(Economics) Don't Show me The Money!

Walking through the front door, you check the mail and finally see it...THE BILL.


"What! $6,000 for freakin Coke & Mentos! Seriously!?"  you begin to shriek. "I don't have that kind of cash!" It says they're running one of those 'Special Promotions.' You don't have to make any payments for '1 Full Year.' But they charge you 27% APR, compounded daily. You do some quick math and learn that after 1 year (with no payments) you'll owe back approximately....?

FOUNDATIONAL TOOL: Compound Interest ---> We covered "Compound Interest." But if you need a refresher, click: The Power of Compound Interest (Economics Pt 1 of 2) ]

(Fluid Mechanics) Liqueur Pressure On a Shot Glass

At an engineering holiday party, instead of guessing how many beans are in a jar full of jelly beans, your quirky friends opt for an engineer's alcoholic version of countin' beans. 

The host sets on the table a layered drink similar to what's depicted below. These kinds of drinks actually aren't hard to make. The requirements are that the densest liquors are at the bottom and the least dense at the top. Then, as long as you pour slowly, the layers will stay separated.

Looks like this recipe in particular is 1/2 part green liqueur with a specific gravity of 0.8, and 1/2 part green liqueur with a specific gravity of 1.0, poured into an open cubed-shaped shot glass with 6 cm sides. (Here's a reference table with the specific gravities of some liqueur)

She says, "Instead of counting beans, which one of you can calculate the total pressure acting on the bottom of the cube shot glass?"

Use latex to write equations.

(Physics - Medium) Spring-loaded Toy Dart Gun

A spring-loaded toy dart gun is used to shoot a dart straight up in the air. The dart reaches a maximum height hmax. Afterwards, the same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. Neglecting friction and assuming an ideal spring...

How far up does the dart go this time?

(Geometry) Max Beach Ball Volume

You want to bring a beach ball to the beach which cannot be deflated because of magic. Your trunk has 60 cubic feet, being 5 feet long and 4 feet deep. What is the maximum volume of a beach ball you can bring?

(Geometry) Circle Section Area

What's the area of the shaded region below? 





                    E) Can I get this slice in pie form?

Use latex to write equations.