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October 16, 2019, 08:10:33 pm

Author Topic: Mathematics Question Thread  (Read 591236 times)  Share 

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fun_jirachi

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Re: Mathematics Question Thread
« Reply #4260 on: June 12, 2019, 11:39:16 pm »
+1
Still not quite sure what you're asking but will do my best to answer :)

If ever in doubt, always plot some points. With sine curves (and trigonometric curves in general) multiples of pi/2 are always good x-values to test out, as they're usually the x-intercepts or turning points of the curve.

eg.


The curve is also the original sine curve compressed by a factor of two, stretched vertically by a factor of 3, then shifted up by 4 units. If you like, the amplitude gets tripled, the period gets halved and it gets shifted up 4 units. ie. x-values will line up with triple the y-value on the curve sin2x shifted up 4.

I hope this makes some sort of sense :)
« Last Edit: June 12, 2019, 11:42:12 pm by fun_jirachi »
Failing everything, but I'm still Flareon up.

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kector

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Re: Mathematics Question Thread
« Reply #4261 on: June 17, 2019, 10:01:38 pm »
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Hi I'm really confused on doing Part III and sketching in general... Thanks for any help. 2004 HSC 7(b) **hopefully the screenshot went thru**

Abhiram

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Re: Mathematics Question Thread
« Reply #4262 on: June 18, 2019, 02:03:10 pm »
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hey Jake i need help doing this question......(i have attached an image i that doesn't work the question is written below

Sarah borrows $450000 from a bank. The loan is to be repaid in 20 years. The interest rate is 6%p.a. compounded monthly. There is no repayment for the first three months. Let A[n] be the amount owing after n months and M be the monthly repayments.
           (i)          Find an expression for A[4] 
          (ii)         Show that A[5] = 450000(1.005)^5 - M(1+1.005)
          (iii)        Find the monthly repayments if the loan is to be repaid in 20 years.                                                                                                                                               

InnererSchweinehund

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Re: Mathematics Question Thread
« Reply #4263 on: June 18, 2019, 02:42:49 pm »
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Sarah borrows $450000 from a bank. The loan is to be repaid in 20 years. The interest rate is 6%p.a. compounded monthly. There is no repayment for the first three months. Let A[n] be the amount owing after n months and M be the monthly repayments.
           (i)          Find an expression for A[4] 
          (ii)         Show that A[5] = 450000(1.005)^5 - M(1+1.005)
          (iii)        Find the monthly repayments if the loan is to be repaid in 20 years.                                                                                                                                               

Hi!

Unfortunately I'm not Jake... but I did do the HSC last year so hopefully my memory is still up to scratch.
I have attached my working and answer to your question below.
Hopefully I got the correct answer ( ??? ) and this can help you out a bit.

If it doesn't, or it's not right, let me know!!  :)

Ps. Sorry if the image is bad quality - I had to resize it so it would attach. Also let me know if you need a better one!!

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4264 on: June 18, 2019, 03:34:35 pm »
+1
Hi I'm really confused on doing Part III and sketching in general... Thanks for any help. 2004 HSC 7(b) **hopefully the screenshot went thru**

Remember that when you're sketching the acceleration, you're essentially sketching the derivative of velocity ie. f'(x) for the graph you already have. As a start, try looking at the graph between x=0 and x=1 + x=3 and x=5: in these restricted domains the derivative is zero since the velocity is constant. As the velocity becomes more negative, you want to make sure the acceleration is somewhere below the x-axis, and at any points of inflexion there must be a max/min for the acceleration :)

Have a go, and if you need more help ask away :)
Failing everything, but I'm still Flareon up.

HSC 2018: Modern History [88] | 2U Maths [98]
HSC 2019: Physics | Chemistry | English Advanced | Maths Extension 1 | Maths Extension 2

Abhiram

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Re: Mathematics Question Thread
« Reply #4265 on: June 18, 2019, 06:30:34 pm »
0
Hi!

Unfortunately I'm not Jake... but I did do the HSC last year so hopefully my memory is still up to scratch.
I have attached my working and answer to your question below.
Hopefully I got the correct answer ( ??? ) and this can help you out a bit.

If it doesn't, or it's not right, let me know!!  :)

Ps. Sorry if the image is bad quality - I had to resize it so it would attach. Also let me know if you need a better one!!

thanks for the reply the image is perfect.

Thankunext

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Re: Mathematics Question Thread
« Reply #4266 on: June 19, 2019, 06:21:03 pm »
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Hello, can someone help with this probability question please. I'm really stuck. :'(
Tim plays a video game 3 times and the probability that he wins at least once is 37/64. What is Tim's probability of winning one game?

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4267 on: June 19, 2019, 06:48:53 pm »
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Hope this helps :)

EDIT: If P(lose) = x, then P(losing all n games) = xn. Conversely, if P(losing all n games) = x, then P(lose) is the nth root of x. In this case, we take the cube root of 27/64.
« Last Edit: June 19, 2019, 09:03:40 pm by fun_jirachi »
Failing everything, but I'm still Flareon up.

HSC 2018: Modern History [88] | 2U Maths [98]
HSC 2019: Physics | Chemistry | English Advanced | Maths Extension 1 | Maths Extension 2

Thankunext

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Re: Mathematics Question Thread
« Reply #4268 on: June 19, 2019, 07:17:24 pm »
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Sorry but how did you get the 3/4?

RuiAce

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Re: Mathematics Question Thread
« Reply #4269 on: June 19, 2019, 09:04:05 pm »
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Sorry but how did you get the 3/4?
\[ P(\text{No wins in 3 games}) = [P(\text{Does not win one game})]^3,\\ \text{therefore }[P(\text{Does not win one game})]^3 = \frac{27}{64}. \]
Hence he took cube roots.

Thankunext

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Re: Mathematics Question Thread
« Reply #4270 on: July 08, 2019, 07:20:15 pm »
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Can someone help with this question please? I think you need to use the derivative given to find the answer, but I'm unsure how. Thank you!
The population of a city is P(t) at any one time. The rate of decline in population is proportional to the population P(t), that is, dP(t)/dt = -kP(t). What will the percentage rate of decline in population be after 10 years?

Thankunext

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Re: Mathematics Question Thread
« Reply #4271 on: July 08, 2019, 09:12:15 pm »
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Can someone help with this one please. Thanks.
If dQ/kQ, prove that Q=Ae^kt satisfies this equation by integrating dQ/dt=kQ.

Kombmail

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Re: Mathematics Question Thread
« Reply #4272 on: July 08, 2019, 11:43:40 pm »
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Can someone help with this one please. Thanks.
If dQ/kQ, prove that Q=Ae^kt satisfies this equation by integrating dQ/dt=kQ.
I think itís one of those were you differentiate the first given formula and break it down to the given answer ie. Ae^kt = kAe^kt = k(Ae^kt) = kQ since Q = Ae^kt
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LoneWolf

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Re: Mathematics Question Thread
« Reply #4273 on: July 11, 2019, 05:49:56 am »
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Hey, think this is the right forum.
Can you help me understand why the second derivative of dy/dx is d^2y/dx^2 not dy^2/dx^2
Im in year 11 and doing a journal assessment!  :D
« Last Edit: July 11, 2019, 06:10:10 am by DrewN20 »

blyatman

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Re: Mathematics Question Thread
« Reply #4274 on: July 11, 2019, 10:51:27 am »
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It's just mathematical convention for the notation of the second derivative. dx^2 is literally the square of the differential. So dy^2/dx^2 would actually be (dy/dx)^2, which is the square of the first derivative. This is not the same as the second derivative, which is completely different. As a result, the notation d^2y/dx^2 is used to avoid confusion.
« Last Edit: July 11, 2019, 10:53:24 am by blyatman »
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