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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?
Thanks, Bob
When encountering vectors in maths, at the introductory level at least, is it appropriate to think of them in terms of displacement?
Take a triangle ABC, with AC being the base
Vectors AB and BC added together give the resultant vector AC, yes?
(imagine arrows going to the right above AB etc)
But this doesn’t mean that the lengths of AB and BC added together equal the length of BC (the added lengths will be longer than BC), yes?
What does it mean then?
Does it mean, or can it mean, the same as we’re taught in physics when dealing with displacement? The distance we end up from our point of origin A when we travel to C is the same regardless of whether we go directly to C, or via B?
So the distance covered going directly from A to C might be, say, 10m
And the distance going from A to C via B might be 12m
But the displacement is the same, i.e, 10m?
...the next calculation?
You perform a calculation
Your answer is 4.5... (long awkward number)
You now want to divide 5 by 4.5...
Is there a shortcut (rather than noting down the long awkward number, and typing in 5 divided by the long awkward number)?
Thanks, Bob.
So 1/12 = 42/N
1*42 = 42
12*42 = N
N=504?
Check;
504 ponies. Catch, tag and release 42.
Now 42/504, or 1/12, are tagged.
Catch 60 expecting 1/12 to be tagged.
5 are tagged which is what you would expect, on average?
Wyatt wants to work out an estimate for the total number of wild ponies in a forest
In July, Wyatt catches 42 ponies in the forest
He puts a tag on each of these ponies and releases them
In August, Wyatt catches 60 ponies in the forest
He finds that 5 of the 60 ponies are tagged
Work out an estimate for the total number of ponies in the forest
My question; Which branch of maths is this?
Also, can you give me a clue as to where to start regards solving this. Just a hint please, not a full explanation.
I'm struggling to even guess at this one. I did think, '60 ponies, 5 of which are tagged, so, 5/60 tagged, which is 1/12
1/12 of the 60 tagged...
How does this relate to the initial number of 42 caught and tagged, then released..?
Of the intial 42 caught, 100% were tagged...
Why did he only catch 42 in July, but caught 60 in August?
Thanks, guys.
I struggled to do this but managed a guess of 2^1
My thinking was √8 = 2, and another way of writing 2 is 2^1
The answer given was 2^(3/2)
Which I understood, eventually, as meaning (√2)^3
which equals (√2)(√2)(√2)
which equals (√4)(√2)
which equals 2(√2)
which equals 2^1*2^(1/2)
which equals 2^1+(1/2)
which equals 2^(3/2)
My question is; are both correct? My answer at the top, and the one I was given?
Thanks
Thanks, guys.
If we have small boxes and medium boxes in the ratio 2:5 does this exclude certain numbers of each box?
E.g, we could have;
2 small, 5 medium
or;
4 small, 10 medium
or;
200 small, 500 medium
Or any combination as long as there are 2.5 as many medium as there are small.
Does this mean we can't have, for example, 3 small (as that would mean 7.5 medium, and we can't have .5 of a box)?
Or, 1 small, 2.5 medium, or 5 small, 12.5 medium, etc, for the same reason?
Thanks, Bob.
I'll check out those links when I have time.
In the meantime, just a quick question.
Regards our saying that y=f(x), when looking for the inverse function; would it be accurate to say, in general (not just with functions), that, for example, y=x, or y=x+2, or whatever, that this is actually shorthand for y(x)=x, or y(x)=x+2, or whatever?
Thanks, everyone
Regards a straight line being somthing lik, Ax+By+C=0 ; would those kind of equations just be rearrangements of y=mx+c?
I can see that y=mx+c can be rearranged, for example, thus;
m=y-c/(x)
x=y-c/(m)
c=y-mx