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March 28, 2024, 07:31:32 pm

Author Topic: Mathematics Question Thread  (Read 1296563 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #270 on: August 01, 2016, 04:02:39 pm »
+3
Could you please elaborate further for what I have attached below because I don't seem to understand that

Thanks  ;D
Applied the definition of a function?

Where there's x I replace it with x+h?

If f(x)=x^2
Then f(a)=a^2
f(2)=2^2 = 4
f(x+h)=(x+h)^2 = x^2+2xh+h^2


And then I just expanded the whole thing out.

isaacdelatorre

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Re: Mathematics Question Thread
« Reply #271 on: August 01, 2016, 07:21:20 pm »
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Hey,
I'm just having a bit of trouble with this question. Could someone please give me an explanation of how to do this. Thank you!!!

Let g(t) be another function defined for all t ≥ 0. The gradient function is given by g′(t) = 33/10 te−kt .
It is given that g′(t) attains the greatest value at t = 7.5 and g(0) = 0. g′(t)

where k is a positive constant. The diagram below shows a sketch of g′(t) against t.

(i) Show that k = 2/15
(ii) Use the trapezoidal rule with four sub-intervals to estimate the shaded area in the diagram above.
(iii) Explain why your answer to (ii) is an estimate for g(12).
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RuiAce

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Re: Mathematics Question Thread
« Reply #272 on: August 01, 2016, 09:37:00 pm »
0
Hey,
I'm just having a bit of trouble with this question. Could someone please give me an explanation of how to do this. Thank you!!!

Let g(t) be another function defined for all t ≥ 0. The gradient function is given by g′(t) = 33/10 te−kt .
It is given that g′(t) attains the greatest value at t = 7.5 and g(0) = 0. g′(t)

where k is a positive constant. The diagram below shows a sketch of g′(t) against t.

(i) Show that k = 2/15
(ii) Use the trapezoidal rule with four sub-intervals to estimate the shaded area in the diagram above.
(iii) Explain why your answer to (ii) is an estimate for g(12).






liiz

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Re: Mathematics Question Thread
« Reply #273 on: August 02, 2016, 05:22:08 pm »
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Hey there, wondering whether someone could please help me out with part b) of this question that I've attached. Not quite sure how to approach it! Thanks so much :))

RuiAce

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Re: Mathematics Question Thread
« Reply #274 on: August 02, 2016, 06:06:05 pm »
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Hey there, wondering whether someone could please help me out with part b) of this question that I've attached. Not quite sure how to approach it! Thanks so much :))



wesadora

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Re: Mathematics Question Thread
« Reply #275 on: August 03, 2016, 11:27:42 pm »
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2U Question. Halp.
Subjects: 3U Maths, Adv. English, Chemistry, Geography, PDHPE

RuiAce

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Re: Mathematics Question Thread
« Reply #276 on: August 04, 2016, 07:11:20 am »
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2U Question. Halp.
This does not look like a 2U question given that I do not believe spirals are so easy to analyse. However this is the best I could come up with.

An assumption is made that the inclination of the string is constant. The basis of this is that the midpoint is collinear to the endpoints of the string, and the line between them is perpendicular to the base.


« Last Edit: August 04, 2016, 07:17:21 am by RuiAce »

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #277 on: August 04, 2016, 09:03:45 am »
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2U Question. Halp.

Just to extend on Rui's answer (I get the same outcome), you could consider it in a similar way. This is definitely 2U content, but a really weird one, they like to do strange stuff with Pythag for some reason :P it could show up in an Extension exam I suppose, but I see it more as a Band 6 2U question  :)

The string is wrapped around a cylinder right, so what we can almost do (bear with me) is assign a cylindrical coordinate system. This sounds complicated, but it's actually easy if we think about it practically.

Picture grabbing the end of the string at the top and unravelling it from the cylinder by pulling directly outward, not changing it's height, and leaving the other end fixed on the ground. This forms a right angled triangle where the string is the hypotenuse (and hence comes back in Rui's method, but I'm considering the whole cylinder at once).

The height of this triangle is still the same as the height of the cylinder (remember I said don't change the height), so that is h. The base is whatever distance the string travelled around the circumference. What I've almost done is initially considered the x (horizontal) axis as wrapped around the cylinder, and then when I unravel it, I've moved back to our regular Cartesian system. But the distance is the same, that string has wrapped itself around that cylinder twice, so the 'horizontal' distance travelled is double the circumference. I've taken the horizontal distance as measured around the cylinder (double the circumference), and stretched it out into a straight line.

Then, as Rui said, we use Pythagoras:



To simplify all that, I copied Rui's method but considered the whole cylinder at once, just to make it more practical. You COULD consider it in terms of changing coordinate systems, but that's unnecessary if you can picture unravelling the string. I threw it in to make myself sound smart ;)

conic curve

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Re: Mathematics Question Thread
« Reply #278 on: August 04, 2016, 06:51:37 pm »
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How do I differentiate this?

RuiAce

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Re: Mathematics Question Thread
« Reply #279 on: August 04, 2016, 06:55:25 pm »
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jakesilove

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Re: Mathematics Question Thread
« Reply #280 on: August 04, 2016, 06:56:15 pm »
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Alternatively, you can just use a straight application of the Quotient rule!
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leila_ameli

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Re: Mathematics Question Thread
« Reply #281 on: August 05, 2016, 08:38:56 pm »
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Heyyy  :) :)

I need some help with how i should approach the following;
The parabola P has the equation y^2=8(x+2).
  i) write down the coordinates of the vertex of P.
  ii) find the coordinates of the focus of P.
  iii) write down the equation of the directrix of P.
  iv) sketch the parabola P showing the features found above, as well as any x or y intercepts.

cheers

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #282 on: August 05, 2016, 08:50:03 pm »
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Heyyy  :) :)

I need some help with how i should approach the following;
The parabola P has the equation y^2=8(x+2).
  i) write down the coordinates of the vertex of P.
  ii) find the coordinates of the focus of P.
  iii) write down the equation of the directrix of P.
  iv) sketch the parabola P showing the features found above, as well as any x or y intercepts.

cheers

Hey there!! No worries I'll give you a hand! ;D

Before we do, we notice that the equation is in the typical form of a 'sideways' parabola:



If we consider it this way, we can immediately read off the coordinates of the vertex (h,k) as (-2, 0):



We can also determine the focal length:



Now, remember that the focus is 'a' units away from the vertex. This is a right facing parabola (try some random points to check), so it is 2 units to the right of the vertex:



The directrix is 2 units the other way (remember, in this case, the directrix is a vertical line since the parabola is sideways):



All of this should help you sketch ;D does that help?

leila_ameli

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Re: Mathematics Question Thread
« Reply #283 on: August 05, 2016, 10:30:59 pm »
+1
Very much so, yes!!!! Thank you so much :D 


Hey there!! No worries I'll give you a hand! ;D

Before we do, we notice that the equation is in the typical form of a 'sideways' parabola:



If we consider it this way, we can immediately read off the coordinates of the vertex (h,k) as (-2, 0):



We can also determine the focal length:



Now, remember that the focus is 'a' units away from the vertex. This is a right facing parabola (try some random points to check), so it is 2 units to the right of the vertex:



The directrix is 2 units the other way (remember, in this case, the directrix is a vertical line since the parabola is sideways):



All of this should help you sketch ;D does that help?

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Re: Mathematics Question Thread
« Reply #284 on: August 06, 2016, 02:30:13 am »
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If they a function is monotonic increasing does that mean f(x)>0 or f(x)>=0? If so why, I can't seem to distinguish between the two