yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Periodicity of algebraic models | Mathematics III | High School Math | Khan Academy


3m read
·Nov 11, 2024

We're told Divya is seated on a Ferris wheel at time T equals zero. The graph below shows her height H in meters T seconds after the ride starts. So at time equals zero, she looks like about two. What is this? This would be one and a half, so it looks like she's about two meters off the ground.

Then as time increases, she gets as high as it looks like this is close to 30, maybe 34 meters, and then she comes back down to looks like two meters and up to be 34 meters again. So let's read the question. The question asks us approximately how long does it take Divya to complete one revolution on the Ferris wheel?

Alright, so this is interesting. This is when she's at the bottom of the Ferris wheel. So then she gets to the top of the Ferris wheel, and then she keeps rotating until she gets back to the bottom of the Ferris wheel again. So it took her 60 seconds, and T is in terms of seconds. So it took her 60 seconds to go from the bottom to the bottom again. Another 60 seconds, she would have completed another revolution.

And so let me fill that in. It is going to take her 60 seconds, 60 seconds. And we, of course, can check our answer if we like. Let's do another one of these.

So here we have a doctor who observes the electrical activity of Finn's heart over a period of time. The electrical activity of Finn's heart is cyclical, as we hope it would be, and it peaks every 0.9 seconds. Which of the following graphs could model a situation if T stands for time in seconds and E stands for the electrical activity of Finn's heart in volts?

Well, over here looks like we peaked at zero seconds, and then here we're peaking a little bit more than one. This looks like maybe at 1.1, now maybe at 2.2 and 3.3. This looks like it's peaking a little bit more than every one second, so like maybe every 1.1 seconds, not every 0.9 seconds. So I'd rule out A.

This one is peaking; it looks like the interval between peaks is less than a second, but it looks like a good business in a second. So it looks like maybe every three-quarters of a second or maybe every four-fifths of a second, not quite nine-tenths. This first peak would be a little bit closer to one, but this one is close.

Choice C is looking good. The first peak is at zero, then the first peak; this looks pretty close to one, was less than one. It looks like a tenth less than one, so I like choice C. Now choice D looks like we're peaking every half second, so it's definitely not bad.

So this looks like a peak every 0.9 seconds. This is the best representation that I can think of, and you can actually verify that you have a peak every 0.9 seconds. You're gonna have four peaks in 3.6 seconds. So one, two, three, four. This is it; this looks like it's at 3.6. Over here, you have one, two, three, four. You've had four peaks in less than three seconds, so this definitely one—this one definitely isn't 0.9.

So instead of just forcing yourself to eyeball just between this peak and that peak, you can say, well, if for every 0.9 seconds, how long would three peaks take or four peaks? Then you can actually be a little bit more precise as you try to eyeball it. So we can check our answer and verify that we got it right.

More Articles

View All
Human population dynamics| Human populations| AP Environmental Science| Khan Academy
What we have here is a really interesting visual that shows world population growth from 1750 all the way to 2100. Obviously, this isn’t 2100 yet, so it’s doing some projecting for roughly the next 80 years. It also shows the absolute world population ove…
Marcus Aurelius' Advice For Better Days
At dawn, when you have trouble getting out of bed, tell yourself, “I have to go to work as a human being. What do I have to complain of if I’m going to do what I was born for? The things I was brought into this world to do.” Or is this what I was created…
Why is the tech industry in the SF Bay Area?
Is there a specific reason, or was there specific events that occurred which has created this strength or grip that the Bay Area has when it comes to technology? I don’t think it is a path dependent history. In other words, I don’t think that Silicon Vall…
Can Sharks Detect Magnetic Fields? | Sharkcano
[music playing] NARRATOR: In Bimini, Bahamas, a team of experts are hoping to entice a couple sharks for an experiment and get more than they bargained for. [music playing] They’re testing if sharks can detect magnetic fields. The answer could unlock a…
Samurai Sword - Linked | Explorer
NARRATOR: See this? This is a samurai, an elite Japanese warrior. And this is his sword, his samurai sword. Watch out! It’s super sharp. They’ve been around for over 1,000 years, as iconic to Japanese culture as cherry trees or Mt. Fuji. And thanks to, o…
Perfect Muzzle Flash Photos - Smarter Every Day 43
Hey, it’s me Destin. Welcome back to Smarter Every Day. So, ah, first things first, let me show you that this weapon is unloaded. And I really like to think about firearms because there’s a lot of science involved here. What causes muzzle flash? Alright…