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Translation into Mathematical Expressions 2538 Views


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Rigging your friend's scale so it looks like she's shedding the pounds: being a good friend, or being a total creeper? Translate a word problem into mathematical expressions and find out for yourself. (Our take: don't try this on any of your friends at home.)

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Transcript

00:04

Translation into Mathematical Expressions, a la Shmoop.

00:09

Slash McFender, lead guitarist for the band Vibradeath is on his way to headline a concert.

00:15

Only one tiny problem...he forgot his guitar at home.

00:19

Thankfully, he has a thick jungle of chest hair which he can pluck to play some tunes.

00:28

Suppose that the frequency of vibration of Slash's chest hair is inversely proportional

00:34

to the hair's length. If one of Slash's hairs is 0.7 inches long

00:43

and vibrates at 5 Hertz... ...what frequency, in Hertz, would a 0.5 inch

00:49

long chest hair have? We start by calling the frequency F and the

00:54

length of the chest hair L. The problem tells us that the formula for

00:59

the frequency of F is one over L. So F equals K over L, where K is the constant

01:07

of proportionality.

01:09

To find K, we can plug in what we know... ...Frequency is equal to 5 in this instance

01:17

and our length is 0.7. By multiplying both sides by 0.7...

01:28

...we see that K equals 3.5. So, plugging this new value into our formula...

01:41

... the frequency F of a 0.5 inch long chest hair must be...

01:51

...7 Hertz. The bad news is that Slash loves Vibradeath's

01:56

new sound so much that he has asked his bandmates to start going shirtless as well.

02:05

He's really redefining the term "hair band."

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