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March 29, 2024, 01:46:45 am

Author Topic: 3U Maths Question Thread  (Read 1230277 times)  Share 

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massive

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Re: 3U Maths Question Thread
« Reply #570 on: August 11, 2016, 01:07:33 pm »
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how do you do this q guys??

massive

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Re: 3U Maths Question Thread
« Reply #571 on: August 11, 2016, 01:45:59 pm »
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guys how do you do part ii?

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #572 on: August 11, 2016, 05:55:12 pm »
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guys how do you do part ii?

Hey! I'm about to head to a tutorial, but have a go at just doing a straight differentiation and finding a maxima!! Remember, d is given, so L is what varies, so you are finding dV/dL and putting it equal to zero! That will give you a length of L in terms of d that maximises the volume (remember to check that it is a maxima) ;D

if the answer doesn't come out, show me your working and I'll see if I can help you figure out what went wrong ;D

how do you do this q guys??

This is tougher. Consider the girth first, it is the shortest distance around the parcel. And then L is the longest side. Based on the dimensions, this gives us two sets of possible equations. The first, if x is the longest side, gives us this:



Or, if y is the longest:



Whoops, have to go, see what you make of this ;)






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Re: 3U Maths Question Thread
« Reply #573 on: August 11, 2016, 07:49:13 pm »
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Hi again,
Another question I couldn't quite grasp - part iv). Could someone please explain? Thank you!!

RuiAce

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Re: 3U Maths Question Thread
« Reply #574 on: August 11, 2016, 07:54:55 pm »
+2
Hi again,
Another question I couldn't quite grasp - part iv). Could someone please explain? Thank you!!
See post #429 here. I have already done this question.

massive

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Re: 3U Maths Question Thread
« Reply #575 on: August 11, 2016, 10:23:04 pm »
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guys how do you part ii :S?

RuiAce

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Re: 3U Maths Question Thread
« Reply #576 on: August 11, 2016, 10:36:40 pm »
+2

jakesilove

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Re: 3U Maths Question Thread
« Reply #577 on: August 11, 2016, 10:39:11 pm »
+1
guys how do you part ii :S?

These questions are all quite similar, so it is worth noting the steps I take so you can use them in an exam.





That last piece of information is given in the question, but as it is in kilometers per HOUR, not per SECOND, I divided by 3600. So,




Therefore


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jakesilove

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Re: 3U Maths Question Thread
« Reply #578 on: August 11, 2016, 10:40:08 pm »
+2
ATAR: 99.80

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Physics: 93
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Studying a combined Advanced Science/Law degree at UNSW

massive

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Re: 3U Maths Question Thread
« Reply #579 on: August 11, 2016, 10:43:53 pm »
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woah i completely missed the km/HOUR, Thanks Rui and Jake!!

Just another question, I can't get part iii, i keep getting 24 but the answer is 37 :/

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #580 on: August 11, 2016, 11:49:08 pm »
+3
Consider the girth first, it is the shortest distance around the parcel. And then L is the longest side. Based on the dimensions, this gives us two sets of possible equations. The first, if x is the longest side, gives us this:



Or, if y is the longest:



Alright, I left off here! Let me know if you need a hand with the other question, it is just differentiation and finding a maxima, give it a go! ;D

So here, we have two potential equations to start with, let's see how they effect the formulae for volume (in both cases, we'll eliminate y):



When we do this, it becomes a little clearer that the top option gives a larger volume for any value of x. I'll leave you to form a mathematical proof with all this information, but that's the basic setup!

To show you the idea of finding the maxima/minima, I'll work through this one for you:



So the dimensions are (using the formulas above), 50/3 by 50/3 by 100/3 ;D

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #581 on: August 12, 2016, 12:22:31 am »
+3
woah i completely missed the km/HOUR, Thanks Rui and Jake!!

Just another question, I can't get part iii, i keep getting 24 but the answer is 37 :/

Hmm, let's have a look. The absolute best thing to do after that extra payment (unless you know EXACTLY what you are doing) is to hit reset and recalculate absolutely everything. By using the formula proved in Part 1, and then subtracting the additional $5000:



From here, we need to re-apply the formula from above, and set the amount owing equal to zero. Do a quick rearrangement:



You can use logarithms to get the exact answer here, but it needs to be an integer so I will use guess and check, and indeed:



Hope that helps! ;D

massive

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Re: 3U Maths Question Thread
« Reply #582 on: August 12, 2016, 12:42:21 am »
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thnx Jamon!

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Re: 3U Maths Question Thread
« Reply #583 on: August 15, 2016, 08:10:39 pm »
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How would you do this:

1. Let f(x)=sin^-1 x
a. State the domain and rage of f(x)

I got "all x" for this and for the range I got -pi/2 =<y=<pi/2

b. Find f'(x) and f''(x)

f'(x)=(sin^-1 x)'

Then I'm not sure of whatelse to do :(

c. Is f'(x) undefined at x=1 and x=-1. Deduce the tangents to the curve at these points
d. Show that the line y=x is a tangent to the curve y=f(x) at (0,0)
e. Sketch y=f(x) and y=x
f. For what value of m does the line y=mx cut y=f(x) at three points
g. Investigate the concavity of the curve and find the coordinates of the point of inflextion

Thanks guys  ;D

RuiAce

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3U Maths Question Thread
« Reply #584 on: August 15, 2016, 08:19:33 pm »
+1
How would you do this:

1. Let f(x)=sin^-1 x
a. State the domain and rage of f(x)

I got "all x" for this and for the range I got -pi/2 =<y=<pi/2
At this point, you need to read the textbook and make sure you understand what inverse sine is.

I'm sorry to say this, but this is because your answer is wrong for a foundation level question.

(In particular, the domain)


Also, the derivative is also in the textbook
« Last Edit: August 15, 2016, 08:22:15 pm by RuiAce »