Today's Topics (July 2020)

[RZ923]

@debbie Sorry if this sounds rude, but can you please update the Fri 10 July livestream topics and overheard?
Thanks

[debbie]

@RZ923 It's not rude; thanks for the reminder! I was swamped with a lot of things yesterday, but I'll make sure to post the Overheard and Today's Topics very soon today.

[debbie]

Topics from the Friday 7/10/20 live stream

• How many subsets of \( (1, 2, 3, 4, \ldots, 12\) have exactly 1 or 2 primes?

• When \(x^2 - 5x + 3c\) is divided by \(x-3,\) the remainder is \(12.\) What is the value of \(c?\)

• One-inch squares are cut from the corners of a \(5\)-inch square. What is the area in square inches of the largest square that can fit into the remaining space?

• In rectangle \(ABCD,\) we have \(A = (6, -22), B = (2006, 178), D = (8, y),\) for some integer \(y.\) What is the area of the rectangle \(ABCD?\)

• Is there a quick way to solve the problem where two cars are coming towards each other and a fly is flying in between? How much distance does the fly travel when the cars collide?

• If you have done 20 questions on the AMC 10, and you have 5 questions you don't know how to do, how many questions should you guess on to have the highest expected score?

[debbie]

Topics from the Friday, 7/17/20 live stream

• How many zeroes are at the end of \(126! - 125!?\) (That's 126 factorial )

• Why are quadratics called quadratics?

• \(ABC\) is a triangle. Let \(D\) be the midpoint of \(\overline{BC},\) \(E\) is a point on \(\overline{AC},\) \(\overline{AB}\) and \(\overline{DE}\) are parallel. \(\overline{AD}\) and \(\overline{BE}\) intersect at point \(F.\) If \(AEF\) has an area of \(1,\) what is \(ABC?\)

• How do you factor quadratics using the quadratic formula?

• If \(AB\) in base \(7\) is equal to \(BA\) in base \(9,\) what is the number in base \(10?\)

• Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(8\) )

• Is it possible for a line to contain irrational points? (Yes, if it's vertical or horizontal.) What if we want a line that has slope not \(0\) or infinite or undefined? (Answer: irrational slope and intercept will do the trick!)

• Which countries share the longest international border? (Answer: U.S. and Canada )

• How many four-digit numbers with two middle digits of \(7\) or \(9\) (not necessarily in that order) are divisible by \(45?\)

• Find all the possible values for \(ln{ (e^x)}.\)

• Can you give an example of an undefinable real number?

• I am a famous mathematician. If you change a letter in my last name, you might be able to measure how tall you are. Who am I? (Answer: Euler)

• Minecraft Po goes mining for diamonds! He finds \(21\) cobblestones, \(1\) diamond, and \(108945\) coal! What percent of the stuff he found is cobblestone?

• Which field of mathematics will grow the most in coming times?

• Is there trigonometry for shapes with more angles than three?

• How long are you going to do live streams?

• How is MOP going?

• Are there any conditions to be on the math team that you run?

[RZ923]

@debbie said in Today's Topics (July 2020):

• Turn me on my side, and I am everything. Cut me in half, and I am nothing. What am I? (Answer: \(\infty\) )

Shouldn’t the answer be \(8\)?

[debbie]

@RZ923 Yes, you're right; thanks!

[The Blade Dancer]

Shouldn't that be 8 because then it becomes infinite

Also Debbie's to do list be like: https://www.youtube.com/watch?v=zGl796352RI

[debbie]

@The-Rogue-Blade Sorry, I missed that... what did you say again? I was looking at my list of things to do...

[debbie]

Topics from the Friday 7/24/20 live stream

• The mean of a list of \(12\) numbers is \(13,\) and the modes are \(a, b, c, d.\) If \(a + 2, b - 6, c + 1,\) and \(d - 3\) are distinct numbers in this list, and none of them are modes of the list, then what is \(a + b + c + d?\)

• In triangle \(\bigtriangleup ABC, AB = 13, BC = 14, CA = 15\) and \(M\) is the midpoint of \(\overline{BC}.\) Let \(P\) be a point on the segment \(AM\) so that \(\angle BPC + \angle BAC = 180^{\circ}.\) Find \(MP \times MA.\)

• Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining dice?

• Which do you think is more important for kids learning math: more depth (digging deeper into only a few topics), or more width (learning more topics, but only learning a bit of each?)

• Po the dolphin answers my question. He answers \(500\%.\) What is the chance that he will answer this problem with \(500\%\) again?

• How to multiply two or more numbers in less than \(15\) seconds without using a calculator.

• I was dumpster diving when I found a broken calculator. \(4 = 1, 3 = 3, 5 = 0, \) and \(6=?\)

• Suppose you are at a distance of \(r\) above a planet of radius \(r.\) How much of the planet is visible?

• How many ways are there to choose \(5\) books from \(12\) books with no neighboring books chosen?

[debbie]

Topics from the Friday 7/31/20 live stream

• How many zeroes are there from all the integers from \(1\) to \(25\) in binary?

• Let \(S\) be the set of points determined by \( \left| |x|-2 \right| + \left| |y|-1 \right| = 1.\) If a model of \(S\) were built from wire of negligible thickness, then what is the total length of wire required?

• \(G\) is an \(8 \times 8\) grid with a \(1\) written in each of its unit squares. An operation consists of multiplying all entries in a row or column by \(-1.\) How many distinct grids can be obtained by applying this operation to \(G\) a finite number of times?

• Is it possible that geometry can be proved by algebra?

• What is your chess rating?

• How hard it is to get into Carnegie Mellon University?

• What majors does Carnegie Mellon specialize in?

• Can you get your channel certified? Like get that check mark next to your channel name?