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March 28, 2024, 10:31:29 pm

Author Topic: VCE Methods Question Thread!  (Read 4802280 times)  Share 

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S_R_K

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Re: VCE Methods Question Thread!
« Reply #18615 on: July 13, 2020, 10:48:49 am »
+1
\( \sin\left( \frac{\pi}{2} - \theta \right) = \cos \theta\) and \( \cos\left( \frac{\pi}{2} - \theta \right) = \sin \theta\).

Use that to rewrite \(\tan \left( \frac{\pi}{2} - b\right) \) in terms of \(\tan b\)

1729

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Re: VCE Methods Question Thread!
« Reply #18616 on: July 13, 2020, 11:13:42 am »
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Hi everyone!

I'm not really sure how to even begin working this question out since I always suck at questions that has only just variable letters *sigh*.

"For f(x)= 3ln(x+x/2),
- If f(u-2) + f(v-2)=f(auv+b) where u and v are positive real numbers, find the values of a and b.

- For what values of u does f(u)+f(-u)=f((u^2)/2) hold?"

Any help would be greatly appreciated! Do I start with equating equations or summ?
Start with log properties, this equation Thencan be combined, since

You can do something similar to combine it with the other side for the second part, at least one of u or -u must be negative or zero, giving you the log of a non-positive number. therefore, f(u) + f(-u) is undefined for all real values of u, so that equation is never true.

M-D

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Re: VCE Methods Question Thread!
« Reply #18617 on: July 13, 2020, 03:25:40 pm »
+1
\( \sin\left( \frac{\pi}{2} - \theta \right) = \cos \theta\) and \( \cos\left( \frac{\pi}{2} - \theta \right) = \sin \theta\).

Use that to rewrite \(\tan \left( \frac{\pi}{2} - b\right) \) in terms of \(\tan b\)

Thanks but the problem I'm facing is that while tan ((pi/2) - b) will equal (cos b)/(sin b) I have not been given any further values apart from sin x = 0.3, cos a = 0.6 and tan b = 0.7

If you could post the full working out that would be great. Thanks.

keltingmeith

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Re: VCE Methods Question Thread!
« Reply #18618 on: July 13, 2020, 03:51:02 pm »
+1
Thanks but the problem I'm facing is that while tan ((pi/2) - b) will equal (cos b)/(sin b) I have not been given any further values apart from sin x = 0.3, cos a = 0.6 and tan b = 0.7

You're actually very close to the final answer! If tan(pi/2 - b) = cos(pi/2 - b)/sin(pi/2 - b), what could cos(b)/sin(b) ALSO be equal to?

If you could post the full working out that would be great. Thanks.


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Re: VCE Methods Question Thread!
« Reply #18619 on: July 13, 2020, 04:12:27 pm »
+1
I worked it out. Thanks

rozmaaate

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Re: VCE Methods Question Thread!
« Reply #18620 on: July 15, 2020, 05:34:13 pm »
+1
Hey guys I need some help with this question as I have no idea how to approach it


How many even two digit numbers can be formed from the digits 4,5,6,7,8 if each digit can be used
only once?

chemistrykind

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Re: VCE Methods Question Thread!
« Reply #18621 on: July 15, 2020, 05:49:42 pm »
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Hey guys I need some help with this question as I have no idea how to approach it


How many even two digit numbers can be formed from the digits 4,5,6,7,8 if each digit can be used
only once?

This one is doable! Note that even two-digit numbers always have an even number at the end (here those digits are 4,6, and 8 ). There's a specific way to approach this with permutations/combinations, but the most intuitive approach is to add up all the even number possibilities for each digit:

a) 54, 64, 74, 84
b) 46, 56, 76, 86
c) 48, 58, 68, 78

Since there are four other digits available for any given even digit, the answer is 3*4=12 possible numbers.
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rozmaaate

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Re: VCE Methods Question Thread!
« Reply #18622 on: July 15, 2020, 06:44:34 pm »
+1
This one is doable! Note that even two-digit numbers always have an even number at the end (here those digits are 4,6, and 8 ). There's a specific way to approach this with permutations/combinations, but the most intuitive approach is to add up all the even number possibilities for each digit:

a) 54, 64, 74, 84
b) 46, 56, 76, 86
c) 48, 58, 68, 78

Since there are four other digits available for any given even digit, the answer is 3*4=12 possible numbers.

Could you please what's the permutation method as that is the way that my teacher + textbook would like me to do it

Azila2004

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Re: VCE Methods Question Thread!
« Reply #18623 on: July 15, 2020, 07:06:43 pm »
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Heyo!

I need help with two questions focusing on logarithms and algebra.
1. Given 3x = 4y = 12z, show that z = xy/(x + y) and 2. Find y if logz(y^2)=4+logz(y+5)

I feel like I'm making some silly mistake or missing out on something. Help would be really appreciated!  (•◡•) /
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james.358

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Re: VCE Methods Question Thread!
« Reply #18624 on: July 15, 2020, 07:57:15 pm »
+3
Heyo!

I need help with two questions focusing on logarithms and algebra.
1. Given 3x = 4y = 12z, show that z = xy/(x + y) and 2. Find y if logz(y^2)=4+logz(y+5)

I feel like I'm making some silly mistake or missing out on something. Help would be really appreciated!  (•◡•) /

I think you might've mistyped the first question! I think you meant 3^x, etc

Anyways heres the solutions to the questions

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Azila2004

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Re: VCE Methods Question Thread!
« Reply #18625 on: July 15, 2020, 08:14:58 pm »
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I think you might've mistyped the first question! I think you meant 3^x, etc

Anyways heres the solutions to the questions

(Image removed from quote.)

Thanks so much! You're a big help :D
I didn't even realise the typo I made in the first question so I'm glad you pointed that out.

For the second one however, it says that the answer is that y=-4 and 20. My problem was that I did not know how to get z out of the equation there to get actual numbers.
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Azila2004

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Re: VCE Methods Question Thread!
« Reply #18626 on: July 16, 2020, 02:21:14 pm »
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Hey is it possible you have misread the question? Because if you sub in 2 as z it would be -4 and 20

I just checked now and you're right :O
Yeah, I write my 2s very similarly to Zs, whoops!
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chemistrykind

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Re: VCE Methods Question Thread!
« Reply #18627 on: July 16, 2020, 02:32:31 pm »
+2
Could you please what's the permutation method as that is the way that my teacher + textbook would like me to do it

Sure! So for this question, we look at permutations rather than combinations (because we specifically need an even number in the units slot). Because we have 5 numbers and we want to know how many arrangements there are of a two-digit even number, we create a formula for each slot (10s with 5 choices and 1s with 3 choices).

10s = 5!/(5-1)! = 5
1s = 3!/(3-1)! = 3

In total, this is 5*3 = 15 permutations, including all number repetitions. However, we need to exclude those (44, 66, 88 ), so we obtain 15-3=12, which is the same answer from earlier :))
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rozmaaate

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Re: VCE Methods Question Thread!
« Reply #18628 on: July 18, 2020, 06:12:29 pm »
0
 The angle of depression of a boat from a cliff 60m high is 10°. How far ,to the nearest metre ,is the boat from the base of the cliff?

Sorry for the basic question I'm not great at math, correct answer is 340m apparently btw


Owlbird83

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Re: VCE Methods Question Thread!
« Reply #18629 on: July 18, 2020, 06:52:09 pm »
+5
The angle of depression of a boat from a cliff 60m high is 10°. How far ,to the nearest metre ,is the boat from the base of the cliff?

Sorry for the basic question I'm not great at math, correct answer is 340m apparently btw


Always draw the triangle first. Then add the numbers and angles you know. (angle of 'depression' means that from the horizontal it's 10degrees, so you'd use 80degrees as the angle in the triangle)
Think about SOH CAH TOA, and pick the formula for the info you have.
In this diagram we have the length adjacent (60m) and we want the opposite length. Using this, pick out the formula with o and a, which is the one with tan, and put the numbers into the formula, and solve for 'o' (or x as I've called it here).

I hope this helps
« Last Edit: July 18, 2020, 06:55:48 pm by Owlbird83 »
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