Fermi's Trivia Tourney (part 4)

Congratulations to Fill for answering question 6 correctly! You've won 600 GN (1200 GN, thanks to Luc)!

 

That's quite generous of you. Just so I have a clear understanding - am I sending players the initial amount, and then you are sending that initial amount to them again?

 

You have the right idea, there's just one problem with it.

 

Ok, thanks. I forgot to post that it ended an hour ago.

 

Answers to Questions (Part 4)

1) What 3 South American countries are not adjacent to Brazil?
Answer:
The three South American countries that are not adjacent to Brazil are Ecuador, Chile, and, of course, Brazil itself.


2) Identify the animal:

- answered by Killerbeast03
Answer:
This animal is called a gerenuk. It is a species of antelope and is found in the Horn of Africa.

3) What type of animal is the only animal that has an odd number of whiskers?
- answered by Killerbeast03
Answer:
The only animal that has an odd number of whiskers is the catfish. All other animals have an even number of whiskers.


4) Solve the expression using only a pencil and paper:
View attachment 12021
- answered by Baerbros
Answer:
The trick here is to use the order of operations (PEMDAS). You begin by simplifying what is contained in parentheses - there are none. Next you simplify exponents - there are none. Next you simplify multiplication and division, and finally you simplify addition and subtraction. Solving from left to right will not yield the correct answer.

5) A 1500-kilogram car is traveling along a circular track that has a diameter of 50 meters. If the track has a constant bank of 15 degrees, and the coefficient of static friction between the car's tires and the track is 0.85, what is the maximum speed that the car can travel along the track without losing traction?
- answered by Luciano
This problem is a little more involved. When analyzing the forces acting on an object traveling in a circle, there is a constant force that is pointed towards the center of the circle (perpendicular to the circle's tangent). This is called the centripetal force. The centripetal force in this scenario is the static friction between the car's tires and the road. Without traction, the car wouldn't move in a circle, and would just fly off the track. However, there is a limit to how fast the car can go. You start by finding out what the normal force created between the banked road and the car is. Then you can calculate the force of static friction. Now we can calculate the centripetal acceleration given that it cannot exceed the static friction's acceleration, since the static friction is the centripetal force. Finally, the maximum velocity can be calculated, which comes out to be about 14.91 m/s.


6) All but one number equals 1 when divided by itself. What number is it, and what does it equal when divided by itself?
- answered by FillWerrel
Any number equals 1 when divided by itself except 0. 0 divided by 0 does not equal 1. So what does it equal? If you guessed 0, you're incorrect. 0/0 is undefined, also called indeterminate. Algebraically, you can see why we call this undefined: If 0x = 0, we can conclude that 0 = 0/x, and therefore 0 = 0. This is a tautological statement and does not define any value for x.
By dividing each side by 0 instead, we find that x = 0/0. This reads as "x is undefined." This just means that the statement does not define x, not that x has a value, per se, of 0/0.


7) The formula for the time it takes for an object to fall is given here:
View attachment 12022
Using this formula, John tried to calculate exactly how long it takes for a ball to fall when dropped from a height of 1,000,000 meters. Now he tests to see if his answer was correct by timing how long it takes. He finds that the time was considerably longer than what he had calculated. Assuming that no human error is involved and that no other object besides Earth exerts a gravitational force on the ball, propose two or more explanations as to why it took longer than he had calculated.
- answered by Luciano
Answer:
There are two factors that John did not consider. This formula is for constant acceleration. Due to air resistance in Earth's atmosphere, there will be varying and eventually no acceleration. This slows the ball down substantially. Also, as you get further from Earth, the gravitational force decreases, thus so does the gravitational acceleration. This means that the acceleration will not be as much initially, and becomes a significant factor when 1,000,000 meters from Earth.

8) Which of the following is a topological sphere and why?
Fork, engagement ring, coffee mug, cheese grater, window screen, donut
Answer:
Did you notice anything from the list that had something or didn't have something that all of the others had? Here's a hint: which one doesn't have any holes? That would be the fork. A topological sphere is essentially any object that doesn't have holes. In the study of topology, shapes are considered the same or of the same "genus" (refers to number of holes) if they are hypothetically able to be distorted into the same shape without breaking or mending any existing connections (dependent on the shapes "connectivity"). If this is possible for two shapes, they are "homeomorphic." If you have a ring, you would have to mend the hole in order to morph it into a sphere, but if you had a fork, you could morph it into a sphere without breaking or mending anything. A common joke between mathematicians is that topologists are people who can't tell a donut from a coffee mug.


9) A red supergiant star implodes on itself millions of light years away, causing a massive amount of energy to be expelled in the form of a supernova. At that exact same point in time, the Hubble Telescope takes a picture of the star. However, instead of getting a picture of a supernova taking place, only a massive yellow star is photographed. Why?
- answered by Lego90210
This is an excellent thought experiment for understanding the finite speed of light. A light year is the distance in which light can travel in one year. If the supernova takes place millions of light years away, it takes millions of years for the light that is reflecting off of the supernova (allowing it to be seen) to reach the observer, which in this case is the Hubble Telescope. However, at that point, the light that reflected off of the star millions of years ago is finally reaching the observer, so we actually only see the star (red supergiants don't usually live more than a million years so we would actually see its previous stage, a massive yellow star). Millions of years from now, we would be able to photograph the supernova, even though it will have happened millions of years ago.


10) What is 9 (currently written in base-10) written in base-1?
Base 1, or "unary," is is a little different from other bases. As opposed to having numbers that only contain digits less than the base or "radix," unary uses 1's to make numbers, as 0's alone have no value. So 9 written in unary is simply 9 1's:
111111111 (a lot like tally marks)

 

-500 GN sent to Baerbros
-1200 GN sent to Lego90210
-900 GN sent to Killerbeast03
-3500 GN sent to Luciano
-600 GN sent to FillWerrel