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

Analyzing relationships between variables using tables and equations | 6th grade | Khan Academy


2m read
·Nov 10, 2024

We're told Rava is researching an electric car. She finds this graph which shows how much range, measured in kilometers, the car gains based on charging time. All right, and they say first fill in the missing values in the table below. If you are so inspired, pause this video and see if you can have a go at that as well.

All right, well, they give us a few points, and I'm assuming these are points on a line. We can see when the charging time is 15 minutes, the range is 180. So we can see when the charging time is 15 minutes, the range is 180. We can see when the charging time is 30 minutes, the range is 360 km. So I could write that there.

Then we see when the charging time is 45 minutes, the range is 540 km. So that's all nice, but then they give us a few other points here. They say what happens when we are at T = 10 or T = 1, which aren't easy to pick out here. But this is where it might be useful if we assume that this is a line. What is the relationship between these?

So let's see. To go from 15 to 180, it looks like you're multiplying by 12. To go from 30 to 360, it looks like we're multiplying by 12. To go from 45 to 540, it looks like we are multiplying by 12. So assuming K is just going to be 12 * T, we know that when T equals 1, K is 12, and when T equals 10, 10 * 12 is 120.

All right, now the second part they say write an equation Rava can use to find out how much charging time T it takes to gain any number of kilometers in range K. All right, well, we already established a relationship. We said that K is equal to 12 times whatever T is; that's what we just established in this table up here.

But that's not what they want. They want to find out how much charging time T it takes to gain any number of kilometers in range K. So what we need to do here is solve for T. So let's divide both sides by 12 to just have T by itself on the right-hand side, and we are going to be left with T is equal to K over 12.

T is equal to K over 12, and notice you could put any number of kilometers of range in here, and you're essentially just going to divide it by 12, and that will give you how much charging time. I guess this would assume an infinitely large battery, which we know doesn't exist, but for the sake of this problem here, we have it. Here is the equation Rava can use.

More Articles

View All
What kind of levers does the Speaker have? | US Government and Civics | Khan Academy
What kind of levers does the Speaker have in relation to the other House representatives? The Speaker has all kinds of levers, both formal and informal. In fact, a lot of them are informal. The Speaker can name a lot of people to the committees, particul…
Is Credit Suisse Triggering another 2008 Stock Market Crash?
I don’t know if you guys use Twitter to Snapchat with what’s going on in the finance world, but I probably checked Twitter maybe two or three times a day. Over the past week, one thing that’s been catching my attention is the amount of people talking abou…
Space Mountain Fears - Smarter Every Day 12
Intro music Hey. It’s Disney World, and it’s magic hours, which means nobody is here, so we get to ride everything. But we’ve always had this fear of Space Mountain; that if you put your arms up, you’ll get ‘em chopped off. So we got this trick we do, sh…
The Physics of Lightsabers | StarTalk
[Applause] Star Talk, we’re back featuring my interview with the British physicist Brian Cox. So I had to bring up the fact that he and I had, like, a Twitter argument over the physics of lightsabers. Aha, yeah! And I just had to bring it up and just ope…
Living Up Close and Personal With an Active Volcano | National Geographic
It matters that there’s a volcano. It matters. It matters a lot because that’s, um, 75% of the identity of this place. The volcano is present; the volcano is breathing. The, uh, the volcano really is a living creature. It’s a bit of a romantic representa…
How to Surface a Submarine in the Arctic Ocean - Smarter Every Day 260
[Man] Seven zero, six up, point four up. Standby for impact! - Welcome back to Smarter Every Day. I’ve made a really long journey to an ice floe in the Arctic Ocean to board the USS Toledo, a U.S. Navy fast attack nuclear submarine, which has punched its …