Math Help

[MrBossmanJr]

Well, this gets into proofs and definitions, but first let's cite the extreme value theorem. The extreme value theorem states that if a function is continuous on an interval that is closed, then the function must have or contain a minimum and a maximum on the interval. This can be written as f© <= f(x) <= f(d), where c is the lowest point and d is the highest point on the x-axis and f© and f(d) on the y-axis respectively.

You are stating that it has no minimum or maximum so it has to be a straight line from left to right based on the interval. Therefore all the values are equal and it means that the requirements of that statement, f© <= f(x) <= f(d), is met.

EDIT: So take straight line values that is 1. 1 is less than or equal to 1 which is less than or equal to 1. I think this is what you mean or wanted.

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And, why do the Pythagorean theorem?

You do the theorem because you have the x and y values of velocity or in this case speed. You want to find the two dimensional value of that object. This ties into mechanical physics. If an object is moving x with a certain amount of speed (2 ft/s) and y with a certain amount of speed (4 ft/s), then you know it isn't just going in one direction. Not just x or just y; it is moving in both directions at the same time. It's hard to come up with an example since I'm not a professor lol. For every second, it is moving 2 feet along the x-axis (right) and 4 feet along the y-axis (up). Can you see how it isn't moving just one direction at a time? You need to find where it is actually going and the pythagorean theorem helps you calculate that diagonal speed.

[MrBossmanJr]

Oh ya, I remembered a little bit more about physics. You can take each direction to be a vector. In this case, x and y will be i (with that line showing its a vector) and j (with that line showing its a vector) respectively. Then it's 2i + 4j. You want k (with that line showing its a vector). Therefore k = sqrt(i^2 + j^2). I would find videos that demonstrate this, but I'm trying to finish a project for my data structs and algo course. Sorry, this doesn't explain much. I think YouTube videos would benefit you more than my half-ass explanations.

[Giantzebra]

Oh ya, I remembered a little bit more about physics. You can take each direction to be a vector. In this case, x and y will be i (with that line showing its a vector) and j (with that line showing its a vector) respectively. Then it's 2i + 4j. You want k (with that line showing its a vector). Therefore k = sqrt(i^2 + j^2). I would find videos that demonstrate this, but I'm trying to finish a project for my data structs and algo course. Sorry, this doesn't explain much. I think YouTube videos would benefit you more than my half-ass explanations.

Thanks for your help