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#176 Re: Help Me ! » Rounding up or down » 2024-07-08 23:12:24

paulb203

Thanks, Bob.
Sorry for the late reply.

Ah, yes, the cupboard example makes sense now.

As for full marks for 14.5; would that mean that they are implying that 14.5, in some (rare?) instances would be rounded down? If so, why might rounding down be appropriate for a bag of potatoes?

P.S. I'm picking this up again because I've come across more examples of this.

#177 Help Me ! » pi for a hexagon » 2024-07-07 22:56:30

paulb203
Replies: 3

Is the ratio of the 'diameter' (corner to furthest corner) of a hexagon to its perimeter 3?

pi for a circle = 3.14

pi for a square (calling that sqi) = 4

pi for a hexagon (calling that hxi) = 3?

#178 Re: Help Me ! » Why πr^2? » 2024-07-07 03:42:04

paulb203

Thanks, Bob.

#179 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-07 03:38:12

paulb203
KerimF wrote:
paulb203 wrote:

x=0.12
and,
y=6

Those would produce points on the graph, as opposed to lines, yeah? If so, why are they classed as linear equations, if they're just points?

For instance,
x=0.12 produces a vertical line if drawn on the conventional y_x plane. [but this is a special case, |m|=infinity and |c|=infinity]
y=6 also produces a horizontal line on y_x plane. [here, m=0 and c=6]

Thanks, KerimF

With x=0.12 why does m, the gradient, =infinity? I thought it would equal zero as there is zero slope?

#180 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-07 03:36:02

paulb203
Bob wrote:

5x= 6 means x = 1.2

An equation that gives rise to a line is why the word linear is used.

It's the absence of any powers eg x^2 that allows this to happen.

This usage has spilt over into equations generally so in your examples linear is used because there's no powers .

Bob

Ah, of course; I knew about lines such as x=1.2, and y=6; it was the 5x, and the y/2, and the rearranging that threw me smile

Thanks.

#181 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-05 21:57:49

paulb203

Thanks, Bob, really helpful

Two of the examples of linear equations on the MIF page are;

5x=6
and,
y/2=3

I rearranged them and got,


x=0.12
and,
y=6

Those would produce points on the graph, as opposed to lines, yeah? If so, why are they classed as linear equations, if they're just points?

#182 Re: Help Me ! » Why πr^2? » 2024-07-05 02:17:21

paulb203
Bob wrote:

hi paulb203

It looked to me like this should be 'provable' using algebra but I've come unstuck with it.  I don't think I'm properly following what you're suggesting.

If a square has side 'a' then the 'diameter' = a and so the 'radius' = a/2 and the perimeter = 4a

sqi = the ratio of the ‘diameter’ of the square to the square’s ‘circumference’

So the ratio of diameter/circumference = a/4a = 1/4.  Ah! Think I've just spotted what to do.

Ratio of circumference/diameter = 4

Then 'area' = 4 x (a/2)^2 = 4 (a^2)/4 = a^2

Bob

Thanks, Bob.

And yes, to all of that.

Just checking I've followed your algebra.

Area = 4 x (a/2)^2 = 4 (a^2)/4 = a^2

First part; 4x(a/2)^2 = 4(a^2)/4
So, with (a^2)^2 you’ve squared the a, and squared the 2?

Second part; 4 (a^2)/4 = a^2
You have 4 times, a^2 over 4, and you’ve cancelled the two 4s, yeah?

#183 Re: Help Me ! » Why πr^2? » 2024-07-05 02:09:00

paulb203
KerimF wrote:

You did well. It is always good to see something from different angles.

For instance, since I have no more a person to tell me if my solution of a problem is wrong or right, I used to find out different ways (two in the least) to solve it.

Thanks, Kerim F smile

#184 Help Me ! » Why πr^2? » 2024-07-04 10:02:14

paulb203
Replies: 6

I know there are videos etc explaining why but I thought I would try to find a way to understand this myself.

Imagine a version of πr^2, but instead of being for the area of a circle, it’s for the area of a square.
Call it sqi ar ^2
sqi = the ratio of the ‘diameter’ of the square to the square’s ‘circumference’ (the ‘diameter’ of the square being a vertical or horizontal line through the square’s centre, and the ‘circumference’ being its perimeter).
So, sqi=4 (like π=3.14...)
ar = the ‘radius’ of the square (half it’s ‘diameter’, just like with a circe and it’s radius)

Now take a square 4 cm by 4cm
And apply sqi ar ^2
Which gives us 4x2^2
Which = 16cm^2
Which matches with the 16cm^2 we would get from the conventional way of finding the area of the square.

This helps make sense of πr^2, for me at least
Any thoughts?

#185 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-02 22:14:08

paulb203

Thanks, Jai Ganesh

I'll check those out.

#186 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-02 22:12:56

paulb203
KerimF wrote:

I guess we all know that 20x+25y=1000 is equivalent to:
y = -20x/25 + 1000/25
y = -4x/5 + 40 [m=-4/5 and c=40]

But this equation is of a special case. Its 'y' and 'x' have to be positive integers or zero only. That is not all points of the straight line which this linear equation represents are valid as a solution.

Any idea?

Thanks, KerimF

I see now that y=-(4/5)x+40, thanks

Can all linear equations be rearranged to the gradient-intercept form?

As for the special case and the straight line etc, I'll need to graph it and get back to you

#187 Re: Help Me ! » Linear Equation Real Life Example » 2024-07-02 05:15:59

paulb203

Thanks, Jai Ganesh

So it's too simplistic to say that a linear equation comes in the form y=mx+c?

They also come in the forms, point-gradient, general form, etc, etc?

Can they all be rearranged into the gradient-intercept form?

#188 Help Me ! » Linear Equation Real Life Example » 2024-07-01 21:54:35

paulb203
Replies: 13

I’m told that a linear equation comes in the form y=mx+c where m is the gradient and c is the y intercept. So far so good.

hen I’m told that an example of a practical application of linear equations is as follows.

You’re buying pizza slices and doughnuts for a party. Pizza slices cost 20 rupees. Doughnuts cost 25 rupees. Your budget is 1000 rupees.
You can then use the linear equation 20x+25y=1000 with x being the number of pizza slices and y being the number of doughnuts. So you can have a play around with various ideas for the number of pizza slices you might want (and find out the number of doughnuts you would be able to buy for each suggested number of pizza slices, and vice versa).

But I thought the ‘linear’ part meant ‘produces a straight line when graphed (?).
How does 20x+25y=1000 relate to y=mx+c?

#189 Re: Help Me ! » Linear graphs (skewed) » 2024-07-01 21:52:16

paulb203

Thanks, Bob.

#190 Re: Help Me ! » Area of plane shapes » 2024-07-01 21:50:56

paulb203

I found out from MIF that the name of this shape is an annulus (the area between two concentric circles).

#191 Re: Help Me ! » Linear graphs (skewed) » 2024-06-29 02:24:39

paulb203
Bob wrote:

When you're learning about y = mx + c it's a big help to have equal scales but there going to come a time when you have to deviate from this.

eg y = 1000x + 100.

The MIF function grapher has equal scales.

My ideal would default to equal scales but give the user the option so rescale each axis.

Bob

Thanks, Bob. Yeah, I get that we can't always have equal scales. And I'll check out the MIF grapher.

#192 Re: Help Me ! » Linear graphs (skewed) » 2024-06-29 02:22:51

paulb203
Phrzby Phil wrote:

A terrible idea.  Visualizing slope is so important, especially to beginners.

Thanks, Phil. And yes, it's important for it to make sense, and for the student not to just go through the steps to get the correct answer. Some might say they don't care, they just want the correct answer, but even for those the more they understand it the more they will get the correct answer.

#193 Help Me ! » Linear graphs (skewed) » 2024-06-28 08:38:10

paulb203
Replies: 6

I've noticed that, on Maths Genie at least, the graphs are often skewed because the squares alloted to the value of 1 vary from the x axis to the y axis. For example the x axis might have two squares for the value of 1, and the y axis only one square for the value of 1. I noticed this when the gradient didn't look right.

I know sometimes they have to do this for the graph to fit on the page, but I looked at several examples, re-did the graph with equal squares alloted to both axes, and it fitted fine. And, obviously, the gradient then looked right. So why do they do this? And is it common elsewhere? And, does it skew anything else?

#194 Re: Help Me ! » Tethered Goat Problem » 2024-06-27 23:07:52

paulb203

Yeah.

#195 Re: Help Me ! » Estimation » 2024-06-27 08:09:31

paulb203

Good point. Reminds me of teachers saying don't round as you go, round when you get the final answer. But I think this is different. I think THE POINT here is to show that you know how to round AS YOU GO. So the aim isn't accuracy, it's to show you know how to estimate each value to 1 sig fig, etc, as you go. I think.

#196 Re: Help Me ! » Tethered Goat Problem » 2024-06-27 08:04:16

paulb203

Brilliant. Thanks a lot, Bob.

Of course, the barn gets in the way of rope. Doh!

Asking myself why I didn't see this. Could I have been thinking 'too mathematically'? I got caught up in pi, and radii, area, etc, that I forgot about the barn being a 3 dimensional object that is going to get in the way of the tether.

One thing about the video. The woman just said something like, "When the goat gets to here there is only 3 metres of rope left"; instead of saying what you said, i.e, here the rope gets caught on the corner of the barn. Maybe she thought it was obvious. And I see now that it was. Doh!

#197 Re: Help Me ! » Estimation » 2024-06-26 21:55:41

paulb203

Thanks, Bob.

It's from Maths Genie, GCSE Maths, Estimation.

Apparently when estimating (when you're not told how to round, specifically) we round each value to 1 significant figure.

I rounded the 43 to 40. Then, for an estimate of the seconds in the year, multiplied 60 by 60 by 20, 400, giving 28,800,000

then divided that by the 40 to get 720,000*

They also rounded the 43 to 40. And 24 to 20, and 365 to 400, but instead of multiplying 60 by 60 by 20 by 40, they mulitplied 60 by 60, and 20 by 400, to get 3600 and 8000 respectively. Then they rounded the 3600 to 4000, and multiplied that by 8000 to get 32,000,000

Then divided that by 40 to get 800,000

They did accept between 600,000 and 900,000 for the answer (which answers my original question; is there more than 1 answer for these questions).

#198 Help Me ! » Tethered Goat Problem » 2024-06-26 07:04:09

paulb203
Replies: 5

https://www.youtube.com/watch?v=QDnT4evo-5w&t=228s

(First question on this video)

Is the answer given correct? I don't get why the goat covers 3/4 of the large circle, but only 2 small fractions of the top left quarter.

I thought the goat could cover the whole circle, minus the area of (most of) the shed/barn (?). I thought it could go 10m in any direction from the bottom right of the shed.

#199 Help Me ! » Estimation » 2024-06-26 04:01:07

paulb203
Replies: 4

A baby is born every 43 seconds in the UK in 2018

Work out an estimate for the total number of babies born in the UK in 2018

*

Is there more than one correct answer to these kind of quesitons?

#200 Re: Help Me ! » Mean, median, mode » 2024-06-25 21:28:57

paulb203

Thanks, Bob, I was hoping it wasn't just me!

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