VCE Methods Question Thread!

[Only Cheating Yourself]

Hey, does anyone have any regrets on anything during units 1 and 2, and if anon could give any other pointers?

Thanks

[Conic]

Find the exact so solution(if they exist) or prove there are no solutions

5(4x+3)=(4x+3)^2+9

I can use the substation method i.e (4x+3) but theres an = sign so i now don't know how to use it…

Let u=4x+3. Now we have , and we can rearrange this to get .

How do we know if a quadratic has solutions? We use the discriminant:



A negative discriminant means we don't have any real solutions.

Instead of remembering specific methods for specific questions, just try to break questions down into their simpler components.

[Only Cheating Yourself]

Let u=4x+3. Now we have , and we can rearrange this to get .

How do we know if a quadratic has solutions? We use the discriminant:



A negative discriminant means we don't have any real solutions.

Instead of remembering specific methods for specific questions, just try to break questions down into their simpler components.

I have learnt the discriminant yet….  but even if i used another method it will be a negative root so there are no solutions thanks.  Also i've used the sub method before how can i tell if i can use it?  if that ^2 wasn't there does that mean i can still use it?

[grannysmith]

Alternatively, you could attempt to use complete the square and end up with (u-5/2)^2+11/4.
Therefore there are no solutions for u

[Conic]

You'd usually substitute a different variable in when you have where f(x) is a function of x.

[M_BONG]

Hey, can someone lend me a quick hand and explain to me what I did wrong:

Question:



My solution:



Actual solutions:




I don't understand how the answer was obtained. I thought to differentiate functions with base "e" was simply to derive the power and multiply the base with the derivative of the power?

[brightsky]

You need to use the product rule. There is a t between the 100 and the exponential.

[lzxnl]

Hey, can someone lend me a quick hand and explain to me what I did wrong:

Question:



My solution:



Actual solutions:




I don't understand how the answer was obtained. I thought to differentiate functions with base "e" was simply to derive the power and multiply the base with the derivative of the power?

Be slightly careful: your question seems to say dy/dx, but you don't have any x's in your expression. I'm assuming it's just a typo, but if not, you'd need a chain rule somewhere

[Bluegirl]

How do you determine how many solutions/or an infinite number of solutions a system of equations has. Is there a quick way or do you have to do trial and error/work it out?

[brightsky]

Depends on how many variables the linear system has. If there are only two variables, then it is easy to work out whether the system has no, one or infinitely many solutions, since the graph of each equation is a straight line. If there are more than two variables, however, it is harder to visualise the graphs, since they will lie in a higher dimension, e.g. R^3 for three variables, R^4 for four variables, etc.

[lzxnl]

You'd have to work it out. Your calculator can do that for you. If you try and solve the equations by hand but get to 0=0 or something, that means you have infinitely many solutions. If you get 1=0, that means there are no solutions.

Brightsky, I'm not sure R^4 makes sense to VCE students

[Bluegirl]

You'd have to work it out. Your calculator can do that for you. If you try and solve the equations by hand but get to 0=0 or something, that means you have infinitely many solutions. If you get 1=0, that means there are no solutions.

Brightsky, I'm not sure R^4 makes sense to VCE students

.
Thankyou!
And Brightsky!

[T-Infinite]

Just a quick question,

range of f= [0, infinity]
domain of g= (-infinity, 3]

which one is larger? book says range of f, someone please explain.. I'm kinda confused. I might have forgotten how to identify which is larger.

[TrueTears]

What do you mean by "larger"?

Both sets are uncountably infinite. To see this, every interval (closed/open/half) is uncountable since you can form a bijection with and is uncountable. Since both and contain some interval, then both sets are uncountable. Therefore, both sets have the same "size" in the sense that .

[T-Infinite]

What do you mean by "larger"?

Both sets are uncountably infinite. To see this, every interval (closed/open/half) is uncountable since you can form a bijection with and is uncountable. Since both and contain some interval, then both sets are uncountable. Therefore, both sets have the same "size" in the sense that .

Lol, sorry if my question didn't make sense. But I was doing a question on composite functions.
The question was asking me to state whether g o f exists/defined. From what I learnt, g o f is defined if the domain of g is greater or equal to the range of f
So yeah, I've found the range of f and the domain of g now I'm wondering whether domain of g is greater/equal to range of f and how so?