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math
Riddle me this
Roman Empire
XTREME MATH
It's not rocket science!
or maybe it is...
100

-5x(-5)

25

100

If all Wibbles are Criggles, all Borkins are Kwumblins, no Hoggles are Borkins, and all Criggles are Borkins, is it true that all Borkins are Criggles?

Nope

100

In this culminating battle of the second civil war of succession, Augustus sent his friend Agrippa to lead his navy against Mark Antony and Cleopatra's combined forces.

What is the Battle of Actium?

100

Explain a superfactorial Symbol.

The term superfactorial has two slightly different definitions: as a product of factorials (Sloane & Plouffe, 1995) or as a tower of factorials involving compound exponents (Pickover, 1995). Sloan and Pouffe’s form is the most common.

1. Sloane & Plouffe’s Superfactorial

A superfactorial is defined by Sloane and Plouffe as the product of the first n factorials. Their definition is equivalent to the integral values for the Barnes G-function.

Examples

The superfactorial of 3 is:
sf(3) = 1 factorial * 2 factorial * 3 factorial = 1 * 2 * 6 = 12

Superfactorials for integers 1 through 11 are (OEIS A000178):

  1. 1
  2. 2
  3. 12
  4. 288
  5. 34560
  6. 24883200
  7. 125411328000
  8. 5056584744960000
  9. 1834933472251084800000
  10. 6658606584104736522240000000
  11. 265790267296391946810949632000000000
  12. 127313963299399416749559771247411200000000000

Pickover’s Superfactorial

Pickover (1995) defines a different superfactorial, one that involves compound exponentiation:


The dollar sign ($) is actually a factorial symbol (an exclamation mark !) overwritten with the letter S (Mudunuru et al., 2017).
This can also be expressed as a tetration:
n$ = n! (n!).

Alternatively, it can be expressed as a tower of exponents, using Knuth’s arrow up notation:
So a ↑↑n, is iterated exponentiation (i.e.tetration), and means to raise a to itself n – 1 times. For example,

a ↑↑5 = aaaaa.

Examples

The first two values are:

  • 1$ = 1,
  • 2$ = 3

From n = 3 this grows very rapidly and up the numbers are huge. $n is roughly 10101036305.

100

A spacecraft's engine ejects mass at a rate of 30 kg/s with an exhaust velocity of 3,100 m/s.  The pressure at the nozzle exit is 5 kPa and the exit area is 0.7 m2.  What is the thrust of the engine in a vacuum?

q = 30 kg/s
Ve = 3,100 m/s
Ae = 0.7 m2
Pe = 5 kPa = 5,000 N/m2
Pa = 0

200

96=8x

x=12

200

 What goes on four legs in the morning, on two legs at noon, and on three legs in evening?

A man

200

What is the name of the Gallic General who Julius Caesar defeated at the Battle of Alesia in 52 BCE?

Vercingetorix

200

Explain a Hyper factorial, Symbol and Equation

H(n) 

H(n)=1^1 x 2^2 x 3^3 x ...n^n

200

The spacecraft in problem 1.1 has an initial mass of 30,000 kg.  What is the change in velocity if the spacecraft burns its engine for one minute?

M = 30,000 kg
q = 30 kg/s
Ve = 3,100 m/s
t = 60 s

300

What is the circumference of a circle with a diameter of 8 in. ( Use 3.14 as PI)

25.12 in

300

One day, a magician was boasting about how long he could hold his breath underwater. His record was 6 minutes. A kid that was listening said, “that’s nothing, I can stay underwater for 10 minutes using no equipment or air pockets!” The magician told the kid if he could do that, he’d give him $10,000. The kid did it and won the money. How?

He filled a glass of water and held it above his head for 10 minutes.

300

What did Emperor Augustus say after his legions were decimated by the traitor Arminius and Germanic forces in the Teutoburg Forest?

"Quinctilius Varus, give me back my legions!"

300


X=30

300

A spacecraft's dry mass is 75,000 kg and the effective exhaust gas velocity of its main engine is 3,100 m/s.  How much propellant must be carried if the propulsion system is to produce a total v of 700 m/s?

Mf = 75,000 kg
C = 3,100 m/s
V = 700 m/s

400

-12x8

-96

400

I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?

An echo.

400

What Roman Emperor reigned from 248 and 253 CE?

Silbannacus

400

C=59(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

  1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
  2. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
  3. A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

The final answer is D.

400
A current NASA space program is named after this Greek Goddess.

What is Artemis?

500

11 to the power of 2 is?

121

500

There are 100 prisoners. Each assigned a number, 1 to 100.

Somewhere in a sealed room: 100 boxes. Each box has a slip of paper inside with one prisoner’s number — randomly assigned, one per box.

The rules are almost offensively simple:

  • Each prisoner enters the room alone
  • They can open any 50 of the 100 boxes
  • They leave the room exactly as they found it
  • Zero communication with anyone after the game starts

If every single prisoner finds their own number, they all go free. One person misses, everyone dies.

They get to strategize beforehand. That’s it. That’s the whole game.

start by opening the box that has your own number on it. Box 1 might point to box 4, which winds through a dozen others and eventually loops back to box 1 — a loop of length 15. Nested inside that same arrangement, boxes 31 through 34 form their own tight loop of four, completely self-contained. Every box belongs to exactly one loop, there are no dead ends, no loose threads — it’s just loops, all the way down.

500

As a young man in his early thirties, Julius Caesar was appointed to a quaestorship in the province of Further Spain. In the course of his administrative duties he visited Cadiz, a city with a long tradition of Greek and Punic culture. There, in the temple of Hercules, he beheld a statue of Alexander the Great, which caused him to reflect that Alexander had conquered the whole of the known world at an age when he, Caesar, had achieved nothing of note. What did Caesar do next?

He wept and vowed to conquer something to be great like Alexander.

500

The equation 24x2+25x−47ax−2=−8x−3−53ax−2 is true for all values of x≠2a, where a is a constant.

What is the value of a?

A) -16
B) -3
C) 3
D) 16

The final answer is B.

500

As a spacecraft approaches Jupiter, it has a velocity of 9,470 m/s, a flight path angle of 39.2 degrees, and a targeted miss distance of -2,500,000 km. At intercept, Jupiter's velocity is 12,740 m/s with a flight path angle of 2.40 degrees.  Calculate the spacecraft's velocity and flight path angle following its swing-by of Jupiter

VP = 12,740 m/s
P = 2.40o
VSi = 9,470 m/s
Si = 39.2o
d = -2,500,000 km