Mathematics Question Thread

[RuiAce]

Couple of Questions:

For my half yearlies, this question was in the practice HSC and I find get the answers:

Question 1: (Pretty sure its just algebra)

(Image removed from quote.)

Question 2 e): (I have completed a-d)

(Image removed from quote.)

Question 3: (Factorise)

(Image removed from quote.)

Thanks for the help!,

Thomas

I saw this whilst I'm in a lecture so I'm a bit busy to do it right now, but for Jamon/Jake/etc 's convenience please post up your answers to anything you've done in advance with Q2.

[dadwwdnnnn]

I saw this whilst I'm in a lecture so I'm a bit busy to do it right now, but for Jamon/Jake/etc 's convenience please post up your answers to anything you've done in advance with Q2.

final answers for q2 (dont know if they are correct, practice test does not come with answers)

a) (1,6)
b)3x+2y-38=0
c)7x-3y+11=0
d)(136/23,233/-23)

[smile123]

How do I differentiate this question 

[1937jk]

How do you know when sketching a graph like y = sin(3x) which values (in radians) to put down on the x axis?

[jakesilove]

How do I differentiate this question 

Hey! So,



a is a constant, so goes to zero when we differentiate. The cos term is differentiated using the chain rule, as shown above.

[jakesilove]

How do you know when sketching a graph like y = sin(3x) which values (in radians) to put down on the x axis?

Hey! Personally, I could never remember stuff like that. So, I would often use my calculator to find zeros (for instance, 0, pi, 2pi and 3pi are all zeros that can be quickly found!) and the use those points as my x-axis. However, it really doesn't matter; choose something that makes sense to you (any regular increment is fine), then use your calculator to figure out what the y coordinate at that point will be.

[f_tan]

How do I do this question?

The cost of running a car at an average speed of v km/h is given by c = 150 + v^2/80 cents per hour. Find the everage speed, to the enarest km/h, at which the cost of a 500 km trip is a minimum.

Thanks!

[dadwwdnnnn]

Couple of Questions:

For my half yearlies, this question was in the practice HSC and I find get the answers:

Question 1: (Pretty sure its just algebra)

(Image removed from quote.)

Question 2 e): (I have completed a-d)

(Image removed from quote.)

Question 3: (Factorise)

(Image removed from quote.)

Thanks for the help!,

Thomas

Could I please get some help?

[RuiAce]

Couple of Questions:

For my half yearlies, this question was in the practice HSC and I find get the answers:

Question 1: (Pretty sure its just algebra)

(Image removed from quote.)

Question 2 e): (I have completed a-d)

(Image removed from quote.)

Question 3: (Factorise)

(Image removed from quote.)

Thanks for the help!,

Thomas

I'll quickly do Q3.

[dadwwdnnnn]

I'll quickly do Q3.

soo this is wrong?
https://www.symbolab.com/solver/step-by-step/factorise%20%5Cleft(2x%5Cright)%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ccdot%5Cleft(x-2%5Cright)%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-%5Cleft(5x%5Cright)%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%5Ccdot%5Cleft(x-2%5Cright)%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D

[jamonwindeyer]

soo this is wrong?

It isn't mathematically incorrect, but it isn't doing the most efficient job, Rui's is neater

Edit: Just fixed a little typo in the last line of Rui's response, check the updated!

[dadwwdnnnn]

It isn't mathematically incorrect, but it isn't doing the most efficient job, Rui's is neater

Edit: Just fixed a little typo in the last line of Rui's response, check the updated!

cheers jamon, you mind helping with the other 2 questions, I have my 2 unit exam tomorrow. Thanks

[jamonwindeyer]

Couple of Questions:

For my half yearlies, this question was in the practice HSC and I find get the answers:

Question 1: (Pretty sure its just algebra)

1st Line to 2nd: Multiplying each term by \(fS_1S_2\)
2nd Line to 3rd: Move \(S_2\)'s to the LHS and factorise
3rd Line to Final: Divide to isolate \(S_2\)

For your second question, I think you can just find the slope of the two segments using the gradient formula on your reference sheet, and use that as your reasoning?

[dadwwdnnnn]

1st Line to 2nd: Multiplying each term by \(fS_1S_2\)
2nd Line to 3rd: Move \(S_2\)'s to the LHS and factorise
3rd Line to Final: Divide to isolate \(S_2\)

For your second question, I think you can just find the slope of the two segments using the gradient formula on your reference sheet, and use that as your reasoning?

Last question, sorry jamon, with question 1d) did I get the points of intersection wrong?

[jamonwindeyer]

Last question, sorry jamon, with question 1d) did I get the points of intersection wrong?

You should have gotten \((4,13)\)