Mathematics Question Thread

[RuiAce]

34i) you could probably get away with by just subbing x=1 into both equations and checking that in both cases y=3

[Wales]

34i) you could probably get away with by just subbing x=1 into both equations and checking that in both cases y=3

True. I found the coordinates rather then proved it. Both works but yours is more efficient

[RuiAce]

Although, important thing in what I said was to sub in ONLY x=1.

Some people will sub in both together and check that it works. This is not acceptable.

[_____]

Going through GAD so I've got a few things to clear up.

1. Are the only possible conditions for a point of inflexion y'' = 0 and y'' changes sign at the point OR y' = 0 and y' does not change sign at the point? If I'm told to find points of inflexion should I typically be trying the y'' condition first?

2. I had one of those questions where a diagram is shown and you have to find the maximum value of the area by changing x. In this question we're told to show that A = 2x(200-x^2)^(1/2) for a rectangle. No problem with that. But to find the value of x, there's a hint that you should differentiate A^2 instead which kind of makes sense as differentiating 2x(200-x^2)^(1/2) is difficult. What does not make sense to me is that I was able to differentiate A^2 and find the value of x for which A is maximum without having to do anything to the final output which was x = 10. Why does squaring the entire equation not change the required value of x in this situation? I would have thought that I'd have to find x^(1/2) to ensure it is converted back since I changed A into A^2. Let me know if I need to explain this better.

3. Question I can't do:

A cylinder of radius r cm and height h cm is inscribed in a cone with base radius 3 cm and height 10 cm. By using similar triangles, show that the height of the cylinder is h = 10 - (10/3)r.

I can't work out how to express the relationship between h/r and 10/3 and change it into that expression. Let me know if you need the diagram scanned.

Thanks!

[RuiAce]

Going through GAD so I've got a few things to clear up.

1. Are the only possible conditions for a point of inflexion y'' = 0 and y'' changes sign at the point OR y' = 0 and y' does not change sign at the point? If I'm told to find points of inflexion should I typically be trying the y'' condition first?

2. I had one of those questions where a diagram is shown and you have to find the maximum value of the area by changing x. In this question we're told to show that A = 2x(200-x^2)^(1/2) for a rectangle. No problem with that. But to find the value of x, there's a hint that you should differentiate A^2 instead which kind of makes sense as differentiating 2x(200-x^2)^(1/2) is difficult. What does not make sense to me is that I was able to differentiate A^2 and find the value of x for which A is maximum without having to do anything to the final output which was x = 10. Why does squaring the entire equation not change the required value of x in this situation? I would have thought that I'd have to find x^(1/2) to ensure it is converted back since I changed A into A^2. Let me know if I need to explain this better.

3. Question I can't do:

A cylinder of radius r cm and height h cm is inscribed in a cone with base radius 3 cm and height 10 cm. By using similar triangles, show that the height of the cylinder is h = 10 - (10/3)r.

I can't work out how to express the relationship between h/r and 10/3 and change it into that expression. Let me know if you need the diagram scanned.

Thanks!

1. Yes. Because we know that possible points of inflexion ONLY occur when y" = 0. That's literally the definition.

y' = 0 only gives you a stationary point. Therefore it does not necessarily cover all points of inflextion. Note that not every point need be a horizontal point of inflexion
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This can also be represented graphically.
As an exercise, you may wish to sketch the cubic y=f(x), where f(x) = (x-1)(x-2)(x-4)+10 on graphing software
and also sketch y=[f(x)]², and then compare the x-coordinates of the stationary points.

[RuiAce]

[Wales]

(Image removed from quote.)

You have a whiteboard on demand for answering questions.

Nice.

Also, how much of a pain is it to code your responses the way you do? It's so much cleaner.

[jamonwindeyer]

You have a whiteboard on demand for answering questions.
Nice.
Also, how much of a pain is it to code your responses the way you do? It's so much cleaner.

It's called LaTex! It's not super hard to learn, a little bit of a learning curve but you'll pick it up fast, Rui wrote a guide on it here!

[Wales]

It's called LaTex! It's not super hard to learn, a little bit of a learning curve but you'll pick it up fast, Rui wrote a guide on it here!

I'll take a look Awesome.

[RuiAce]

My whiteboard was a birthday present lol

[jamonwindeyer]

My whiteboard was a birthday present lol

I have at least half a dozen whiteboards scattered around for tutoring

[K9810]

Hey!
How can I solve for the points of intersection between y=x^2 and y=e^x
If I let x^2=e^x, how do I solve for x?

[jamonwindeyer]

Hey!
How can I solve for the points of intersection between y=x^2 and y=e^x
If I let x^2=e^x, how do I solve for x?

Hey! There's no easy way to find points of intersection in that case (even I personally don't know the Maths behind it) - Perhaps the question would suit an approximation obtained by guess and check?

[K9810]

Hey! There's no easy way to find points of intersection in that case (even I personally don't know the Maths behind it) - Perhaps the question would suit an approximation obtained by guess and check?

The question was to find the area between the curves, I guess I should solve the points of intersection graphically?

[jakesilove]

The question was to find the area between the curves, I guess I should solve the points of intersection graphically?

I like don't think there are two points of intersection. Are you sure that you've interpreted the question correctly?