Prelim 2016 Maths Help Thread (4 Viewers)

eyeseeyou · Jun 7, 2016

davidgoes4wce said:
What is integrand's qualifications? I'm guessing he has to have a PhD

I don't think he wants to reveal due to privacy reasons

Green Yoda · Jun 7, 2016

eyeseeyou said:
Okay, he's an expert in maths and physics and I don't think chem so much

Also to me "by inspection" doesn't show any proper knowledge since I don't find reasoning "By inspection"

Its probably obvious or a little research doesn't go astray

leehuan · Jun 7, 2016

Rathin said:
Its probably obvious or a little research doesn't go astray

You know you're such a stalker for doing that extensive research mate

You remind me of...kawaiipotato

davidgoes4wce · Jun 7, 2016

Im guessing PhD, or he has a studied at a Top 20 ranked university in the world, or he has worked in the high school setting somewhere in the past, or studied a maths major of some sort..........

Green Yoda · Jun 7, 2016

leehuan said:
You know you're such a stalker for doing that extensive research mate

You remind me of...kawaiipotato

he called me a stalker for stalking all the chicks he reeled

LOL

davidgoes4wce · Jun 7, 2016

eyeseeyou said:
So currently I have a mind blank right now. Need help with this question:

f(x)=-x^2,x≥0

$Domain and range of the function f(x)$

$Domain : \{ x \in \mathbb{R}, x \geq \ 0} \}$

$Range: \{y \in \mathbb{R}, y \leq \ 0} \}$

$Determining the inverse function$

$$ Domain and Range of the inverse function $ f^{-1} (x)$

$Domain: \{x \in \mathbb{R}, x \leq \ 0} \}$

$Range : \{ y \in \mathbb{R}, \geq \ 0} \}$

$x=-y^2$

$-x=y^2$

$\sqrt{-x}=y$

davidgoes4wce · Jun 7, 2016

eyeseeyou said:
So currently I have a mind blank right now. Need help with this question:

2.f(x)=tan⁡(π/2),-π≤x≤π

You have to re-write that question again, I can't read it

$$ I'm assuming you mean graph $ tan^{-1}\frac{\pi}{2} $ between $ -\pi \leq x \leq \pi$

If that were the case there would just be a horizontal line

leehuan · Jun 7, 2016

Rathin said:
he called me a stalker for stalking all the chicks he reeled LOL

HAHA seems legit.

eyeseeyou · Jun 8, 2016

davidgoes4wce said:
$I decided to do the first one for you$

$y=\frac{x-2}{x+2}$

$Domain:\{{x \in \mathbb{R}}: x \neq -2 \}$

$Range: \{{y \in \mathbb{R}}: y \neq -1 \}$

$To determine the inverse function$

$x=\frac{y-2}{y+2}$

$x(y+2)=y-2$

$xy+2x=y-2$

$yx-y=-2-2x$

$y(x-1)=-2-2x$

$y=\frac{-2(1+x)}{x-1}$

$$ Domain of the Inverse Function: $ \{{x \in \mathbb{R}}: x \neq -1 \}$

$Range:\{{y \in \mathbb{R}}: y \neq -2 \}$

Here is the graph below of the function and the inverse.

why is the range y is not equal to 1?

eyeseeyou · Jun 8, 2016

davidgoes4wce said:
You have to re-write that question again, I can't read it

$$ I'm assuming you mean graph $ tan^{-1}\frac{\pi}{2} $ between $ -\pi \leq x \leq \pi$

If that were the case there would just be a horizontal line

No just tan (pi/2) where the restrictions are -pi is less than or equal to x is less than or equal to pi

eyeseeyou · Jun 8, 2016

eyeseeyou said:
Some more maths Q's (circle geometry without the diagram)

1. ABCD is a cyclic quad. Angle ABCE is parallelogram. Prove CE=ED
2. Two circles O and C touch A. The smaller circle also touches the radius OA at P. The common tangent at A cuts the radius OD produced to F. Prove O,C and A are collinear
3. Prove tha a parralelogram which is a cylic must be a rectangle
4. A,B, C are 3 points on a circle and triangle ABC is acute angled. AD is drawn parrallel to BC&CD is drawn parrallel to BA. Prove D is not cyclic
5. C us any part on a cirle with a diameter AB. P&Q are points on minor arc AC&BC. Prove angle APC+ angle CQB=270 degrees

eyeseeyou said:
So currently I have a mind blank right now. Need help with this question:
Find the inverse function of the following. Also state the domain and range of the inverse function:
Y= (x-2)/(x+2)
Also
sketch on one graph y=f(x)and y=f^(-1) (x):Make sure the diagrams are to scale
1.f(x)=-x^2,x≥0
2.f(x)=tan⁡(π/2),-π≤x≤π

Did someone forget to answer circle geomretry and this question?

eyeseeyou · Jun 8, 2016

eyeseeyou said:
Some more maths Q's (circle geometry without the diagram)

2. Two circles O and C touch A. The smaller circle also touches the radius OA at P. The common tangent at A cuts the radius OD produced to F. Prove O,C and A are collinear
3. Prove tha a parralelogram which is a cylic must be a rectangle
4. A,B, C are 3 points on a circle and triangle ABC is acute angled. AD is drawn parrallel to BC&CD is drawn parrallel to BA. Prove D is not cyclic
5. C us any part on a cirle with a diameter AB. P&Q are points on minor arc AC&BC. Prove angle APC+ angle CQB=270 degrees

Forget about the first question

Drongoski · Jun 8, 2016

leehuan said:
Well, his identity is one of the biggest secrets ever on BoS.

He is the Saviour Robot, sent down from Heaven, to save all of you who are struggling in maths.

Drongoski · Jun 8, 2016

eyeseeyou said:
Some more maths Q's (circle geometry without the diagram)

1. ABCD is a cyclic quad. Angle ABCE is parallelogram. Prove CE=ED
2. Two circles O and C touch A. The smaller circle also touches the radius OA at P. The common tangent at A cuts the radius OD produced to F. Prove O,C and A are collinear
3. Prove tha a parralelogram which is a cylic must be a rectangle
4. A,B, C are 3 points on a circle and triangle ABC is acute angled. AD is drawn parrallel to BC&CD is drawn parrallel to BA. Prove D is not cyclic
5. C us any part on a cirle with a diameter AB. P&Q are points on minor arc AC&BC. Prove angle APC+ angle CQB=270 degrees

Q3)

Opp angles of cyclic quadrilaterals are supplementary. The only parallelograms that have this property are rectangles. So the diagonals of such parallelograms must be diameters of the circumscribing circles.

davidgoes4wce · Jun 8, 2016

eyeseeyou said:
why is the range y is not equal to 1?

$The Domain and Range of $ f(x) $ and $ f^{-1}(x) $ simply swap.$

davidgoes4wce · Jun 8, 2016

eyeseeyou said:
No just tan (pi/2) where the restrictions are -pi is less than or equal to x is less than or equal to pi

$tan \frac{\pi}{2} $ would be undefined in that interval $$

eyeseeyou · Jun 8, 2016

davidgoes4wce said:
$tan \frac{\pi}{2} $ would be undefined in that interval $$

there was an answer. Could you please graph it for me David?

Nailgun · Jun 8, 2016

eyeseeyou said:
Did someone forget to answer circle geomretry and this question?

nah

Nailgun · Jun 8, 2016

davidgoes4wce said:
Im guessing PhD, or he has a studied at a Top 20 ranked university in the world, or he has worked in the high school setting somewhere in the past, or studied a maths major of some sort..........

Or he is just a god among men

kawaiipotato · Jun 8, 2016

leehuan said:
You know you're such a stalker for doing that extensive research mate

You remind me of...kawaiipotato

Actually laughed
But seriously I am not a stalker

Prelim 2016 Maths Help Thread (4 Viewers)

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