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
Car insurance basics | Insurance | Financial Literacy | Khan Academy
So cars are something that usually involves some type of insurance. One, cars are a pretty expensive asset that many of us own. The other issue is cars are driving around pretty fast, and they can actually cause a lot of damage to property or to people. …
How Your Eyes Make Sense of the World | Decoder
When you look at this painting, what do you see? A woman looking out a window? How about now? This famous painting by Salvador Dali is based on something called the “Lincoln illusion.” The effect shows how blurring pixelated images can make it easier to r…
Valley of the Boom: Trailer #1 | National Geographic
That little A and At? See, that’s what I said. Mm-hm. Um, Katie said she thought it was “about.” Yeah. Oh. MAN: But I’d never heard it. KATIE COURIC: Or around or about. MAN: I’d never heard it said. I’d always seen the mark but never heard it said. Y…
Long run average total cost curve | APⓇ Microeconomics | Khan Academy
We’ve talked about the idea of average total cost in several videos so far, where it was the sum of your average variable cost and your average fixed cost. But when we’re talking about fixed costs, by definition, that means we’re talking about things in t…
Safari Live - Day 257 | National Geographic
This program features live coverage of an African safari and may include animal kills and carcasses. Viewer discretion is advised. Good afternoon and welcome to a sweltering, well, slightly warm Sabi Sands private game reserve in the beautiful South Afri…
What Basic Game Theory Teaches Us About Startups
They never get the lessons in little dabs along the way. Like, you know, as kids, we’re used to getting these little lessons along the way. For these zero-sum games, often the lesson just comes fast and hard at the end. It’s like, “Oh!” This is Michael Se…