Login

Welcome, Guest. Please login or register.

March 30, 2024, 01:02:01 am

Author Topic: 3U Maths Question Thread  (Read 1230717 times)  Share 

0 Members and 7 Guests are viewing this topic.

frog1944

  • Trendsetter
  • **
  • Posts: 163
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #2115 on: May 30, 2017, 09:13:03 pm »
0

chelseam

  • Trendsetter
  • **
  • Posts: 185
  • Respect: +45
Re: 3U Maths Question Thread
« Reply #2116 on: May 31, 2017, 09:16:30 pm »
0
Hi! I'm not sure how I should be approaching this question and I'm getting 71º or 6º as my answer. Could someone please help me? Thank you :D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: 3U Maths Question Thread
« Reply #2117 on: May 31, 2017, 10:25:15 pm »
+2
(Image removed from quote.)

Hey! This is a tough one - So we are given that the point is moving around the circle at a uniform speed of \(2\text{ms}^{-1}\). What we have to do, similar to what we do in projectile motion (you might not have done projectiles yet) - We separate this speed into horizontal and vertical components.



Now \(\frac{dx}{dt}\) will eventually be our subject - But what about \(\frac{dy}{dt}\)? We use the chain rule to get rid of that:



That expression at the front there comes from differentiating the upper semicircle, \(y=\sqrt{1-x^2}\). Now put that together (squaring both sides to make it easier):



So that's the rate of change of the \(x\) coordinate. At the point (0,1), this is equal to 2 metres per second. This makes sense - At the peak of the semicircle all the speed goes in the x-direction ;D does this make sense?

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: 3U Maths Question Thread
« Reply #2118 on: May 31, 2017, 10:36:37 pm »
+2
Hi! I'm not sure how I should be approaching this question and I'm getting 71º or 6º as my answer. Could someone please help me? Thank you :D

Hey! There's a few ways - I think the easiest would be to substitute the x-equations into the y-equations to get the Cartesian equation of the projectile:



This substitution is very standard for projectile questions - Make it a priority to understand it and be able to perform it VERY quickly! ;D from here, we use the identity \(\sec^2{\theta}=1+\tan^2{\theta}\), and substitute \(x=35,y=1\) to hit our target:



This is a quadratic equation for \(\tan{\theta}\) - From here, rearrange and solve using the formula, you'll get two allowable values of your launch angle. Choose the one that is less than 45 degrees, such that the assumption that air resistance is minimal can hold ;D

This is just the main bits of the process, happy to go into more detail if you need it! ;D

chelseam

  • Trendsetter
  • **
  • Posts: 185
  • Respect: +45
Re: 3U Maths Question Thread
« Reply #2119 on: May 31, 2017, 10:42:08 pm »
0
This is just the main bits of the process, happy to go into more detail if you need it! ;D
Thanks Jamon I get it now! :D
Also, when should we be using degree mode and not radians on the calculator? Is degree mode only used when things involve angles? Thanks again! ;D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #2120 on: May 31, 2017, 10:43:32 pm »
+4
Thanks Jamon I get it now! :D
Also, when should we be using degree mode and not radians on the calculator? Is degree mode only used when things involve angles? Thanks again! ;D
You're expected to use radians 95% of the time.

For the angle of projectile motion it's useless to use radians, because we're talking about a physical application of angles. Same goes for trigonometry.

Stuff like calculus cannot be done in degrees, which is why radians is the norm.

chelseam

  • Trendsetter
  • **
  • Posts: 185
  • Respect: +45
Re: 3U Maths Question Thread
« Reply #2121 on: May 31, 2017, 11:14:04 pm »
0
Stuff like calculus cannot be done in degrees, which is why radians is the norm.
Okay, thanks Rui! :D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

legorgo18

  • Trendsetter
  • **
  • Posts: 168
  • A future lawyer.
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #2122 on: June 02, 2017, 12:15:07 am »
0
2 quick questions:

1) The area in the first quadrant under y=1 and above y= 2- 2/x is rotated about the x-axis. Find the volume so formed. (Nothing hard, but i keep getting 4pi(ln2 -2) whilst the answer is 4pi(2ln2 -1) ... starting to think maybe ans is wrong)

2) Find limit x->0 (sin^2(x)/x), is the only method using L'Hôpital's rule?
HSC 2017: Advanced English(94), 2U Maths(97), 3U Maths(49), Bio(91), Chem(88), Chinese in context(88)

Atar: 97.55

Studying a bachelor of  actuarial studies/ bachelor of laws at UNSW

Tutoring details: https://highschooltutors.com.au/tutor/12153

2017 Blakehurst internals: https://drive.google.com/drive/folders/13l8nV_efhmYwlA1hM5grQnymew5pznrn

ellipse

  • Forum Regular
  • **
  • Posts: 50
  • Respect: 0
Re: 3U Maths Question Thread
« Reply #2123 on: June 02, 2017, 07:02:27 am »
0
2) Find limit x->0 (sin^2(x)/x), is the only method using L'Hôpital's rule?


99.55
unsw engo/sci

mx2-99
mx1-98
phys-94
chem-94
eng-88 (rip me)

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #2124 on: June 02, 2017, 08:31:07 am »
+1
2 quick questions:

1) The area in the first quadrant under y=1 and above y= 2- 2/x is rotated about the x-axis. Find the volume so formed. (Nothing hard, but i keep getting 4pi(ln2 -2) whilst the answer is 4pi(2ln2 -1) ... starting to think maybe ans is wrong)

2) Find limit x->0 (sin^2(x)/x), is the only method using L'Hôpital's rule?
WolframAlpha confirms your answer for 1

legorgo18

  • Trendsetter
  • **
  • Posts: 168
  • A future lawyer.
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #2125 on: June 02, 2017, 04:49:03 pm »
0
Quick q Find the simultaneous solutions of l 3-2x l < 5 and l x-1 l > or equal to  1

ty
HSC 2017: Advanced English(94), 2U Maths(97), 3U Maths(49), Bio(91), Chem(88), Chinese in context(88)

Atar: 97.55

Studying a bachelor of  actuarial studies/ bachelor of laws at UNSW

Tutoring details: https://highschooltutors.com.au/tutor/12153

2017 Blakehurst internals: https://drive.google.com/drive/folders/13l8nV_efhmYwlA1hM5grQnymew5pznrn

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #2126 on: June 02, 2017, 05:17:38 pm »
+1
Quick q Find the simultaneous solutions of l 3-2x l < 5 and l x-1 l > or equal to  1

ty



The solutions of the independent equations and their intersections may be represented on a number line for clarity
« Last Edit: June 02, 2017, 05:51:16 pm by RuiAce »

legorgo18

  • Trendsetter
  • **
  • Posts: 168
  • A future lawyer.
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #2127 on: June 02, 2017, 05:35:08 pm »
0
Super quick q how do i find maximum speed and acceleration when v squared = 15 + 2x - x squared and how do i find an equation for the position x as a function of time do i just let v=dx/dt sorry haven't done this topic since last term
HSC 2017: Advanced English(94), 2U Maths(97), 3U Maths(49), Bio(91), Chem(88), Chinese in context(88)

Atar: 97.55

Studying a bachelor of  actuarial studies/ bachelor of laws at UNSW

Tutoring details: https://highschooltutors.com.au/tutor/12153

2017 Blakehurst internals: https://drive.google.com/drive/folders/13l8nV_efhmYwlA1hM5grQnymew5pznrn

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: 3U Maths Question Thread
« Reply #2128 on: June 02, 2017, 08:09:12 pm »
+2
Super quick q how do i find maximum speed and acceleration when v squared = 15 + 2x - x squared and how do i find an equation for the position x as a function of time do i just let v=dx/dt sorry haven't done this topic since last term


legorgo18

  • Trendsetter
  • **
  • Posts: 168
  • A future lawyer.
  • Respect: +2
Re: 3U Maths Question Thread
« Reply #2129 on: June 02, 2017, 09:25:45 pm »
0
Yes rui i got that step but i forgot how to get max speed and acceleration which is the next sub q

Anyway can you please quickly verify this as i dont believe the answers:Find area under curve of y= e^x -1 for x= -2 to x=1. The solution subtracted the 2 areas instead adding them up so wtf it is shaded from 1 to 0 then negative region 0 to -2 so i abs the negative bit and added them but ans subtracted. Ty
HSC 2017: Advanced English(94), 2U Maths(97), 3U Maths(49), Bio(91), Chem(88), Chinese in context(88)

Atar: 97.55

Studying a bachelor of  actuarial studies/ bachelor of laws at UNSW

Tutoring details: https://highschooltutors.com.au/tutor/12153

2017 Blakehurst internals: https://drive.google.com/drive/folders/13l8nV_efhmYwlA1hM5grQnymew5pznrn