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March 29, 2024, 03:11:09 am

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MB_

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Re: Mathematics Question Thread
« Reply #4245 on: June 12, 2019, 06:37:48 pm »
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Guys help pls! If the question is given f(t)=sin2t, fins the rate of change when t=pi/6, I end up with 11pi/6 but the answer is one in the book?
Rate of change is \(f'(t)=2\cos(2t)\), at \(t=\frac{\pi}{6}\) then \(f'(\frac{\pi}{6})=2\cos(\frac{\pi}{3})=1\)
« Last Edit: June 12, 2019, 06:40:41 pm by MB_ »
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emilyyyyyyy

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Re: Mathematics Question Thread
« Reply #4246 on: June 12, 2019, 06:49:46 pm »
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Hi all,

I need help in where the values of the x-axis line up to the graph in this question (i hope that makes sense):
Sketch the curve y = 4 + 3sin2x for 0<x<2p

Like I know what the graph should look like, just not sure where the x-values line up

Thanks!!

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4247 on: June 12, 2019, 11:39:16 pm »
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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 »
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kector

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Re: Mathematics Question Thread
« Reply #4248 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 #4249 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 #4250 on: June 18, 2019, 02:42:49 pm »
+3
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 #4251 on: June 18, 2019, 03:34:35 pm »
+2
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 :)
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Abhiram

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Re: Mathematics Question Thread
« Reply #4252 on: June 18, 2019, 06:30:34 pm »
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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 #4253 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 #4254 on: June 19, 2019, 06:48:53 pm »
+1


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 »
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Thankunext

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Re: Mathematics Question Thread
« Reply #4255 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 #4256 on: June 19, 2019, 09:04:05 pm »
+1
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 #4257 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 #4258 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.

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Re: Mathematics Question Thread
« Reply #4259 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 it’s 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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