[Maths HELP!] Factorising...

[Issac]

EDIT: Doublepost due to server downtime? remove ktxbye

 

[Hyperlisk_]

All it want's is for you to get x... it's actually quite easy...
now for the a)

pythagoras theorem or whatever the name is in english= X^2 + Y^2 = Z^2
where X= OT, Y = AT. Z = OA.

this is: x² + (x² + 10x + 25) = (x² + 16x + 64)
now move the right side over to the left by subtraction:
x² + (x² + 10x + 25) - (x² + 16x + 64) = 0
and solve it => x² - 6x - 39 = 0

b)

using the formula above:
(x - 3)² - (-3² + 39) = 0

(x - 3)² = -3² + 39
(sqrt() = square root of...)
x - 3 = sqrt(-3² + 39)

x - 3 = (+ or -) sqrt(9 + 39)

x = (+ or -)sqrt( 30 ) +3

and this gives the answer X = sqrt( 48 ) +3 (+ and not - since a radius can't be negative..)
(And maybe you can round sqrt(48) to 7.... since sqrt (49) is 7... i dont know... and that'd give the radius x = 10....

though it seems weird.. someone has to confirm this

Assuming it's a right triangle

 

[Issac]

it is.

since it's a radius and a tangent... a tangent is .."planar?" to the curve.. and the radius is straight out

so it's a right triangle!

side note: it's a shame threads like these appear in the testing area, since I'm kinda active in these, but still has a relatively low post count compared to many newcomers...

 

[Hyperlisk_]

it is.

since it's a radius and a tangent... a tangent is .."planar?" to the curve.. and the radius is straight out

so it's a right triangle!

That doesn't make it a right triangle... Right triangles have a single 90 degree angle. Just because the radius touches the tangent line doesn't make it have a 90 degree angle XD

 

[Dylaan]

Ugh, we've got our Maths paper on Thursday and I need to know the same sorts of stuff... Factorising is a bitch, I'm pretty right with everything else though.

 

[Agjsdfd]

COOL Issac.

The "b)" part completely makes sense.

Need to do another question to understand "a)" part.
Thanks

@Hyperlisk_
This question also involves circle geometry. Which I didnt realize until Issac solved it...

 

[Agjsdfd]

Ok, got it.

 

[moozxy]

Ok another question, as I see Issac used it in the last question.

What do you do when you have:

(3x+x)² ?

Whats the answer after expanding?

This is what I am talking about :
"x² + (x² + 10x + 25) = (x² + 16x + 64)"

OA = Z

Z² = (x+8)²
z² = x² + 8x² + 64
isnt it?

I haven't read the rest of the thread but the bolded part is wrong.
If you have (x+8)², you just do (x+8)(x+8)
Which is x²+16x+64

 

[Agjsdfd]

Roflmao,
thats why. yep thats it. It finally mathches the answer.
Thanks. I get it now.
Always make mistake with square of brackets, since 8th grade...
edit:
No need to continue with quadratic equations. Way of solving any question is very easy.
Just wasnt sure about the tangent line, which makes the angle 90°, and clearly a very easy thing to solve. As its rightangled triangle.

 

[Deleted member 110780]

If you're a visual person, you should get into the habit of doing this for a while:

Add the terms and it equals x²+16x+64

 

[Agjsdfd]

LoL. Cool.
But I usually learn by heart. Also formulas in other subjects, I just learn by heart.

Eg. V = IR , R = V/I , I = V/R
or
F = MA, A = F/M, M = F/A

Theres that triangle method, which everyone uses. Looks easy when other people do it, than when I try it, get mostly wrong.
So visual doesnt really work for me..

 

[Issac]

it is.

since it's a radius and a tangent... a tangent is .."planar?" to the curve.. and the radius is straight out

so it's a right triangle!

That doesn't make it a right triangle... Right triangles have a single 90 degree angle. Just because the radius touches the tangent line doesn't make it have a 90 degree angle XD

I am well aware of that.
and I made an image since I'm not good explaining in english.

There, an tangent is always supposed to look like that, and T is in the middle of that line. and the radius goes to T, thus making it a 90 degree angle.

 

[Agjsdfd]

Yep thats true.
Usually we learn it in year 10, circle geomatry, right after the angle chapter(alternate angles, parallel angles etc...)

 

[Issac]

^^ yeah, I do remember some of that old stuff haha... we use it a lot in the university studies as well

 

[Agjsdfd]

LoL.
Got another question, its about averages using frequency.

Median is = 1/2 (n + 1).

But my teacher told something about not using the "+1" when finding it using graphs.

Same goes for lower quartile and upper quartile.

1/4(n+1)
3/4(n+1)

So when do we use the "+1"

Is it wrong when we dont use +1?
As I remember doing some past papers with my teacher not using the +1.

Btw,
whats the difference between:

-2²
and
(-2)²

as the calculator gives -2² = -4
and
(-2)² = 4

 

[Issac]

Well yes.. I think it's because you see the median in graphs, while you don't do it with numbers when frequency is in the picture. (since 0 is a frequency as well you have to take it into consideration... i MSPainted a picture again ^^):

EDIT:

that question is really simple actually... you'll slap your forhead i believe

-2²

the sqare is on the 2 alone, not the minus sign... so it's the same as -(2)² = - (2*2) = -4

(-2)²

the sqare is on both the 2 and minus sign... (-2)² = -2 * -2 = --4 = 4
(minus times minus is plus

)

 

[rhyguy]

-2² shouldnt equal -4

when you multiply/divide a negative by a negative number it should be positive

I think you calculator reads -2² as 0-2²

 

[Issac]

-2² shouldnt equal -4

when you multiply/divide a negative by a negative number it should be positive

I think you calculator reads -2² as 0-2²

Calculators often do that... equal -2² with -4 becuase it thinks you mean "you have something MINUS 2²" which is something - 4
so with calculators ALWAYS use parantheses on the right places

 

[Agjsdfd]

Alright cool.
Nicely explained. Thanks.

I had some questions about y = mx+c, but figured out myself.
But just need to make sure I am right.

So:
gradient of a line is = Difference in Y axis/Difference in X axis.

is that correct?

 

[Issac]

If you mean the slope.. yes!

We've been talking about other forms of gradients in some university classes...

And I doubt you mean those

but yeah, you're right!

EDIT:

This is what we've done

http://en.wikipedia.org/wiki/Gradient