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March 29, 2024, 02:55:47 am

Author Topic: 3U Maths Question Thread  (Read 1230297 times)  Share 

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dux99.95

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Re: 3U Maths Question Thread
« Reply #1710 on: March 24, 2017, 11:59:49 pm »
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Hey Jake, thanks so much for this. It's truly helpful for us students!

1)
Solve x+2 < 4 / (x-1)

2) Sketch
a) y = sinx + cos x
b) y = cos2x - sin2x

3) Integrate 2^(2x+4)

4) attached

 


RuiAce

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Re: 3U Maths Question Thread
« Reply #1711 on: March 25, 2017, 08:31:57 am »
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4) attached




_____________________________________



VydekiE

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Re: 3U Maths Question Thread
« Reply #1712 on: March 25, 2017, 10:29:33 am »
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Hi, I need some help with this perms and combs question,
1) The three judges for Australian Idol have to vote on three singers, listing their order of preference. In how many ways can the judges vote so that any two of them agree in their order of preference, while the third differs?
Thank you!!

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #1713 on: March 25, 2017, 10:40:49 am »
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Hi, I need some help with this perms and combs question,
1) The three judges for Australian Idol have to vote on three singers, listing their order of preference. In how many ways can the judges vote so that any two of them agree in their order of preference, while the third differs?
Thank you!!

Hey! So basically, by forcing two judges to match, that really means that we need two different arrangements - One held by two judges and something different from the third.

First do the arrangement that is matched:



The second judge can have ANY arrangement except the one held by the other two judges. So they have 5 choices. Therefore



But, we can also change the judge that doesn't match. There are three judges that could deviate, so we triple our answer. The final answer is 90 ;D

I hope this helps! Hopefully I've interpreted it correctly ;D
« Last Edit: March 25, 2017, 10:42:24 am by jamonwindeyer »

VydekiE

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Re: 3U Maths Question Thread
« Reply #1714 on: March 25, 2017, 10:52:57 am »
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Hey! So basically, by forcing two judges to match, that really means that we need two different arrangements - One held by two judges and something different from the third.

First do the arrangement that is matched:



The second judge can have ANY arrangement except the one held by the other two judges. So they have 5 choices. Therefore



But, we can also change the judge that doesn't match. There are three judges that could deviate, so we triple our answer. The final answer is 90 ;D

I hope this helps! Hopefully I've interpreted it correctly ;D

Thank you!!

dux99.95

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Re: 3U Maths Question Thread
« Reply #1715 on: March 25, 2017, 12:00:35 pm »
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Thank you RuiAce!!

How did you get the last part where its

1/2 = (1-1/2) ?

RuiAce

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Re: 3U Maths Question Thread
« Reply #1716 on: March 25, 2017, 12:11:07 pm »
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Thank you RuiAce!!

How did you get the last part where its

1/2 = (1-1/2) ?
Last part was just the sum of an infinite geometric series
a/(1-r)

Also one minus a half is a half. Just say that aloud or put it in a calculator if that was the confusion haha

dux99.95

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Re: 3U Maths Question Thread
« Reply #1717 on: March 25, 2017, 02:58:14 pm »
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Last part was just the sum of an infinite geometric series
a/(1-r)





Ohh yep that explains a lot! I didn't know the formula for infinite geo series!
So a = 1/2, r =2

Shouldn't it be (1/2) / 1-2?

Or is r = 1/2 because
(1/4) / (1/2) = 1/4 x 2/1 = 1/2 ?


Your answer is correct! :)   

RuiAce

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Re: 3U Maths Question Thread
« Reply #1718 on: March 25, 2017, 03:08:10 pm »
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Ohh yep that explains a lot! I didn't know the formula for infinite geo series!
So a = 1/2, r =2

Shouldn't it be (1/2) / 1-2?

Or is r = 1/2 because
(1/4) / (1/2) = 1/4 x 2/1 = 1/2 ?


Your answer is correct! :)


dux99.95

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Re: 3U Maths Question Thread
« Reply #1719 on: March 26, 2017, 07:04:35 pm »
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Got it, thanks so much!

How do we solve these other questions?

1) Sketch
a) y = sinx + cos x
b) y = cos2x - sin2x

2) Integrate 2^(2x+4)

Mahan

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Re: 3U Maths Question Thread
« Reply #1720 on: March 26, 2017, 07:17:45 pm »
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Got it, thanks so much!

How do we solve these other questions?

1) Sketch
a) y = sinx + cos x
b) y = cos2x - sin2x

2) Integrate 2^(2x+4)
2) Note
then


« Last Edit: March 26, 2017, 07:30:03 pm by Mahan »
Mahan Ghobadi

Maths Tutor- ESL (80)| 2 Unit maths (96)(2013) | 3 Unit maths (99)| 4 Unit maths(95)| Physics (88)| music1(93)

Get more answers for your questions, as well as weekly tips and blog posts, from my friends and I at: HSC http://bit.ly/HSC-Help
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Mahan

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Re: 3U Maths Question Thread
« Reply #1721 on: March 26, 2017, 07:36:02 pm »
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Got it, thanks so much!

How do we solve these other questions?

1) Sketch
a) y = sinx + cos x
b) y = cos2x - sin2x

2) Integrate 2^(2x+4)
For part a) the easiest way I can think of is to just sketch the functions then add the y values together, for instance:
Draw sin(x) and cos(x) separately then add the y values of each at any point x to get sin(x)+cos(x)
for part b) there are two approaches:
one is to draw cos(2x) and sin(2x) separately, then at any point x, subtract the y value of sin(2x)from y value of cos(2x)
the second approach is to draw cos(2x) and -sin(2x) then add the corresponding y-values. I prefer the second method because you don't need to deal with subtraction, for me addition is easier than subtraction. :)
Mahan Ghobadi

Maths Tutor- ESL (80)| 2 Unit maths (96)(2013) | 3 Unit maths (99)| 4 Unit maths(95)| Physics (88)| music1(93)

Get more answers for your questions, as well as weekly tips and blog posts, from my friends and I at: HSC http://bit.ly/HSC-Help
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RuiAce

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Re: 3U Maths Question Thread
« Reply #1722 on: March 26, 2017, 07:38:52 pm »
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Got it, thanks so much!

How do we solve these other questions?

1) Sketch
a) y = sinx + cos x
b) y = cos2x - sin2x

2) Integrate 2^(2x+4)


teapancakes08

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Re: 3U Maths Question Thread
« Reply #1723 on: March 26, 2017, 11:05:04 pm »
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Find indefinite integrals (primitive functions) of the following with respect to x. Note that "a" is a constant.
e) a^(5x)

Apparently the answer's (a^(5x)/5lna) + C , so something probably went really lopsided in my working out. (Got up to 5x = 1/ylna or something and everything went weird from there...)
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Mahan

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Re: 3U Maths Question Thread
« Reply #1724 on: March 27, 2017, 12:33:20 am »
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Find indefinite integrals (primitive functions) of the following with respect to x. Note that "a" is a constant.
e) a^(5x)

Apparently the answer's (a^(5x)/5lna) + C , so something probably went really lopsided in my working out. (Got up to 5x = 1/ylna or something and everything went weird from there...)
Well, the standard trick is to express

then

« Last Edit: March 27, 2017, 03:20:42 pm by Mahan »
Mahan Ghobadi

Maths Tutor- ESL (80)| 2 Unit maths (96)(2013) | 3 Unit maths (99)| 4 Unit maths(95)| Physics (88)| music1(93)

Get more answers for your questions, as well as weekly tips and blog posts, from my friends and I at: HSC http://bit.ly/HSC-Help
VCE  http://bit.ly/VCE-Help