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(x+a)^2= x^2 + 2ax + a^2
The 2ax term is missing . Only explanation is a=0. Similarly for 2by.
Bob
Thanks. Where does (x+a) come from (in the general equation it's x-a)?
Keep_Relentless wrote:Other way around: with replacement means putting the item back in, thereby replacing it, yielding independent events.
Without replacement means not putting the item back in, i.e. not replacing it, yielding dependent events.
Yeah, it's all clear now but I must put myself to the test by answering a few more questions just to be sure.
I think this is called conditional probability, when we don't put the first marble back in (so the probability of the second pick is conditional on the first).
I think the probability is small but positive, but the probability drops the later in the day it is.
Probability is; Outcome / Possible Outcomes, yeah?
E.g, Single zero roulette wheel when betting on 36; P(1/37)
But if you say the probability for a Jesus comeback small does that mean you are assuming it is possible? If so, why?
It surprises me when scientists, sometimes reknowned ones, say, "Well, anything is POSSIBLE." Is anything possible?
From the format the centre is (0,0). The general equation is (x-a)^2 + (y-b)^2 = r^2. Centre (a,b)
Bob
Thanks, Bob.
I get that the a and b in the general equation are the centre of the circle, but how do we know a=0, and b=0?
@mathxyz
Pre-calculus. GCSE Higher Tier (UK)
The line L is a tangent to the circle
(X^2) + (y^2) = 68 at the pont P
P is the point (2,8)
Work out the equation of the line L
Q. How do we do this without knowing where the centre of the circle is?
Thanks.
I found out that I had to split the bottom left right angle into 2 45 degree angles, and draw a diagonal from there (point B)
Above that line is considered nearer AB, below it nearer BC.
I'm not sure I understand that though.
Is it because you can't have more than infinity, so infinity plus any number/concept won't equal more than infinity?
You could add a trillion to infinity but end up with no more than infinity
You could add a quadrillion to infinity but end up with no more than infinity
You could add the largest number we have a name for to infinity but end up with no more than infinity
And you could add infinity to infinity but end up with no more than infinity
I'm guessing this is a reminder that infinity is not a number, it's an idea?
Here is a scale drawing of a room
The scale is 1cm to 2m
Link for image of drawing (Question 11); https://www.mathsgenie.co.uk/resources/4-loci-and-constructionans.pdf
In case link doesn’t work;
Image; a rectangle, corners marked A at the top left, B at the bottom left, C at the bottom right, and D at the top right.
A to D; 11cm
A to B; 5.5cm
I’m not sure if the dimensions are important or not.
A chair is going to be placed in the room
The chair must be closer to AB than BC
The chair must be less than 14m from D
Shade the region where the chair can be placed
*
I first worked out the scale of the distance from D, i.e, 7cm for the 14m.
Then set my compasses at 7cm and drew an arc to represent 14 m from D
I’m assuming the chair has to be placed somewhere in that region between D and the arc
But I’m puzzled regards the chair having to be closer to AB than BC
Does AB mean all the points on the line AB?
Does BC mean all the points on the line BC?
If so, is the point B on both lines AB, and BC?
As this comes under Loci and Construction I’m assuming I have to set my compasses in relation to AB / BC / and the arc I've drawn, and make some small arc marks?
Beyond that I’m stuck
Thanks guys.
Thanks, guys.
How do we know which is the height, and which is the base?
h=54/b
h=54/12=4.5
h=54/4.5=12
??
Also, although this answer comes from a quadratic equation and the quadratic formula can we get it from a simultaneous equation? I ask because someone in class said it was a sim.eq.
A rectangle has height h and base b
The area of the rectangle is 54cm^2
The perimeter of the rectangle is 33cm
h=54/b
Work out the height and base of the rectangle
*
hb=54
2h+2b=33
h=54/b
therefore,
2(54/b)+b=33
(108/b) + b = 33
I’ve got a feeling I’ve gone down a blind alley here.
Any hints?
Thanks, Bob.
When rotating a shape, instead of using tracing paper to physically rotate the shape, can we use maths to work out the co-ordinates of where the shape will be rotated to?
I'm talking about GCSE maths, so, fairly basic algebra perhaps, maybe vectors too?
Also, when we are shown the rotation and asked to describe it, rather than using trial and error (with tracing paper) to find the co-ordinates about which the the shape has been rotated can we use maths instead to work it out?
Thanks a lot, Bob.
And, Doh! I forgot to post the link to the question (and graph);
https://www.mathsgenie.co.uk/resources/9-velocity-time-graphs.pdf
Question 4.
Q. Work out the average acceleration during the 50 seconds?
I see that you can find this out by drawing a tangent to the graph, and working out the gradient of the line. And you can check this by a=delta v/(t)
Q. Estimate the time during the 50 seconds when the instantaneous acceleration = the average acceleration?
So, when does the inst.acc = 0.6m/s/s?
How do you find this out?
Thanks, guys.
I applied the formula and it worked, obviously.
So trial and error seems the order of the day?
I've been given this question.
Here is a sequence;
2,5,11,23,…
Find the next two terms.
*
I can see that each term is 2 times the previous term, plus 1.
But I can’t find the formula for the nth term.
I know that with arithmetic sequences the difference is the same each time
I know that with a geometric sequence the terms double, each time, or treble each time, or, etc, etc, and the formula is Un=ar^n-1
I know that with a quadratic sequence the second difference is the same each time and the formula is an^2+bn+c
But I don't know how to find the formula for the nth term for this sequence
Thanks, guys.
What does this mean? And does it have to be y?
By rewriting, for example, f(x)=2x+3, as y=2x+3, are we simply stating that something = 2x+3; and in the first case we’re calling that something f(x), and in the second case we’re calling it y?
Does the y have anything to do with the y axis in x,y coordinates? Or is just a randomly chosen letter? Could it just as well be z, or a, or b, etc?
Not the area of a circle, but the surface area of a circle.
Thanks, guys.
The force, F newtons, exerted by a magnet on a metal object is inversely proportional to the square of the distance d cm
When d=2cm, F=50N
Express F in terms of d
***
I got as far as F = 200/(d^2)
But then wasn't sure if that was enough. Do I have to somehow isolate d, so that F is expressed in terms of d, not in terms of d^2?
On the iteration page it suggests using the following method to establish the square root of a number;
Example: to find a Square Root:
a) start with a guess
b) divide by the guess
c) add that to the guess
d) halve that for the new guess
e) now repeat (iterate) from step (b)
For the square root of 10, starting with a guess of 4 we get:
• 4
• 3.25
• 3.163
• 3.1623
etc...
My question. Regards, "b) divide by the guess" ; divide what by the guess?
Thanks, Bob.
That’s helpful; thinking of the vectors around a square adding to zero.
Although I’m slightly confused with your zeros and ones in brackets.
At first sight I thought they were column vectors (the top number meaning, ‘across’, the bottom number meaning, ‘up or down,’ relating to the x and y axis; and positive or negative before the value relating to right/left, up/down).
So I was expecting (1,0)(0,-1)(-1,0)(0,1).
But your numbers are (1,0)(0,1)(-1,0)(0,-1)
Do these amount to the same thing, or are you expressing this using a different method?
!! I think I might have it. I’ve imagined my origin as the top left of the square; have you imagined yours as the bottom left? I’ve started going across to the right, then down, etc. You, I think, have started going across to the left, then up, etc?