Wednesday, August 11, 2010

The Wednesday Quiz III:11 -- Vaguely Recalled Math Concepts!

The Wednesday Quiz -- Season III -- Quiz 11

Vaguely Recalled Math Concepts!

The Wednesday Quiz is a "closed-book" test of knowledge and intuition; please do not look up answers, ask others for help, or answer as a team.

Questions about the rules and the ~Fabulous Prizes~ are answered here.


Having dragged you through the Math, and the Physics, the Wednesday Quiz now drags you back through the Math. Don't worry, it will all be over soon. Ten questions worth ten points apiece, to keep the math simple. Enjoy!

1. What's the difference between a mean and a median?

2. What's the formula for the volume of a cylinder?

3. What's a hypotenuse?

4. Simply, what would the formula x = 5y-15 look like on a graph?

5. Express x^7 using only the "x" and shift keys of your keyboard.

6. What are significant digits? Give a clever example.

7. Pi, e, and the square root of six are "irrational" numbers. What does that mean?

8. In an imaginary number like 77i, what is the value of "i"?

9. I hate to do this to you, but what is the sine of an angle?

10. Also, what's the asymptote of a curve?

Submit your answers in the comments!


Aviatrix said...

1. The mean is all the values added up divided by the number of values, while the median is the middle value. The difference depends on the set of values and may be zero if the data values are balanced above and below the median.

2. V = πr<sup>2</sup>h where r is the radius and h is the height. For some reason the sup tag is forbidden in comments.

3. The hypotenuse is the side opposite the right angle in a right triangle.

4. A straight line with a 1/5 slope that intercepts the x-axis at -15 and the y-axis at +3. If that's not simple enough, it's a line sloping up to the right.

5. xXxXxXxXxXxXx
(where x = x and X is the multiplication symbol)

6. Significant digits are those which are meaningful in terms of precision. If I need to reduce the airplane weight by 250 pounds by burning fuel that weighs 6.1 pounds per gallon then a calculator tells me that I need to burn 40.98 gallons, but as I only have two significant figures for the weight per gallon, I don't get to magically have four for the burn required. To two significant figures that's 41 gallons I need to burn. But that's not clever at all, is it?

7. Irrational numbers cannot be fully represented as a ratio of two integers, and their decimal representations continue forever without becoming a regularly repeating sequence.

8. The value of i is the square root of negative one.

9. Draw a right triangle including the angle in question. Its sine is the ratio of the side opposite the angle to the hypotenuse. It's more normal to explain it with a circle, but that's challenging without a diagram.

10. The asympote is a line that the curve approaches but never reaches.

I reserve the right to amend the answer to #6 if I manage to think of a clever example of significant digits.

La Gringissima said...

Just give me a big ole goose egg on this one.

Elaine said...

1. The mean is the average; the median is simply the center score.
2. pi times diameter times height.
3. The diagonal line connecting the two short legs of a right triangle. the square of the hypotenuse is equal to the sum of the squares of the other two side.
4. a dot
5. Xxxxxxx
6. I'm holding up a significant digit right this minute, M5000.
7. They express quantities that continue infinitely
8. i = the square root of negative one
9. the angle times the square root of 2 (1.141)
10. I don't remember. Maybe the degree of curvature?
In fact, obviously I have forgotten most of my maths, since the last class I took, as a junior in college, was in 1967.

Elizabeth said...

1. You are mean. The median is the center strip on a road. Also, the first one is the average of a set of numbers and the second is the number in the middle of the set.

2. Pi x r squared x h

3. The side of a right triangle opposite the right angle.

4. No idea.

5. X x X x X x X x X x X x X

6. 42. It's the answer to life, the universe, and everything.

7. It means they cannot be expressed as finite numbers, more or less. There's always more to them than you see. Also I am *not* irrational. Not always, anyway.

8. The price of pork bellies on the Chicago Exchange at 8:13am less the difference between a cab fare from JFK to the Statue of Liberty and a dozen roses purchased on a street corner in Bangkok, because you're feeling suddenly romantic and want to give them to your partner.

9. No you don't. You're enjoying this. All angles are Capricorns.

10. When it starts coughing and has a rash that just won't go away.

Cartophiliac said...

1. Unkind and someone not quite in middle age
2. pi x r squared x length
3. something about a triangle
4. a line in need of viagra
5. X x X x X x X x X x X x X
6. my middle finger
7. numbers that only exist in Superman's bizarro world (do not exist in the real world)
8. square root of 1
9. trick question, not sine but sin
10. a curve in the opposite arc

mrs.5000 said...

1 A mean is a not very nice and a median is the strip in the middle of a divided highway. Also, a mean is the arithmetical average (a sum of numbers divided by how many were added together), whereas a median is the most frequently occurring number in a set.
2 pi r squared times height
3 the longest side of a right triangle (opposite the right angle)
4 I think that's a line with a 1 in 5 slope, sloping up to the right and intersecting the y axis at -15
5 I think you mean XxXxXxXxXxXxX
6 If I said, that little caterpillar crawling up your sleeve looks about 2/3 of an inch long, and you reported in your blog that it measured .66666666667 inches, the excessive number of digits would convey a misleadingly precise measurement. Significant digits (we called them sig figs in HS chemistry) round off the data to reflect an appropriate level of accuracy.
7 All them messy digits to the right of their decimal point just keep going and going, they don't stop or repeat
8 I think it's the square of -1.
9 Hoo boy. Well, I think it's the angle's tangent times its cosine, for one thing. You may be looking for something more like how it would introduce itself at a cocktail party, but it's been a long time since I've been at one of those parties.
10 Oh, the asymptote is the line that a curve approaches and never quite arrives at.

PB said...

Ooh, I used to be good at math. Here we go:

1. The mean is the average of a set of numbers. The median is the middle number of the set.
2. The height of the cylinder times pi times the radius of the circular part of the cylinder squared (this would be much simpler to write if I knew how to write pi and superscipts in Blogger comments).
3. The longest side of a right triangle.
4. A line that crosses the x-axis at 3 and slopes up at a rate of 1 unit up for every 5 units to the right.
6. Significant digits are one more digit than can be exactly measured using the tools at hand (meaning you estimate one digit). For example, if Michael5000 were to be forced to eat tomatoes and made it through about 3 and a third of them, he could be estimated to have eaten 3.3 tomatoes; 3.33 would go beyond what could be accurately estimated using significant digits.
7. The digits after the decimal point continue infinitely without ever repeating.
8. The square root of negative 1.
9. The sine of an angle is the ratio of the opposite side to that angle to the hypotenuse of the triangle.
10. An asymptote of a curve is any place where the derivative (and therefore the slope) of the curve is 0.

Kate said...

Aw, Morgan will be disappointed that he missed this one! He is at cross country camp -- no computers there.

Ben said...

Morgan will swear that you plan these topics so that the ones he is strong on are posted the weeks he's out of town away from a computer.

I, on the other hand, seem to HAVE no strong topics.

1. A mean is the average of a group of values (add 'em all up and divide by the number of values). A median is the particular value that is the middle of the range (if I have 9 values, the median would be the 5th one).
2. πr² times the length of the cylinder (that's pi-r-squared, in case my symbols don't come across).
3. It's one of the angle points in a triangle that is used for measurments related to the triangle. I'm not sure if it matters WHICH of the three points it is.
4. It would be a straight line sloping up from the left (lower) to the right (higher).
5. XxXxXxXxXxXxX (in this case the big Xs are X and the little xs are times symbols--I thought that looked clearer than the other way around).
6. It's the number of decimal places in a number that are important to whatever calculation or data you're working with. For example, US currency has two significant digits--like $53.09--unless you're referring to the price of gas.
7. The decimal places go on to infinity.
8. the negative square root of 1.
9. I don't think you hate to do this to me at all. Maybe you should have asked me what the sine of the times is instead. In either case, I don't know the answer.
10. No idea.

Michael5000 said...

The L&TM5K supports youth scholarly and athletic achievement, and therefore this Quiz will not be graded until Morgan gets back from Cross Country Camp.

Elaine said...

There's a whole lotta bombing goin' on, though Aviatrix and Architect have an edge to begin with. Wanna know how many of my special ed students needed me to teach the Unit Circle?

I used to be a contenda (she sniffled.)

UnwiseOwl said...

Wooh, maths! Time for the youth contingent shine using their freshly imprinted knowledge...
1. A mean is the average number of a set, a median is the central value (which is only really applicable in non-contiguous data sets). The difference between the two can inform you of any skewing in you data.
2. Let's see, area of the base (2piR^2) multiplied by the height of the cylinder.
3. The side opposing the right angle in a right-angled triangle. Alt: Better than the hypota-weather.
4. A straight line passing through the x-axis at x=-15 and the y axis at y=3.
5. "XxXxXxXxXxXxX" or "XXXXXXX". Both are correct but kinda dumb.
6. Significant figures are the digits in a number which are meaningful, it terms of portraying the accuracy of data as well as succintness. 6 million has one significant figure (the 6), and reflects either the inability of the author to provide more accurate numbers (like 6.354 million) or simply that (s)he thought that 6 million jews dying in the holocaust was all the precision we needed to know to get the idea.
7. Irrational numbers are numbers that cannot be portrayed in decimal form to full accuracy as they have an infinite number of non-recurring decimals.
8. The square root of negative one.
9. The sine of an angle is the opposite side from the angle divided by the hypotenuse if the angle were imagined as part of a right-angled triangle.
10. A line that a function gradually draws infintely near to but never actually touches.

Wow...I think that's the first time this quiz season that I've managed to pull off a perfect score. I hope that I haven't anything too dumb.

UnwiseOwl said...

I jsut saw what I did that was dumb.

Kate said...

Morgan gets back on Sunday -- I might even let him take the quiz before he takes a shower, which is saying a lot since it will have been over a week....

Aviatrix said...

I thought of a possibly clever example for number six. I want to compare my physical attributes to those of an American movie star, but the American's measurements are given in inches and I only have Canadian measuring tapes. So I take my 92 cm measurement and divide by 2.54 to get inches, getting 36.220472440944881889763779527559 in Windows calculator. Seeing as I only know my metric measurement to two significant figures, the result should be rounded to the same, so 36 inches. The significance of this depends on whether the original measurement is my waist or my bust.

Aviatrix said...

The significance of my figure, I mean.

balaywho said...

Oh, math, never touch the stuff...

1. the difference is the "di" of course.
2. Pi r squared X height?
3. part of the triangle
4. huh?
6. index, middle, ring, and pinkie
7. they don't respond to a well reasoned arguement (and after the decimal, they just go on forever. So irrational!)
8. i is imagination
9. that which is not the cosine
10. a swerve?

I give up.

cecil said...

‎1. Mean=average, median=halfway
2. pi r squared cubed
3. Opposite the right angle in a triangle.
4. Diagonal line going sw
...6. 7.52 = 7
7. Imaginary numbers
8. Oz
9. cosine of the tangent
10. the volume inside the curve

chuckdaddy said...

1. Mean is the average,the median is the middle number (when the numbers are lined up smallest to largest)
2. pi times radius squared times height
3. The side opposite the right angle in a triangle
4. It would "intercept" the y-axis at 3 and go up at a slope of 1/5
5. x*x*x*x*x*x*x
6. ?
7. You can't represent them with a regular fraction
8. square root of -1
9. The side opposite that angle divided by the hypotenuse
10. Hmmmm... Hold on it might by coming back to me... I think I have it, but a picture would be better. Isn't that when a line is curving up at a point, and it gets as close as theoretically possible, but never quite reaches it. I think it happens when a particular x gives an answer that is a something over zero.

DrSchnell said...

1. mean is what most people call "average" - total of all values divided by number of values. Median is the middle data value of an ordered data set (or, in the case of a data set with an even number of values, the mean of the two middle values).
2. pi(r)squared x height
3. the side of a right triangle opposite the right angle
4. a straight line. Intersecting the Y axis at 3. Sloping up as it goes from left to right, intersecting the X axis at -15.
5. XxXxXxXxXxXxX
6. The opposeable thumb! um.... something about the number of digits in a value that actually matter, given the input numbers. So, umm..... if you have 10 bananas and you divide them among three monkeys, each monkey gets (mathematically) 3.333333333333... bananas (Xeno's banana). But, given that your original data only had two digits, each monkey gets 3.3 bananas. Or something like that.
7. They each describe Sarah Palin fans... No, I mean that they can't be expressed as a fraction, and they just go on and on and on and on and on. Kind of like Sarah Palin.
8. square root of -1
9. If you had a right triangle with that angle as one of the angle, it is the length of the side of the triangle opposite that angle divided by the hypotenuse (see #3 above). SOHCAHTOA - thanks Col. Lunger (trig. teacher from high school).
10. line that a curve gets closer and closer and closer to without ever reaching it.

Morgan said...

1. Mean is all numbers in a group added together and divided by the number of items in said group, median is the number that is smack in the middle of a group, if said group is put in numerical order.
2. (pi*r^2)*h
3. The side opposite the right angle in a right triangle.
4. The slope will be upward, and the x-intercept will be at -15.
5. XxXxXxXxXxXxX
6. In an equation using real-life inputs, we assume that our measurements have a margin of error. For example, 1.55 could potentially mean 1.5500000002, or 1.549999999993. Therefore, the number of SIGNIFICANT DIGITS in the answer must be the same as those in the inputs, otherwise we must round. The significant digits are the non-zero numbers. 0.0000023 has two significant digits. 12000 has 2 as well. However, 12000. (note the appending decimal point) shows that the final three zeroes are correct using accurate measurements, and therefore should be treated as significant digits.
7. The numbers, if shown in decimal format, would be never-ending and would not repeat.
8. The square root of negative one.
9. The ratio of its opposite side and its hypotenuse, if said angle was in a right triangle.
10. An asymptote is a line which a curve approaches but never reaches, on into infinity.

Aviatrix said...

A lot of people are using the space bar and other keys in their expansion of x^7. I hope to see them duly disqualified.

Michael5000 said...

1. The mean is just the average; the median is the "middle" number of a series.

2. The volume of a cylinder is pi times the radius squared, like for a circle, times the height.

3. A hypotenuse is the side of a right triangle across from the right angle.

4. The formula x = 5y-15 would look like a gradualing rising line crossing the y axis at 3 and the x axis at -15.

5. Yeah, yeah.

6. Significant digits are the number of decimal points that such-and-such can be measured with meaningful accuracy.

7. "Irrational" numbers never run out of digits. Like pi -- we say it's 3.1415927, but that decimal actually keeps going on and on forever in a mind-blowing fashion.

8. "i" is the value of the square root of -1.

9. The sine of an angle is the ratio of the length of the "opposite" side to the length of the hypotenuse. And I did too hate doing it to you.

10. Per Chuckdaddy, the asymptote of a curve is when a line is curving up at a point, and it gets as close as theoretically possible, but never quite reaches it.

Michael5000 said...

Making the winners, with their more or less perfect scores, Aviatrix and DrSchnell and Morgan. The Owl and PB scored 90, and Chuck and the Mrs. scored 85 each.

Aviatrix said...

*high fives all the high scorers*

"And those other people in math class said they were never going to use this knowledge for anything!"

I use numbers 1, 3, 6 and 9 in the course of my job, consider 2 to be obvious assuming you know pi-r-squared and are familiar with the concept of volume, had to get out paper for 5, and consider 7, 8 and 10 to be mostly useless remnants of a proper education. Like being able to name the principle characters in Wuthering Heights, or knowing the names of the Saxon kings in succession order. Number four was an odd orthographic challenge. I'm still curious as to what you were hoping for.

Michael5000 said...

I was hoping to delight and entertain, naturally.

Morgan said...

Thanks for holding the scoring off :) Sorry for making people wait.

Nichim said...

I would have done well on this, but I was busy living in a boring postcard of southern Idaho.