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March 29, 2024, 06:08:23 am

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Thankunext

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Re: Mathematics Question Thread
« Reply #4215 on: May 31, 2019, 08:09:18 pm »
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Hello, can someone help with this. Many thanks!

How do you draw a tree diagram for this question and solve:
If 4 dice are thrown, find the probability that the dice will have only one 6.
I can work this out manually but not with a tree diagram because I don't know how to draw it.

RuiAce

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Re: Mathematics Question Thread
« Reply #4216 on: May 31, 2019, 08:44:33 pm »
+2
Hello, can someone help with this. Many thanks!

How do you draw a tree diagram for this question and solve:
If 4 dice are thrown, find the probability that the dice will have only one 6.
I can work this out manually but not with a tree diagram because I don't know how to draw it.

Trying to list out all the options {1,2,3,4,5,6} will probably take forever. At times like these, because we know that only the number 6 is important, we can just squash all the other cases into some dummy variable.

Kombmail

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Re: Mathematics Question Thread
« Reply #4217 on: June 01, 2019, 02:51:16 pm »
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Algebra is on!
I did a few factorization questions but I did not understand how you get the answers!

Q1) (x-3)^2 + 5(x-3) = (x-3)(x+2)
Q2) a(a+1)-a(a+1)^2= -(a+1)

Please help me in understanding these someone?
-KgkG-

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4218 on: June 01, 2019, 03:37:59 pm »
+1
For Q1 (x-3) is a common factor. Hence, you can write this as (x-3)(x-3+5), which is just (x-3)(x+2). Similarly, for Q2, a(a+1) is a common factor, and thus it can be factorised to become a(a+1)(1-(a+1)), which should be -a^2(a+1), not what you've got there :)
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Kombmail

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Re: Mathematics Question Thread
« Reply #4219 on: June 01, 2019, 08:13:23 pm »
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For Q1 (x-3) is a common factor. Hence, you can write this as (x-3)(x-3+5), which is just (x-3)(x+2). Similarly, for Q2, a(a+1) is a common factor, and thus it can be factorised to become a(a+1)(1-(a+1)), which should be -a^2(a+1), not what you've got there :)

Thanks again!
-KgkG-

Kombmail

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Re: Mathematics Question Thread
« Reply #4220 on: June 01, 2019, 10:02:14 pm »
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Random question... if I have a test in exactly two weeks (from the coming week from 3rd June) till the 21st (date of the test) , and there’s 36 applications of calculus to the physical world and 26 on series and sequences excluding finance... how long should I take to do each and in what intervals? (By intervals I mean should I do the 26 every 2 days? Etc.)
-KgkG-

Thankunext

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Re: Mathematics Question Thread
« Reply #4221 on: June 02, 2019, 01:53:18 pm »
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(Image removed from quote.)
Trying to list out all the options {1,2,3,4,5,6} will probably take forever. At times like these, because we know that only the number 6 is important, we can just squash all the other cases into some dummy variable.
Ah I see. Thank you for your diagram!

Kombmail

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Re: Mathematics Question Thread
« Reply #4222 on: June 02, 2019, 03:08:13 pm »
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Question 7 I do not understand. I’ve only so far found x=9 as a stationary point. And so far when integrating I’ve gotten (9-x^2)^3/2 / 3/2

Please someone help mehhh!!!

Here is question 7: write the definite integral for the area of the region under the curve y= root 9-x^2 . By using appropriate area formulae, find the value of this area.
-KgkG-

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4223 on: June 02, 2019, 03:26:06 pm »
+1
Hey there!

Note that this is in fact a semicircle with radius 3, centred at the origin. You can write this as:


But you should probably evaluate the area using the area of a semicircle:


Note: You can't integrate quadratics like that using the reverse chain rule. This only works for linear equations ie. ax+b. Refer to the reference sheet for the appropriate formula! You also shouldn't need to be finding stationary points when integrating!

Hope this helps :)
« Last Edit: June 02, 2019, 03:28:41 pm by fun_jirachi »
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Thankunext

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Re: Mathematics Question Thread
« Reply #4224 on: June 02, 2019, 03:27:13 pm »
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Can someone help with drawing a tree diagram for this question? I tried many attempts but dont think I drew it correctly.
There are 34 men and 32 women at a party. Of these, 13 men and 19 women are married. If 2 people are chosen at random, find the probability that
A) both will be men
B) 1 will be a married woman and the other an unmarried man
C) both will be married.
Thank you.

Kombmail

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Re: Mathematics Question Thread
« Reply #4225 on: June 02, 2019, 07:28:29 pm »
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Hey there!

Note that this is in fact a semicircle with radius 3, centred at the origin. You can write this as:


But you should probably evaluate the area using the area of a semicircle:


Note: You can't integrate quadratics like that using the reverse chain rule. This only works for linear equations ie. ax+b. Refer to the reference sheet for the appropriate formula! You also shouldn't need to be finding stationary points when integrating!

Hope this helps :)

Thanks and yes it does:)
-KgkG-

Kombmail

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Re: Mathematics Question Thread
« Reply #4226 on: June 02, 2019, 07:30:47 pm »
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Can someone explain what it means by limiting velocity pls?
-KgkG-

RuiAce

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Re: Mathematics Question Thread
« Reply #4227 on: June 02, 2019, 07:56:45 pm »
+4
Can someone help with drawing a tree diagram for this question? I tried many attempts but dont think I drew it correctly.
There are 34 men and 32 women at a party. Of these, 13 men and 19 women are married. If 2 people are chosen at random, find the probability that
A) both will be men
B) 1 will be a married woman and the other an unmarried man
C) both will be married.
Thank you.
Note that there is no single correct tree diagram. This tree diagram is quite generic, but is completely overkill for parts A and C. Yet simpler tree diagrams would probably be insufficient for part B.

Can someone explain what it means by limiting velocity pls?
It means the velocity as \(t\to \infty\).

Thankunext

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Re: Mathematics Question Thread
« Reply #4228 on: June 03, 2019, 06:00:22 pm »
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Note that there is no single correct tree diagram. This tree diagram is quite generic, but is completely overkill for parts A and C. Yet simpler tree diagrams would probably be insufficient for part B.
(Image removed from quote.)It means the velocity as \(t\to \infty\).
Thank you for the tree diagram! Will the HSC ask us to draw a complex one like that? Because it takes quite some time to get the answers.

stella_atarnotes

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Re: Mathematics Question Thread
« Reply #4229 on: June 03, 2019, 06:03:26 pm »
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Thank you for the tree diagram! Will the HSC ask us to draw a complex one like that? Because it takes quite some time to get the answers.

They usually won't ask you to draw a tree diagram, and if you do it shouldn't be that hard. Tree diagrams should mainly just be used as part of your working out, and for most questions there would be another way to go about it if you have to draw a tree with too many branches.