she agrees to travel along for a bit, as long as she returns in time for the next test. On their journey through out various points in time and space, the Doctor and Thetford encounter some Daleks. Epic action and adventure ensues, leading up to a few particularly awesome things, including explosions. You have:
A=πr^2
C=2πr
dr/dt = 25ft/s^2
C=100πft
What fun! This time, we happen to be explosion and action-packed adventure free. So sad. Instead of explosions, we have sno-cones. Before returning to THE BEST CALCULUS CLASS EVER, Thetford and the Doctor get a sno-cone. Good thing we aren't going to do a problem for that. You have:
dx/dt= 2.4 ft/s
h1=8 ft
h2=5 ft If a Dalek explodes in a circular pattern, and the radius of the explosion is increasing at 25 feet per second, how fast is the area the shrapnel covers increasing when the circumference is 100π feet? C=2πr
100π= 2πr
r=50ft A=πr^2
dA/dt=2πr dr/dt
dA/dt=2π(50)(25)
dA/dt=2500πft/s^2 Well, that was fun. Obviously the best kind
of related rates. EXTERMINATE
EXTERMINATE 5/8=x/x+y
5x + 5y = 8x
5y = 3x
5dy/dt = 3dx/dt
5dy/dt = 3(2.4)
dy/dt = 1.44 ft/s dx/dt + dy/dt = tip of shadow
2.4 + 1.44
3.84 ft/s As the TARDIS dematerializes and the Doctor says farewell, it emits a light. If the TARDIS is 8 feet tall, and Thetford is 5 feet tall, how fast is the tip of her shadow changing when Thety is walking away from the dematerializing TARDIS at a rate of 2.4 feet per second? 8 5 x y
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