Let’s get some math going today. Here come the questions. Let’s F***in’ GOOOOOO!
1. 473 x 22
10,406
2. A right triangle has a hypotenuse of 13 units and one leg measuring 5 units. What is the length of the remaining leg?
13^2 - 5^2 = x^2
144 = x^2
12 = x
3. Seven people—Sally, Bob, Ted, Maria, James, Alex, and Chris—must travel in two cars.
Sally cannot ride with Bob.
Ted cannot drive.
Alex and James must ride together.
Maria must drive one of the cars.
Each car must have exactly one driver.
Each car can hold no more than five people.
Provide one valid arrangement of drivers and passengers
Car 1: Maria, Ted, Bob, Chris (the fun car)
Car 2: Sally, Alex, and James (the bitchy car)
4. What the hell is going on between Sally and Bob?
Seriously. Just get in the car, Sally.
Young love sometimes doesn’t work out.
Bob didn’t have a good plan in place for who he wanted to be, and Sally just wasn’t ready for commitment. Those 2 ingredients were like fire and hotter fire for Bob and Sally’s own issues. Bob was afraid of abandonment, and Sally was afraid of stagnation because her dad was horribly depressed and just did his job day in and day out until her mother left him. Like I said, it was like fire mixing with more and hotter fire. In months the entire friend constellation will implode since Chris has had a crush on Sally for 2 years. It is a bit of a tragic tale.
5. Find the derivative of: 3cos(x)+200-tan(x)
Okay.. trig derivatives for: d/dx [3cos(x) + 200 - tan(x)]... I haven’t done this for a minute. I will definitely need to do some review for this. Let’s do this… coefficients don’t alter.. So the 3 stays. -Sin is the derivative of Cos… Derivative of Tan is Sec^2… sooo
d/dx[3cos(x) + 200 -tan(x)] = -3sin(x) -sec^2(x)
I had to look up the tangent trig identity on that one.
6. A coffee mug and a doughnut are considered topologically equivalent. Explain why.
They each have 1 hole in them, the missing center of the doughnut, and the empty space in the enclosed handle of a typical mug… this answer becomes incorrect if the mug does not have a handle, there are 2 connected loop handles on the mug, or the mug’s handle is not a connected loop
Yes, a mug is a torus.
7. Carol leaves Chicago traveling east at 45 miles per hour. Steve leaves from the same location 15 minutes later, traveling east at 50 miles per hour.
Let (x) represent the amount of time it takes Steve to catch Carol?
What assumptions do we make concerning time and time travel?
I think the big assumption is linearity of temporal propagation. If space/time is a surface, time could have hills and valleys… so… Carol and Steve may be experiencing time differently. At the speeds we are talking about though, that difference is negligible and regular old boring Newtonian physics can take place.
8. A vertical rectangular gate is submerged in water with its upper edge 3 feet below the surface. The gate is 6 feet wide and 10 feet tall.
Determine the total hydrostatic force acting on the gate. Assume water weighs 62.4 pounds per cubic foot.
This is why we have computers. I know it requires getting the derivative/integral 🤷♂️to account for the compounding force of the weight of the water… but that’s all I got on this one.
9. You win a $250 million lottery jackpot. You may receive either:
a lump-sum payment of $112 million today, or
30 annual payments totaling $250 million, with each payment 5% larger than the previous one.
Which option should you choose? Show your assumptions.
You should choose the lump sum. No question. The annual annuity does pay more over time, but there are a whole bunch of assumptions you have to make about that (will I live long enough to collect all my winnings, what does inflation do to the value of the dollars… what happens to the annuity if I declare bankruptcy {an all too common occurrence with lottery winners}). Take the lump sum, and don’t lose your mind because you have some money.
10. A family has two children. At least one of them is a boy born on a Tuesday. What is the probability that both children are boys
I don’t know the probability… but the chances are 50/50… it happens or it doesn’t…. BOOM! Logic!
11. Evaluate: 1+1+1+1 in base three.
11
12. How much wood could a woodchuck chuck if a woodchuck could chuck wood?
I have worked this out before…
A woodchuck is about 8.5 lbs and 16 inches long or so. Let’s state that “to chuck wood” is to move a piece of wood a full body length in one fluid motion.
So for an animal that weighs 8.6 lbs to move an item 16 inches through the air, I would imagine that the item in question would need to be no more than 1 lb in size (and that is being generous). I’m going to limit that weight to ½ lb for repetition’s sake (the equivalent of a 200lb person throwing something 10lbs).
So let’s say on average we give the woodchuck in question a typical labor job where the worker has to do an 8 hour shift with a 30 minute lunch and two 15 minute breaks. So that is 7 hours of time just chucking wood. Let’s say that a woodchuck can chuck some wood every 5 seconds over the course of a shift.
So, let’s see how many throws a woodchuck could do in one shift. 5,040 chucks a shift with a total of 2,520lbs of wood. A cord of wood is 2000 to 3000 lbs…. sooooo… Next time someone asks, 1 cord of wood.
13. What is the fundamental assumption upon which Euclidean geometry is built?
Okay, here are the 5 postulates of Euclidean geometry:
Postulate 1: You can draw a straight line between any two points.
Postulate 2: Any straight line can be extended indefinitely in a continuous straight line.
Postulate 3: A circle can be drawn with any center point and a radius.
Postulate 4: All right angles are equal to one another.
Postulate 5: Parallel lines never intersect
Postulate 5 is the big one. It falls apart with polar spaces and spherical spaces.
14. A swimming pool can be filled by one hose in 6 hours. A drain can empty the full pool in 10 hours. If the hose and drain are both open while the pool is empty, how long will it take to fill the pool?
Imma just estimate… a bit over half a day. You do the math… sheesh.
15. A barber shaves every man in town who does not shave himself, and no man who shaves himself. Who shaves the barber?
Oh, Russell’s paradox. Let’s make this one easy.
Let’s say the barber is a woman (maybe Barbara the Barber)…. Meaning that the barber is outside of the presented conditions. The barber does not actually exist in this defined set.
16. A double pendulum is released from rest. Describe why the long-term behavior of the system cannot be accurately predicted.
It is a non-linear dynamic system.. The initial conditions will make the system outcome have a definable overall pattern, but not a precisely predictable position. It is a chaotic system.
17. A signal is detected from a distant star. Using Bayesian reasoning, determine the probability that it is artificial.
A Bayesian analysis requires a prior probability, a likelihood function, and evidence with which to update the prior into a posterior probability.
This question has none of those.
Sooo... I’m going to say the probability approaches zero.
We do not know how common life is
How often life becomes intelligent
How often intelligence produces detectable signals
How many natural phenomena might produce something similar
Sooooo, that probability is approaching 0 really fast.
18. Prove the ε-δ theory of limits.
No. I failed “Intro to Analysis 1” the first time I took it in college. Bad professorial match (seriously, he really loved fishing and did not like me, was actually surprised when I told him my grades in other mathematics classes. Actually said, “I just do not understand how you got A’s in topology, linear algebra, and differential equations and you can’t get this. You probably shouldn’t have gotten A's in those classes.” Nah, my dude… you just were not a good teacher for me in Analysis… since I got an “A” the following year in both Intro to Analysis 1 and 2… with a better prof… dean of the school kind of prof…. Not that I am bitter… ) and heady concepts did not mesh.You want an answer to this one? Take an upper division mathematics course on proving analyses.
19. A spherical Earth must be represented on a flat map. Which geometric properties can be preserved, which must be distorted, and why?
The three main trade offs are distance, direction, and area.
You can preserve one of those completely
You can maintain a second reasonably
But you completely fuck the 3rd over.
Different map projections are meant for different purposes.
20. Solve for x: x= 1/0
Okay, so I say that x = 1/0 = ∅₀…. is nothing that does not exist. And I suggest that 1/∞ is U₀…. everything that does not exist. Let’s make a new set of mathematics so these things are defined. Like in Question 15. Barbara is a member of the U₀ set (U₀ = [∅₀, Barbara, A lazy bee, married bachelor, the smallest positive rational number,.., Tomorrow]) .
Thank you for coming to my Ted Talk.
To Recap:
My UX gig is fun
I would be getting so much more done if I could charge more hours
The store job is less enjoyable
Change in store management has made that position not nearly as fun
Side gig work should be more fun
But main gig work should have more hours
This mortgage is not going to pay itself
God, I wish it would
This is a rough economy, to be sure
This post was really oddly collaborative between me and ChatGPT
I tried the voice interface with ChatGPT
Did not like
1: it did not sound like the voice I had in my head
2: the voice options were bad
3: waaaaaay over anthropomorphized the interaction
I can see how people can develop “relationships” with an LLM
If you need someone in your life to agree with you and tell you that you are awesome
It is a trap to easily fall into
I have been trying to train away the sycophantic behavior
Takes effort
I think it is worth the trouble
ChatGPT agrees with me….
Hey… wait a second…
Do the substack thing
Do the medium thing
Or don’t… Gonna do this anyway
Have a great week everyone