Math Is Fun Forum

...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)?

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?

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?

Is the equation for a straight line graph always in the form y=mx+c?

If so, is an equation for a straight line such as y=4 shorthand for y=0x+4?

In a function is the part to the left hand side of the equals sign the OUTPUT?

For example, regards g(x) = x+2, is the following correct;

g(x) = OUTPUT

x = INPUT

x+2 = RELATIONSHIP

I know that if, regards the above, x=4, then we put 4 in and get 6 out, so 4 is the input and 6 is the output; but is g(x) also considered to be the OUTPUT? Or, in this case, g(4)?

I’ve just completed a straight line graph for the equation y=4x-4.

y=mx+c tells me that the gradient(m)is 4 (and the y intercept is -4)

But the y values on the grid go up in 2s (2,4,6,8, etc) with 1 grid square for each value of 2. Whereas the x values on the grid go across in 1s (1,2,3) with two grid squares for each value of 1.

So the straight line graph on the grid looks like a y=x graph, with a gradient of 1, a line of 45 degrees, even though the gradient according to the values is 4, and would therefore be steeper, if drawn to scale.

I’m pretty sure the values on the grid were marked out this way due to the restriction of the page size (the y values went up to 16 and down to -12, so to give a whole square to the value of 1 would take up too much space vertically). But the x values only went from -2 to 3 so space wasn't an issue there.

So why don’t they do the grid to scale, where possible, which would make the line, and therefore the gradient, to scale? I think this would help the novice student grasp the steepnees of lines relative to various equations etc, and get the hang of graphs that appear frequently in maths.

I redrew the grid giving the x values 1 square for every value of two, like the y values to square ratio, and, for me, it looks better, and feels right. The other way just looks, and feels 'wrong'.

Also, just double checking on the difference between the grid and the graph. The grid is the thing we’re presented with on the page, the thing we have in front of us before we start drawing little dots or crosses on, before we draw a line through them; and the graph is the line itself, yeah? Or is the whole completed thing the graph?