You will find everything you want to know about HYPERBOLAS **HERE.**

Just another WordPress.com weblog

So Mathspig is helping the kid next door with Grade 11 Math.

Here is the revision Q:

This is the sort of Q that makes students hate ALGEBRA. (Solution by Mathspig below)

POINTLESS

GRINDING

HEADACHE INDUCING

This equation looks like a chicken ran through some ink and ran across the page.

Why do so many MATH work sheets look like this?

The result:

One way to tackle a long and complexmath problem is to **defront the classroom** and solve it in groups.

Here is the Q in orginal form:

NOTE: With a proof, you have to prove that one side of the equation

equals the other.

A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.

This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

The Earthquake Engineering website offers a simple explanation.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

Details Base Isolation Specialists

Details Damper Supplier

** **

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly vomit inducing (barfomatic?).

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

But I’m going to use a student friendly equation from Wind Engineering for Large Structures.

Calculus Equation **here.**

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.

Structural Engineer Ron Klemencic explained on the Discover News that a simple rule of thumb for calculating skyscraper sway was to simply divide the buildings height in by 500 because the building codes demand the building fit a 1:500 sway ratio.

The tallest building in the world at 2,716 feet (828m), the Burj Khalifa, Dubai, would sway back and forth about 5.5 feet or 1.7 m.

**Ahhhhhhhhh! But you would have to drag Mathspig onto the 168th floor screaming.**

**But mathspigs you can work out the sway on the top ten tall buildings in the world.**

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: **Caffeine Pharmacology**

Caffeine interferes with sleep. **One study** found that consuming caffeine **6 hours** before bedtime reduced total sleep time by **1 hour**.

Caffeine content sources **Caffeine Content Data Base**

Street art by **JEKS**, South Carolina

The Half life equation is an exponential function.

The **Mayo Clinic **advises up to 400mg Caffeine a day for adults, which would be;

10 black teas

7 instant coffees

4 cappuccinos

2 dark roast brewed

less than one cup of Black Insomnia Coffee.

Approx half this amount of caffeine for 14 yos.

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine **6 hours** before bedtime reduced total sleep time by **1 hour**.

Caffeine content sources Caffeine Content Data Base

Street art by JEKS, South Carolina

The Half life equation is an exponential function.

The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;

9 black teas

6 instant coffees

4 cappuccinos

2 dark roast brewed

less than one cup of Black Insomnia Coffee.

Approx half this amount of caffeine for 14 yos.

Remember the best calculator to use is the **WEB 2.0 Calculator** as it shows the worked equation as you go.

**CAREERS:** It’s not only health workers who need to understand these calculations, but also creatives running health campaigns online, on TV, radio and in magazines.

PDF WORKSHEET HERE:**How**** much blood can you lose and still survive? WORKSHEET METRIC**