Math help (1 Viewer)

deswa1 · Oct 10, 2012

Fawun said:
So what you're saying is, is that any whole number to the power of 5 will have a .2 in the end? lol

No lol- but you are summing 0.2 + 1 + 5 + 25 +...

Everything to the right of the 1 is a whole number. So when you add them you get a whole number. So basically, when you add ALL the terms (including the 0.2 at the front), it has to end in 0.2 but the answer doesn't which is an easy way to tell its wrong.

Fawun · Oct 13, 2012

$\text{Show that }\sum^{18}_{n=1} n^{\frac{n}{2}} = 1022 + 511\sqrt{2}$

I used the sum of gp formula but I got an answer with decimals...

deswa1 · Oct 13, 2012

Obviously your answer will have decimals because root 2 is irrational. Check whether your decimal thingo is the same as the RHS

Fawun · Oct 13, 2012

I got something like 4.999998 or something like that and 1022+511 root 2 is 1744.663 ?

Sy123 · Oct 13, 2012

Fawun said:
$\text{Show that }\sum^{18}_{n=1} n^{\frac{n}{2}} = 1022 + 511\sqrt{2}$

I used the sum of gp formula but I got an answer with decimals...

This question isnt a Geometric Series:

$\sum_{n=1}^{18}n^{0.5n}=1^{0.5}+2^1+3^{1.5}+4^2+...+17^{8.5}+18^9$

And the only way I can see doing this question is evaluating all the whole numbers seperately then all the surds then simplifying all them together to get the answer (very very tedious and not a very good question)

(But then again 18^9 is a very very big number so there must be a typo in your question)

Fawun · Oct 13, 2012

Sy123 said:
This question isnt a Geometric Series:

$\sum_{n=1}^{18}n^{0.5n}=1^{0.5}+2^1+3^{1.5}+4^2+...+17^{8.5}+18^9$

And the only way I can see doing this question is evaluating all the whole numbers seperately then all the surds then simplifying all them together to get the answer (very very tedious and not a very good question)

(But then again 18^9 is a very very big number so there must be a typo in your question)

Oh shit yes you're right :L I read the question wrong sorry! It's

$\text{Evaluate }\sum^{18}_{n=1} 2^{\frac{n}{2}} = 1022 + 511\sqrt{2}$

Which I still have no idea what to do. I think that's a gp though...

How did you get the end numbers again? Carrot tried to explain it on the previous page but i still don't get it :s

Sy123 · Oct 13, 2012

Fawun said:
Oh shit yes you're right :L I read the question wrong sorry! It's

$\text{Evaluate }\sum^{18}_{n=1} 2^{\frac{n}{2}} = 1022 + 511\sqrt{2}$

Which I still have no idea what to do. I think that's a gp though...

How did you get the end numbers again? Carrot tried to explain it on the previous page but i still don't get it :s

So, its best to write our series in expanded form in order to get a good gist of it at first (later on you will become stronger with series and hence be able to spare yourself writing it out expanded form)

$\sum=2^{0.5}+2^{1}+2^{1.5}+...+2^{8.5}+ 2^{9}$

So its a Geometric Progression with a common ratio of

$r=2^{0.5} >1$ (by observation or by dividing any two consecutive terms in the series)

The number of terms is 18

The first term is $a_1=2^{0.5}$

Now we are all but ready to plug into our formula, the only thing we have to notice is the difference between

$S_n=\frac{a(r^n-1)}{r-1} \ \ \ \ and \ \ \ \ S_n=\frac{a(1-r^n)}{1-r}$

We have to pick which formula to use, now our absolute value of our common ratio is greater than 1 (which is why I specificed that earlier), so we have to use the first formula. Lets plug in our values:

$S_{18}=\frac{2^{0.5}((2^{0.5})^{18}-1)}{2^{0.5}-1}=\frac{511\sqrt{2}}{\sqrt{2}-1}$

Rationalise our denominator by multiplying both top and bottom by conjugate of denominator

$S_{18}=\frac{511\sqrt{2}}{\sqrt{2}-1} \cdot \frac{\sqrt{2}+1}{\sqrt{2}+1}=\frac{1022+511\sqrt{2}}{\sqrt{2}^2-1^2}=1022+511\sqrt{2}$

Fawun · Oct 19, 2012

"The equation of the latus rectum of the parabola is given by y=-3. The axis of the parabola is 0, and it's vertex is (0,0). Find the equation of the parabola."

wtf.

Demento1 · Oct 19, 2012

Fawun said:
"The equation of the latus rectum of the parabola is given by y=-3. The axis of the parabola is 0, and it's vertex is (0,0). Find the equation of the parabola."

wtf.

lol wut? Had to google this.

deswa1 · Oct 19, 2012

Fawun said:
"The equation of the latus rectum of the parabola is given by y=-3. The axis of the parabola is 0, and it's vertex is (0,0). Find the equation of the parabola."

wtf.

Latus rectum is the line passing through the focus that is parallel to directrix. The axis of parabola is x=0. So the focus of the parabola is (0,-3). Now can you do it?

Fawun · Oct 19, 2012

deswa1 said:
Latus rectum is the line passing through the focus that is parallel to directrix. The axis of parabola is x=0. So the focus of the parabola is (0,-3). Now can you do it?

Damn it i did not see this. I knew that the axis of the parabola is perpendicular to the latus rectum so I full did the point gradient formula and got the same thing as I started with -.-

Thanks des!

Demento1 · Oct 19, 2012

Fawun said:
Damn it i did not see this. I knew that the axis of the parabola is perpendicular to the latus rectum so I full did the point gradient formula and got the same thing as I started with -.-

Thanks des!

lol, I have no idea what you guys are talking about. Going to be crushed by fawun in maths in HSC - oh well.

deswa1 · Oct 19, 2012

Demento1 said:
lol, I have no idea what you guys are talking about. Going to be crushed by fawun in maths in HSC - oh well.

Haha bro you'll be fine. I had no idea what this stuff was in Year 10. I still find the term latus rectum hilarious though

Fawun · Oct 19, 2012

Demento1 said:
lol, I have no idea what you guys are talking about. Going to be crushed by fawun in maths in HSC - oh well.

lolno

Fawun · Dec 6, 2012

"An upturned cone of semivertical angle 45 degrees is being filled with water at a constant rate of 20cm^3/s. Find the rate at which the height, the area of the water surface, and the area of the cone wetted by the water, are increasing when the height is 50cm."

Okay

1. What the hell is an upturned cone? LOL
2. What does the angle have to do with anything?
3. All I know is that I have to differentiate the surface area with respect to time but even then I think I got that wrong haha

seanieg89 · Dec 6, 2012

An upturned cone is a cone with vertex pointing downwards.

The angle determines the shape of the cone, so is of course very relevant. It might be very skinny or very fat. Semivertical angle being 45 means that it is exactly in between these extremes.

Fawun · Dec 14, 2012

"A ladder 8 metres long rests against a wall, with its base x metres from the wall and its top y metres high. Explain why x^2 + y^2 = 64, and differentiate the equation implicitly with respect to time. Find the rate at which the top is slipping down when the base is slipping out at a constant rate of 2cm/s and is 2 metres from the wall."

Siddy123 · Dec 14, 2012

Fawun said:
"A ladder 8 metres long rests against a wall, with its base x metres from the wall and its top y metres high. Explain why x^2 + y^2 = 64, and differentiate the equation implicitly with respect to time. Find the rate at which the top is slipping down when the base is slipping out at a constant rate of 2cm/s and is 2 metres from the wall."

3z+4a=234.67

work from there

Sy123 · Dec 14, 2012

Fawun said:
"A ladder 8 metres long rests against a wall, with its base x metres from the wall and its top y metres high. Explain why x^2 + y^2 = 64, and differentiate the equation implicitly with respect to time. Find the rate at which the top is slipping down when the base is slipping out at a constant rate of 2cm/s and is 2 metres from the wall."

Woah, 4U already? Why are you even learning implicit differentiation o_o

Anyway, if we draw our diagram we immediately notice a right angle triangle.

Hence by Pythagoras: $x^2+y^2=8^2 \ \ \ x^2+y^2=64$

Let us differentiate implicitly:

$x^2+y^2=64 \ \ \ 2x+2y y'=0$

$-yy'=x \ \ \ \therefore \frac{dy}{dx}=-\frac{x}{y}$

We are asked to find the rate of y decreasing when x is increasing at 2cm/s

Establish the given:

$\frac{dx}{dt}=+2$

Establish what we need to know:

$\frac{dy}{dt}=? \ \ $at x=2$$

We use related rates logic

$\frac{dy}{dt}=\frac{dy}{dx} \cdot \frac{dx}{dt}$

dx/dt = 2

Now see above how we found dy/dx = -x/y ?

Well let us use that:

$\frac{dy}{dt}= -x/y \cdot 2 = \frac{-2x}{y}$

Now that is in terms of x and y. We are being asked to find dy/dt WHEN x=2.
$\frac{dy}{dt}= -\frac{4}{y}$

Ok.... how do we get y? Well of course we can use our right triangle from before and this time sub in x=2 to get our y value:

$2^2+y^2=64 \\ \therefore y=\sqrt{60}=2\sqrt{15}$

Sub this in:

$\frac{dy}{dt}=\frac{-4}{2\sqrt{15}}= \frac{-2\sqrt{15}}{15}$

Fawun · Dec 14, 2012

Siddy123 said:
3z+4a=234.67

work from there

wut how did you get that?

Sy123 said:
Woah, 4U already? Why are you even learning implicit differentiation o_o

Because my tutor is being retarded and is testing me on this tomorrow morning (he's trying to make my life miserable) and I don't even want to do 4U.

We use related rates logic

$\frac{dy}{dt}=\frac{dy}{dx} \cdot \frac{dx}{dt}$

Wait how did you get that lol (i probs wasnt paying attention when this was taught)

and thank you!

(i'm going to fail this)

Math help (1 Viewer)

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