Archive for the ‘Base 10’ Category

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YouTube Clip Money Making Maths

June 26, 2017

………………..How much money does a popular

………………………YOUTUBE clip make?

You will learn everything you need to know at 1 Million YouTube Views.  Now let’s do the maths!

Here are the TOP 3 YouTube Clips Ever. Their popularity is measured by Number of Views. 

1. PSY – GANGNAM STYLE

2,879,287,942 views

View here.

2. Taylor Swift – Blank Space

2,088,564,435 views

View here.

3. Wiz Khalifa – See You Again. Charlie Puth (Furious 7)

2,850,776,581 views

View here.

YouTube uses an algorithm (ie. a formula) for calculating the amount of income earnt by a clip from advertising. There are multiple issues involved including how long viewers watch the ad, the demographics (age group) and the actual sales (Retailers actually do review ad costs vs increased sales. Always. They are not idiots.)

Here is  the basic method used to calculate ad revenue for a Youtube creator. Remember, a creator must have a minimum of 10,000 hits on their channel before any revenue is paid.

Of course, pop stars use Youtube as a promotion platform. They can earn money through multiple Youtube clips, sponsors, merchandise and live perfomances. Nevertheless, it is surprising how little money is earned by each clip.

eg. ONE DIRECTION

521,126,151 views

View here.

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How to pig out and save the planet

January 2, 2015

Aussie physicist and TV present – that does sound like an oxymoron – Reuben Meerman (A meer man after all. Old joke) had an article published in the BJM (British Medical Journal) with Andrew Brown describing where fat goes when you lose it.

When you burn fat which is a triglyceride or a three-pronged hydrocarbon the formula is:

Picture 1

You breath out the FAT as CO2 and H2O.

BUT:

Oxidizing 10 kilos of human fat requires inhaling 29 kilos of oxygen to produce 28 kilos of carbon dioxide and 11 kilos of water. You can check out how much carbon dioxide you add to the atmosphere when you diet in the following graph:

Picture 3

Mathspig Kilo carbon dioxide released per kg FAT

 Picture 3

When you lose weight you add carbon dioxide to the atmosphere, but when you gain weight you take carbon dioxide out of the air. Your carbon footprint from Time for Change blog (See table below) can be neutralised if you put on the following weight:

Mathpig Carbon Footprint by pig out

 

Picture 3

 

We can Pig Out and Save the Planet:

Pig Out Australia 2

 

Picture 3

Pig Out UK 2

 

Picture 3

 

Pig Out USA

 

Picture 3

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The Rosetta Project … like throwing a dart from Sydney to Perth and hitting the bullseye

November 28, 2014

Many commentators in Australia claimed that the Philae landing was:

This is equivalent to hitting the bullseye of a dartboard in Perth from Sydney. With a billion euro ($1.4bn) dart. While blindfolded (as the mission was powered down for almost the entire journey). ABC The Drum

Did they get the maths right?

Inner bullseye of dartboard = 12.7 mm

1 Dartboard

67P comet = 4.1 km = 4,100 m at widest point

Distance comet from earth = 520 million km

 Actually, hitting the 67P comment was more like roulette as the Rosetta mothership swung into orbit. And, as the earth and the comet are moving, the distance constantly changes, but you can watch the distance changing here.

Fabulous Graphics from the Daily Telegraph

Fabulous Graphics from the Daily Telegraph

In the Dart Throwers Universe

We will assume someone can stand on earth and throw a dart at the comet … Yes! They would need very big triceps.

3  Dart throwers universe correction

 

So the commentators aren’t even close. It would still be a feat hitting a bullseye with a dart from 160km, but that would be from Sydney to, um, Nowra on the coast. 

WHY?

Comet vs bullseye ratio mathspig

Mt Everest RAtio

4 Dart Throwers universe 3

The distance from Sydney to Perth is 4100 km. At best the commentators would be talking about throwing a dart from Brisbane to Adelaide is 2044km (below).

Brisbane to Adealide

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Maths Cure for Wolverine

July 25, 2013

Jackie from Straight Ace Learning ( Maths & Movies ) asked Mathspig to come up with a formula for Wolverines super fast super healing powers. He can regenerate or heal in 5 seconds. In the latest Wolverine Movie he becomes mortal ….

Wolverine Facts:

No. Cells in a human/X-man Body

= 75 trillion cells  = 75 x 1012

(Mid-point of 60-90 trillion cells cited on the fab AskaBiologist website)

Imagine Wolverine is slashed/shot/wounded in the abdomen.

Human Trunk

= 44% of the body.

(See Body Segment Data here)

Estimate Cell Damage

= 1/4 of trunk = 44/4 = 11% = 0.11

Number Cells Damaged

= 75 x 1012 x 0.11 = 8.25 x 1012

You will need your Web 2 Scientific Calculator (See diag below).

W 1

W 2

W 3

This is what the calculation looks like on the WEB 2 Scientific Calculator. 

Tell MIDDLE SCHOOL STUDENTS that

 log2X

is just REVERSE ENGINEERING of 

2x

W 4 calcs

 

 

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500,000 Hog Hits

April 27, 2013

Mathspig is sooooooo excited

about reaching:

5 etc hits

To celebrate 500,000 or 5×105 hog hits

 and to continue showing mathspiggies everywhere

that maths is fun

and relevant to all

Mathspig presents

The MATHEMATICAL

CABINET OF

500,000

CURIOSITIES!!!

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1

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If you took a sample of

500,000 US teens

how many DO YOU THINK fall

asleep at school

at least once a week?

asleep

You will find amazing US teen stas here:

28% report falling asleep once a week

 500,000 x 28/100

= 140,000

Snoring to the left of you. Snoring to the right of you. You are not alone.

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happy-2nd-birthday
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What volume of coke is there in 500,000 cans?

coke shower

Coke can vol = 355 ml = 12 fl oz

500,000 x 355 = 177,500,000 ml

= 177, 500 l = 177.5 m3

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An average bath uses 150 litres water per bath.

How many bathtubs would 500,000 cans of coke fill?

177,500/150

= 1,183 baths in coke!!!

Hey mathpiggies, wanna bubble bath? You’d be tickled pink.

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In a crowd of 500,000 how many people

would have their birthday

on the same day as yours?

bd cake

There are 365 days in the year so the probability of anyone having their birthday on the same day as you (ignoring leap years) is:

1 in 365 or 1/365.

 

In a crowd of 500,000 the number of people who have a birthday on the same day as you is most likely:

500,000 x 1/365 = 1,370

That’s a lot of birthday cake!!

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4   How heavy is $500,000 dollars?

 money bag

Australia:

$ Aus

Wt Aus $1 coin = 9.0 g

If the bank gave a bank robber $500,000 in $1 coins it would weigh:

500,000 x 9.0 = 4,500,000 g

= 4,500 kg = 4.5 tonne

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UK:

UK [pound coin

.

Wt UK £1 coin = 9.5 g

500,000 x 9.5 = 4,750,000 g

= 4,750 kg = 4.75 tonne

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USA:

$ usa

Wt US $1 coin = 8.1 g

500,000 x 8.1 = 4,050,000 g

= 4,050 kg = 4.05 tonne

You will find all you need to know about the size and weight of US coins and notes here.

$500,000 in $1 notes would only weigh

11 lb or 5 kg.

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So, um, bank robbers do the maths!!!!!!!!!!!!!!!!!!

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5

How far would you walk in 500,000 steps?

We’ll assume you take a big step of 1m.

step

So 500,000 m = 500 km.

A comfortable walking rate is 5 km/hr.

How long would it take you to walk 500 km without a break?

500/5 = 100 hrs.

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6 049_tns6 bugatti-veyron-super-sports-480

The Bugatti Veyron Super Sport  hits a maximum speed of 267 mph (429 km/h).

How long would it take the Bugatti travelling at top speed – not including refueling time – to clock up 500,000 km?

500,000 /429  = 1165.5 hr

= 48.5 days

The speed of an average sized commercial passenger plane ≈ 500 mph 0r 800 kph or

≈ twice the speed of the Bugatti.

So it would take a passenger plane approx 24 days to travel 500,000 km.

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7 A&E

How long would it take you to count to 500,000?

kid counting

Assuming you count at the rate of 1 per second the time it would take is 500,000 seconds.

500,000/ 60 = 8333 mins = 833/60 hrs

= 13.88 hrs or 13 hrs 53 mins

Come on! You could do that mathspiggies!!!!!

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8gloom

 In a group of 500,000 US teens how many are serious cave dwellers or, to be more accurate, how many spend less than 3 hrs a week outdoors?

It is an amazing 30.1%.

500,000 x 30.1/100

= 150, 500 creatures of the gloom.

Come on you teen gloomagogs get outdoors. You need the sun. You need the Vitamin D.

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9m&ms

How many calories in 500,000 m&ms?

There are an amazing 400 million m&ms produced everyday in the US. One m&m weighs 0.7g.

And calories in 1 m&m =  3.4 cal

500,000 m&ms weigh:

500,000 x 0.7 = 350,000 g

= 350 kg

As 400 million or 8 x 500,000 m&ms are produced each day, that is 8 x350 kg or 2800 kg or 2.8 tonne.

Calories in 500,000 m&ms is:

500,000 x 3.4 = 1, 700, 000 Cal

m&m kid

As the average consumptionof chocolate in the US is 5.18 kg per year eating 500,000 m&ms would take:

ranking_of_consumption_chocolate_2007

350 kg/ 5.18 kg

= 67.6 years!!!!!!!!!!!!!!!!!!!!!!!!

You better get going!!!!!

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10ablink

Blink rates vary but the average blink rate in a laboratory setting for a human is 10 blinks per minute.

How long would it take for you to blink 500,000 times?

500,000/10 = 50,000 minutes

= 50,000/60 hrs = 833.3 hrs

= 833.3/24 = 34.7 days

= 34 days 17 hrs 17 mins

But don’t think it or you’ll go blink crazy!!!!

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Pump Up the volume or Knock, Knock Knockin on Your skull wall!

February 18, 2013

Well, little Mathpiggies, lots of students want to be Sound Engineers. It is time to tell cool middle school students that Sound Engineers NEED maths.

olden days sound guy

According to Salford Uni’s Guide to Decibels:

Just about every piece of audio equipment (microphones, loudspeakers, sound cards, amplifiers, mixers, etc) will have specifications expressed logarithmically (i.e. in dBs).

We don’t want to frighten junior sound engineers with complicated formulae. But we can have a little peak at SOUND ENGINEERING.

Here’s the deal.

You want to be a Sound Engineer like this:

sound engineer 1……………………………………………………………….

Not like this:

Sound engineer 2

Sound is tricky. It is a wave of compressed air travelling through the air to your ear.

It is measured in INTENSITY (Air Pressure per sq m) or Power (eg. Energy carried per sec in, say, Kilowatts).

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If you have ever been to a Rock Concert you can feel the pressure of the sound wave of the BASS hitting your chest.

At an ELTON JOHN concert Mathspig could feel BENNIE AND THE JETS POUNDING ON HER CHEST …. COULD HARDLY BREATH.

Elton John

The problem, however, is your ears can detect sound pressure over an astounding range of 1 to 1 trillion. Imagine a volume Dial if we used o to a trillion:Vol dial

The other problem is your ears aren’t accurate. Your ears can detect doubling the intensity of a dripping tap but not doubling the sound of a jackhammer. This is why we can easily damage our hearing. We perceive the loudness as linear when it is not.

sound graph 1

To measure sound volume engineers use Powers or Exponents:

Start with 1 million:

1000000 = 10 x 10 x 10 x 10 x 10 x 10 = 106

we call 6 the index and 10 the base.

Similarly 100000 = 105, 10000 = 104, 1000=103, 100=102, 10=101, 1=100; so why not express numbers from 0 to 1000000 as:

1,2,3,4,5,6.

We use decibels, which are 1/10 th of a Bell to measure sound.

Sound Power RAtion

But the sound intensity as measured in decibels dB is a ratio compared to the Threshold of Hearing (TOH), which is set at 100 = 1. Sometimes the sound intensity is a negative number because there are plenty of sounds below our hearing range. Just ask a dog or a bat.

Over the Threshold of Hearing

This chart is from the excellent Physics Classroom

A noise that is 3B or 30 dB louder than another noise is hitting your ear drums with 103  or 1000 times more pressure. Ahhhhhhhhhhhh!

Here is a typical sound levels chart:

typicalsoundlevelscr

Here is the ear safety chart:Ear Safety Chart

Turn Down the volume Exercise:

First, look at the chart above and compare dB readings. Note: Every 20 dB or 2 B increase in sound intensity increases the sound pressure on your ear drum by a factor of 100.

Now, we are going to convert the sound pressure in dB on the typical sound levels chart chart back from the dB (or log scale, mathpig teachers) to real scale by:

Convert to B by dividing each measurement by 10 and turning into a power and calculating value:

eg Ordinary Conversation:  60 dB = 6.0 B = 106 intensity = 1,000,000

   Rock Band: 120 dB = 12.0B = 1012 intensity = 1,000,000,000,000

If you are interested in simple explanation of volume and Guitar Amplifiers go here:

or here

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Harry Potter Needs Maths

February 1, 2012

What has Harry Potter to do with Maths?

Watch this video of Harry Potter and the Half Blood Prince: Death Eater Attack.

You can click on the link here or below (Video will only play on You Tube site):

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A recent article in The Guardian, UK, explained the link between Harry Potter and Maths:

‘(Alex)Hope, managing director of the visual effects firm Double Negative said: “In Harry Potter [and the Half Blood Prince], the opening sequence has Death Eaters flying across the river Thames, destroying the (Millennium) Bridge between St Paul’s and the Tate Modern.’

“The way you create that is people who understand computational fluid dynamics, they know how water moves. They take the physics that’s used in modelling rivers and the flow of water and apply that in our world. People doing it need an artistic sensibility as well. An understanding of maths and science is fundamental to many of the disciplines in our industry.”

Fluid Dynamics is the study of fluid flow. You can look at this picture (below) and see the similarity to the Death Eaters water-flowy appearance.

Here is a experiment showing lamina Vs turbulent flow in water. Mathspig did experiments like this at university in Chemical Engineering. Equations can be scary, mathspigs, but not necessarily.

Here is a water flow equation for a sharp edged weir with a V notch out let from AQUATEXT:

Q = 0.266 x cB x (2g)0.5 x H1.5

where;

Q = water flow rate, m3/sec

B = width of the weir at the flowing rate

c = discharge coefficient, average 0.62

g = gravitational constant, 9.81

H = Height of the water over the weir, measured behind the weir edge, m

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Here is a real flood caused when water was released from a real weir or dam.

In 2011 operators of the Wivenhoe Dam in Queensland (above) had to release water to stop the dam collapsing during severe floods.  8,000 properties were flooded.

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More @ News Limited 


Combine the flow maths for a weir (equation above) with computer graphics and you have a realistic flood film sequence!!!!!!

Or maybe a really unrealistic but terrrrrrrrifying sequence:

Aghhhhhhhhhh!!! We’re all gonna die or …. like …

have a really amazing white water raft ride, maths dudes!!!!!!!