Author Topic: Mathematics Question Thread (Read 1307963 times) Tweet Share

RuiAce · « **Reply #1785 on:** April 30, 2017, 09:28:35 pm »

Quote from: Thebarman on April 30, 2017, 09:21:17 pm

Hey guys, can someone help me with the following questions please? I keep getting 0 as the answer, and i'm not sure why.

1) Find the area bounded by the curve x=y^2-2y-3 and the y-axis

2) Find the area bounded by the curve x=-y^2-5y-6 and the y-axis

$\text{A quick sketch of }x=y^2-2y-3\text{ shows the }y\text{-intercepts are at }(0,3)\text{ and }(0,-1)$
$\text{Looking at the sketch, it is clear that}\\ \begin{align*}A&=\left|\int_{-1}^3 (y^2-2y-3)dy \right|\\ &= \left|\left[\frac{y^3}{3}-y^2-3y\right]_{-1}^3\right|\\ &= \frac{32}{3}\text{ units}^2\end{align*}$
$\text{If you are getting 0 then you are probably using a wrong process}\\ \text{and should post up your working for reference.}$

Thebarman · « **Reply #1786 on:** April 30, 2017, 09:39:25 pm »

Ohhh! I was integrating the entire curve as one instead of integrating each part of the equation separately.
After fixing that mistake, I answered both correctly. Thank you very much!

BarnesK01 · « **Reply #1787 on:** May 01, 2017, 01:35:58 pm »

Need help integrating a trig function!!!!

Evaluate giving exact answers, for Sin(pi X) dx with the boundaries, x=0 and x=1/2

jamonwindeyer · « **Reply #1788 on:** May 01, 2017, 01:41:49 pm »

Quote from: BarnesK01 on May 01, 2017, 01:35:58 pm

Need help integrating a trig function!!!!

Evaluate giving exact answers, for Sin(pi X) dx with the boundaries, x=0 and x=1/2

Welcome to the forums Barnes!! Sure thing, here is the working, let me know if it doesn't make sense

$\int^\frac{1}{2}_0\sin{\pi x}dx=\left[-\frac{1}{\pi}\cos{\pi x}\right]^\frac{1}{2}_0\\=\frac{-1}{\pi}\left(0-1\right)=\frac{1}{\pi}$

bananna · « **Reply #1789 on:** May 02, 2017, 04:36:57 pm »

hi can someone pls help with q 7.4, q 1, (f) and (j)?

thank you!!!

jakesilove · « **Reply #1790 on:** May 02, 2017, 04:38:22 pm »

Quote from: bananna on May 02, 2017, 04:36:57 pm

hi can someone pls help with q 7.4, q 1, (f) and (j)?

thank you!!!

Not seeing an attachment!

bananna · « **Reply #1791 on:** May 02, 2017, 04:43:28 pm »

haha so sorry!
i just realised i forgot to attach the screenshot

7.4 (f) and (j)

thank you!

RuiAce · « **Reply #1792 on:** May 02, 2017, 04:47:59 pm »

Quote from: bananna on May 02, 2017, 04:43:28 pm

haha so sorry!
i just realised i forgot to attach the screenshot

7.4 (f) and (j)

thank you!

$\text{A series is arithmetic if successive terms involve a }\textbf{common difference}\\ \text{i.e. there is some }d\text{ such that }\boxed{d = T_2-T_1 = T_3-T_2 = \dots}$
$\text{Of particular interest is the part }\boxed{T_2-T_1=T_3-T_2}$
$\text{If the series written in j is arithmetic, then}\\ \begin{align*}(3t+1)-(2t-3)&=(5t+2)-(3t+1)\\ t+4&=2t+1\\ t&=3\end{align*}$

bananna · « **Reply #1793 on:** May 02, 2017, 05:17:19 pm »

Quote from: RuiAce on May 02, 2017, 04:47:59 pm

$\text{A series is arithmetic if successive terms involve a }\textbf{common difference}\\ \text{i.e. there is some }d\text{ such that }\boxed{d = T_2-T_1 = T_3-T_2 = \dots}$
$\text{Of particular interest is the part }\boxed{T_2-T_1=T_3-T_2}$
$\text{If the series written in j is arithmetic, then}\\ \begin{align*}(3t+1)-(2t-3)&=(5t+2)-(3t+1)\\ t+4&=2t+1\\ t&=3\end{align*}$

thank you!!!

jakesilove · « **Reply #1794 on:** May 02, 2017, 05:17:55 pm »

Quote from: bananna on May 02, 2017, 04:58:43 pm

thank you!

sorry, i mostly didnt understand how to do (f)

Same methodology as Rui outlined above.

$(x-1)-32=51-(x-1)$
$x-33=52-x$
$2x=85$
$x=\frac{85}{2}$

kylesara · « **Reply #1795 on:** May 02, 2017, 06:33:22 pm »

Hi, could i please have help with this question.

A chord 8mm long is formed by an angle of 45* subtended at the centre of the circle. Find
a) The radius of the circle
b) the areas of the minor segment to 1 dp

Thanks

Sukakadonkadonk · « **Reply #1796 on:** May 02, 2017, 08:14:29 pm »

Hi,

What is the purpose of the differential of an exponential growth and decay equation? Can you use it to find something?

Thanks.

RuiAce · « **Reply #1797 on:** May 02, 2017, 10:19:05 pm »

Quote from: Sukakadonkadonk on May 02, 2017, 08:14:29 pm

Hi,

What is the purpose of the differential of an exponential growth and decay equation? Can you use it to find something?

Thanks.

In history, the differential equation is where everything all began. The exponential form P=Ae^(kt) is the solution to the equation.

RuiAce · « **Reply #1798 on:** May 02, 2017, 10:21:55 pm »

Quote from: kylesara on May 02, 2017, 06:33:22 pm

Hi, could i please have help with this question.

A chord 8mm long is formed by an angle of 45* subtended at the centre of the circle. Find
a) The radius of the circle
b) the areas of the minor segment to 1 dp

Thanks

The area of the minor segment is just a formula you need to substitute in to.
$\text{For the radius of the circle, draw a diagram}\\ \text{It should be clear that the cosine rule is needed}\\ 8=r^2+r^2-2r^2\cos45^\circ$

jamonwindeyer · « **Reply #1799 on:** May 02, 2017, 10:47:02 pm »

Quote from: Sukakadonkadonk on May 02, 2017, 08:14:29 pm

Hi,

What is the purpose of the differential of an exponential growth and decay equation? Can you use it to find something?

Thanks.

Quote from: RuiAce on May 02, 2017, 10:19:05 pm

In history, the differential equation is where everything all began. The exponential form P=Ae^(kt) is the solution to the equation.

And speaking practically, you use it to find the rate of change of the quantity at any instant! So say the differential form of an equation modelling population growth is $\frac{dP}{dt}=0.1P$ - This means that the population is increasing at a rate equal to 10% of the total at any given time. Sometimes we don't just care how much there is, we care about how quickly it is going up/down

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