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

Interpreting equations graphically (example 2) | Mathematics III | High School Math | Khan Academy


2m read
·Nov 11, 2024

Let F of T be ( e^{2T} - 2T^2 ) and H of T be ( 4 - 5T^2 ). The graphs of Y = F(T) and Y = H(T) are shown below. So, Y = F(T) is here in green, so this is really ( Y = e^{2T} - 2T^2 ). We see F(T) right over there, and Y = H(T) is shown in yellow.

Alright, now below that they say which of the following appear to be solutions of ( e^{2T} - 2T^2 = 4 - 5T^2 )? Select all that apply, and I encourage you to pause the video and try to think about it.

Now, the key here is to realize that ( e^{2T} - 2T^2 ) that was F(T) and ( 4 - 5T^2 ) is H(T). So another way of thinking about it: select all of the T's for which F(T) is equal to H(T). So all of the T's where F(T) is equal to H(T, well that's going to happen at the points of intersection.

For example, at T1, we see at this point right here T1, ( Y1 ). So this tells us ( F(T1) = H(T1) ), which is equal to ( Y1 ). So F(T) is going to be equal to H(T) at T = T1, and we see that there because it's a point of intersection.

Now let's keep on going. Well, they have another point of intersection right over here at T4, T4, ( Y4 ). If you took F(T4), you're going to get ( Y4 ), or if you take H(T4), you're going to get ( Y4 ). So ( F(T4) = H(T4) ).

Thus, ( F(T4) = H(T4) ). If you took ( e^{2 \cdot T4} - 2T4^2 ), that is going to be equal to ( 4 - 5 \cdot T4^2 ). So ( T4 ), since it satisfies both F(T) and H(T), equals each other when T is equal to T4.

These two things are going to equal each other when T is equal to T4, and those are the only ones that are at a point of intersection. I think we are done. Check my answer, and got it right.

More Articles

View All
Everest Glaciology - Truth is in the Ice | National Geographic
The very idea that the highest part of the planet has been impacted by human activity ought to be a real wake-up call for everybody. We’re working close to the top of Everest. No other scientists work. The big goal of this National Geographic project is t…
Your Sneakers Are Part of the Plastic Problem | National Geographic
(chill music) [Narrator] You can tell a lot about a person based on their shoes. And today, there’s a ton of options. In 2018, footwear was a $250 billion industry, with over 24 million shoes produced globally. Just look at Kanye. His shoe and apparel lin…
Substitution and income effects and the Law of Demand
In other videos, we have already talked about the law of demand, which tells us—and this is probably already somewhat intuitive for you—that if a certain good is currently at a higher price, then the quantity demanded will be quite low. As the price were…
Swap The Vice President #shorts #new
Is Biden going to be the nominee or not? I believe he will be. The only chance to change the ticket to make it stronger to the Independents is to swap out Harris, the Vice President, who is probably the most unpopular Vice President in history. Can’t it …
15 of the Worst Life Decisions Anyone Can Make
What is rock bottom, really? Perhaps it’s sitting outside alone in the dark. You’re broke, no friends or family to call, feeling mentally and physically sick. Your addiction, calling your name with no end in sight, sounds pretty rock bottom. But how does …
Artificial selection and domestication | Natural selection | AP Biology | Khan Academy
Most of us are familiar with dogs, oftentimes known as man’s best friend. What’s fascinating about them is that they are one species, even though different types of dogs, different breeds, could look very, very different. The fact that they’re one species…