4U Maths Question Thread

[RuiAce]

Oops. I forgot how to do mental arithmetic. A positive answer also seems more legit

But yeah, in that case there's still a typo in that n+2 should be n+1

[beau77bro]

ok so does that fix it? omg yes my mate stresses so much about not being able to do his tutoring, im sure he appreciates this lots thanks rui!!!

[beau77bro]

I seriously can't get question 1a. I think they did something weird I can't see or work out. Thankyou.

[RuiAce]

(Image removed from quote.)

I seriously can't get question 1a. I think they did something weird I can't see or work out. Thankyou.

If there's no velocity surely that means there's no centripetal force, and thus the only two forces in play are the normal reaction and the gravity?

[beau77bro]

But there is still a frictional force or something, so u can't use components

[RuiAce]

But there is still a frictional force or something, so u can't use components

Where's the friction if you aren't moving?

[xboxer]

True

[beau77bro]

Where's the friction if you aren't moving?

the reaction force will push it away and down the slope - the friction up the slope will mean it stays put, so you cant just disregard friction (i think - i couldnt get the answer doing that)

[RuiAce]

Ok. I think this is the idea

Vertical resolution - Do it as normal
Horizontal resolution - The friction and normal reaction cancel out to 0 instead of resolve to give \(mr\omega^2\)

I'm about to go study for my exam coming up so I won't be able to prepare a solution just yet. Would appreciate if you could post up your working out if you're stuck though.

[Jyrgal]

heyo!

i was just wondering if there is any smart tips or tricks to do graph transformations for cos^-1(f(x)), sin^-1(f(x)) and tan^-1(f(x))?
so far, I've had to get domain, range, intercepts, then limits for x->0 & infinity, and then finally draw the general transformation, plugging into calculator to make sure each value is correct. this takes an absurd amount of time and i just wanna know some good tricks that i can apply to this transformation thatll make my life easier, like for reciprocal graphs when f(x) ->0+, 1/f(x) -> infinity+

Thanks 

[RuiAce]

heyo!

i was just wondering if there is any smart tips or tricks to do graph transformations for cos^-1(f(x)), sin^-1(f(x)) and tan^-1(f(x))?
so far, I've had to get domain, range, intercepts, then limits for x->0 & infinity, and then finally draw the general transformation, plugging into calculator to make sure each value is correct. this takes an absurd amount of time and i just wanna know some good tricks that i can apply to this transformation thatll make my life easier, like for reciprocal graphs when f(x) ->0+, 1/f(x) -> infinity+

Thanks 

Whilst that list of things should always be looked out for, you're usually not going to need all of them for every single curve. It will depend on the exact example you're given which ones are of relevance.

[dux99.95]

Where do i check for notifs? Is there a button that takes me directly to the exact post bc usually I go on the new replies and then scroll through the last few pages of the recent posts to find my post and see for any replies

2nd q
Am I able to copy and paste pictures here (it doesnt work when i copy from google docs)

Main q
Shouldn’t limits be -a and a instead of a and 0 when you do a volumes by cylindrical shells method question? (not sure if i've explained it right - i'd post a picture but not sure how to work this)


thanks so much your help is appreciated a lot!! 

[RuiAce]

Main q
Shouldn’t limits be -a and a instead of a and 0 when you do a volumes by cylindrical shells method question? (not sure if i've explained it right - i'd post a picture but not sure how to work this)


thanks so much your help is appreciated a lot!! 

This question is arbitrary and only makes sense if we assume that the rotation is about the y-axis (the line x=0, as opposed to say x=1). Assuming this:

The method of cylindrical shells is designed based off the formula for an arbitrary cylinder and the area of just a cross section formed by cutting down the radius of the cylinder, not the entire diameter. We choose to rotate about an angle of 360 degrees to map out our cylinder.

If instead we chose to slice down the whole diameter, we would only have to rotate about an angle of 180 degrees, not 360 degrees. The formula is then no longer \(V=\int_0^a 2\pi r h\, dr\), but \(V=\int_{-a}^a \pi r h\, dr\). (There is a subtle link to even functions here.)

The reason this ends up being π instead of 2π is because intuitively speaking, rotation by 180 degrees only maps out half of the cylinder and not the entire thing.

In summary - this only happens because of how the method was designed to begin with

Questions related to how to use the forum should be posted in their respective sections. Before doing so, you should also read the article on how to use the forums before posting a question about it.

[theblackswan]

Hi,
In regards to the arg (z) bit of complex numbers, how do you know if the locus of say, arg (z-2) - arg (z+2) = pi/2 is the semicircle above or below the x - axis? And for solving a question say, Re [(z-i)/(z+1)] how can you find arg (z) geometrically instead of algebraically? Thanks!

[RuiAce]

Hi,
In regards to the arg (z) bit of complex numbers, how do you know if the locus of say, arg (z-2) - arg (z+2) = pi/2 is the semicircle above or below the x - axis? And for solving a question say, Re [(z-i)/(z+1)] how can you find arg (z) geometrically instead of algebraically? Thanks!

Your second question is ambiguous. That's just an expression for the real part and not an equation, so nothing can be inferred about the argument.