2 unit maths revision (4 Viewers)

lalala369 · Feb 21, 2011

ohexploitable said:
$\\\text{Let }y=x\sqrt{x+1}\\y=(x^3+x^2)^\frac12\\y'=\frac{3x+2}{2\sqrt{x+1}}$

wait how did you get the second line from the original equation? i got different working out

Bored Of Fail1 · Feb 21, 2011

bought the x inside the square root by squaring it ( thus it became x^2(x+1) in the sqrt )

appartently he is too good for product rule, though it is interesting method which I havent seen before

ohexploitable · Feb 21, 2011

Chain rule is quicker imo, I try to use it whenever possible.

ohexploitable · Feb 21, 2011

lalala369 said:
wait how did you get the second line from the original equation? i got different working out

$y=(x^3+x^2)^\frac12\\y'=\frac12(x^3+x^2)^{-\frac12}(3x^2+2x)\\y'=\frac{3x^2+2x}{2\sqrt{x^3+x^2}}\\y'=\frac{3x+2}{2\sqrt{x+1}}$

HSCAREA · Feb 21, 2011

hscishard said:
Sorry, I didn't see the function correctly.
(x+2)^2 = 4-x^2
Since I've caused you some confusion, i'll post the solution

x^2 + 4x +4 = 4-x^2
2x^2 +4x = 0
x=0 and -2. Check by subbing it back into each function to make sure they yield the same value. In this case they do.

Now it's $\\\int_{-2}^{0}\sqrt{4-x^2}-(x+2)dx\\\int_{-2}^{0}\sqrt{4-x^2}dx - \int_{-2}^{0}(x+2)dx\$
You can calculate the first one quite easily. It's just 1/4 of the area of a circle. The radius is 2, so pi(2)^2 / 4 = pi
Now it's
$\pi - \int_{-2}^{0}(x+2)dx\$
The integral isn't hard to find, i'll assume you know how to do it.
The answer should be pi-2

okay think I got it now. yes I did get (pi - 2) units^2

so for the quarter of a circle, you don't use integration as it won't give you the exact answer of pi. (requires the user to look at a different angle when solving this question)

HSCAREA · Feb 21, 2011

I think the answer for the book is wrong on this question:

Integrate through indefinite integral: (2x + 5)^7

SpiralFlex · Feb 21, 2011

Let $u = 2x + 5$

= $u^7$

$\frac{dy}{dx} = \frac{dy}{du}*\frac{du}{dx}$

$\frac{dy}{du} = 7u^6$

$\frac{du}{dx} = 2$

$\frac{dy}{dx} = 7u^6 * 2$

$\:\:\:\:\:\:\:\:\:\:=14u^6$

$\therefore \frac{dy}{dx}=14(2x+5)^6$

HSCAREA · Feb 21, 2011

SpiralFlex said:
Let $u = 2x + 5$

= $u^7$

$\frac{dy}{dx} = \frac{dy}{du}*\frac{du}{dx}$

$\frac{dy}{du} = 7u^6$

$\frac{du}{dx} = 2$

$\frac{dy}{dx} = 7u^6 * 2$

$\:\:\:\:\:\:\:\:\:\:=14u^6$

$\therefore \frac{dy}{dx}=14(2x+5)^6$

lol wut? the answer is (2x + 5)^8 / 16 + C

SpiralFlex · Feb 21, 2011

Did you mean integrate?

HSCAREA · Feb 21, 2011

SpiralFlex said:
Did you mean integrate?

ah yes yes, sorry LMAo, I'm all over the shop today. yes find the indefinite integral (primitive function)

SpiralFlex · Feb 21, 2011

$\int (2x+5)^7dx$

Use: $\int (ax+b)^n dx=\frac{(ax+b)^n^+^1}{a(n+1)}+C$

$= \frac{(2x+5)^7^+^1}{2*(7+1)} + C$

$= \frac{(2x+5)^8}{16} + C$

We better inform Sir Isaac Newton that integration somehow changed into differentiation. How is it definite?

cutemouse · Feb 21, 2011

New question:

An ordinary analogue clock shows the time 2:00. Find the angle between the hour and minute hands.

SpiralFlex · Feb 21, 2011

Is this a trick question?

cutemouse · Feb 21, 2011

SpiralFlex said:
Is this a trick question?

I made this question up. ie. it's not from anywhere.

hscishard · Feb 21, 2011

HSCAREA · Feb 21, 2011

jm01 said:
I made this question up. ie. it's not from anywhere.

60 degrees. (180 / 6) = 30 degrees, its 2 o clock - 30*2

note: divide by 6 because there are 6 hours within the 180 degrees. i.e 1,2,3,4,5,6

cutemouse · Feb 21, 2011

hscishard said:
60

Are you serious? 60 degrees? lol... Think.

Squishxmishyx · Feb 21, 2011

ohexploitable said:
What happened to MrBrightside's marathon thread? Anyway,

New Question:

Find the area of the shaded region.

What's the answer in exact value??
$0.36 \pi$ - $\frac{0.6^{2}}{2} (\frac{\pi }{3} - sin\frac{\pi }{3}) ??$

ohexploitable said:
$y=(x^3+x^2)^\frac12\\y'=\frac12(x^3+x^2)^{-\frac12}(3x^2+2x)\\y'=\frac{3x^2+2x}{2\sqrt{x^3+x^2}}\\y'=\frac{3x+2}{2\sqrt{x+1}}$

If we square x, don't we square $\sqrt{ x+1} ??$
Wouldn't it be $x^{2} (x+1)$ (Don't go harsh on me)

$OMG THAT WAS MY FIRST TIME USING TEX BITCHES!$

Question.
a) The sum of the radii of two circles is 100cm. If one of the circles has a radius of x cm, show that the sum of the areas of the two circles is given by
$A=2\pi(x^{2}-100x+5000)$

b) Find the value of x for which A is least.

cutemouse · Feb 21, 2011

HSCAREA said:
60 degrees. (180 / 6) = 30 degrees, its 2 o clock - 30*2

note: divide by 6 because there are 6 hours within the 180 degrees. i.e 1,2,3,4,5,6

lmao. Think.

60 deg would be 4:00

Squishxmishyx · Feb 21, 2011

jm01 said:
lmao. Think.

60 deg would be 4:00

It's 60 degreez.
$12 hours = 360^{\circ}$
$2 hours = x^{\circ}$

Cross multiply x= $360^{\circ}\times 2 \over 12$
$x=60^{\circ}$

Alternatively, grab a protracter and hold it against your clock and measure the angle when it's 2:00.

2 unit maths revision (4 Viewers)

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