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Direct Variation 2678 Views


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Description:

Direct variation helps to calculate exponential proportions and is an easy way to figure out relations. If Godzilla were chasing you, which car would you rather pick: the heavier or lighter one? Watch the video to find out.

Language:
English Language

Transcript

00:04

Direct Variation, a la Shmoop. Godzilla just attacked the Indianapolis Motor

00:10

Speedway. Looks like Dario Franchitti's going to have

00:14

to wait until next year to win his fourth Indy 500.

00:18

That is, if he hasn't been crushed by a mutant lizard foot before then.

00:26

So... it's time for the drivers to book it out of there.

00:31

Suppose that each car's top speed varies directly to the car's weight when it is squared.

00:40

For the rest of this problem, assume the following relationship: a car weighing 500 kilograms

00:46

would have a top speed of 200 kilometers per hour.

00:51

Dario drives a car that weighs 700 kilograms. That's 1,500 pounds...ish.

00:54

What's the top speed he can attain as he tries to flee from the monster?

01:00

Here are your choices: In this scenario, the heavier a car is, the

01:06

faster it can go. Hmm... maybe rocket fuel weighs a lot.

01:07

Since the top speed... "T"... varies directly with the weight of the car... "W"...

01:12

...the equation relating the two will be "T equals kW squared."

01:18

This is exactly what direct variation is -- a relationship between two variables in which

01:24

one changes in proportion to the other. The k snuck in there because the top speed

01:32

is related proportionally to the square of the weight, but not exactly.

01:41

In other words, the weight of the car is not exactly the square of the top speed...

01:45

...but the weight of the car squared increases at the same rate as the top speed.

01:51

Okay, so we're given two values... ...a top speed of 200 and a weight of 500.

01:57

When we plug them into our equation, we get 200 equals k times 500 squared, which equals

02:04

k times 250,000. When we divide both sides by 250,000, we are

02:10

left with k equals point-zero-zero-zero-eight. Now that we've got our "k," we can just plug

02:18

in the value for Dario's 700 kilogram car. T equals point-zero-zero-zero-eight times

02:25

700 squared, or... ...T equals 392 kilometers per hour.

02:34

We're going to hitch a ride with Answer D. That speed should be enough to get Dario to

02:38

safety. Godzilla is scary, but he's not exactly quick

02:42

on his feet.

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