Quiz Question

One of a continuing series

Continuing into the new year, here are two easy geometry problems.

Compute the perimeters of the two shapes. Enter your answer in the comments section below.

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Quiz Question

One of a continuing series

A break from geometry problems on this, the first day of 2018. Here is a short geography quiz. Following is a list of American cities, in pairs. Your job is to, for each pair, pick the city with the largest population. Some of these are easy, others not so much so. After you finish picking, post your answers in the comments section and then grade yourself by going to Wikipedia. Use the population figures from the city’s Wikipedia entry. Some cities have the same name as others in other states. Assume the most prominent in case of conflict.

  1. Dallas – San Diego
  2. Austin – San Francisco
  3. Philadelphia – Chicago
  4. Houston – Boston
  5. Muleshoe – Lipan (both in Texas)
  6. Santa Fe – Denver
  7. Kansas City (Kansas and Missouri)
  8. Topeka – Memphis
  9. Minneapolis – Fort Worth
  10. Miami – Phoenix
  11. Oklahoma City – Baltimore

Update and answers:

  1. Yes, San Diego is more populous than Dallas. Just barely. That’s one I missed.
  2. In the rankings, Austin is number 11, San Francisco is number 14.
  3. Chicago 3, Philadelphia 5.
  4. Houston 4, Boston 21.
  5. This is an easy one. Muleshoe, Texas is much larger than Lipan.
  6. Denver is number 23, Santa Fe does not make the top 100.
  7. Kansas City, Missouri, ranks number 37. Kansas City, Kansas, does not make the list.
  8. Memphis is number 20, larger than Boston. Topeka does not make the list.
  9. Fort Worth, 17, is way ahead of Minneapolis
  10. Phoenix, at number 6, far out-ranks Miami.
  11. Baltimore 26, Oklahoma City 29.

Quiz Question

One of a continuing series

Merry Christmas. Here is an easy one. Make the usual assumptions from the drawing. What is the value of x? Post your answer as a comment below.

Update and solution

I expected somebody would solve this quickly, and Mike nailed it within hours of posting. Mike only provided the solution. See the comment below. Here is how it unravels. See the image.

Obviously this is a semicircle and a square with a line tangent to the circle. We now have a right triangle ABC, tangent to the circle at D.

From  basic geometry we know that DB = 2. Also x = EA = AD. From there everything falls out quickly.

AB2 =AC2 + CB2

(x + 2)2 = (2 – x)2 + 4

x = ½

Quiz Question

One of a continuing series

A

B

Two photos of the moon, taken from my house in San Antonio, Texas, two nights apart. Which photo was taken first?

No fair running to an astronomy book. No fair going outside to look at the moon. Post your answer as a comment below.

Update and answer

Anybody who’s spent a lot of time outdoors knows this. In the northern hemisphere, especially as far as 30° north looks up at the moon from the north. That means the terminator, the significant aspect of moon phases, moves from right to left day after day. That means that photo B was taken before photo A. In this case two days before.

Quiz Question

One of a continuing series

Keeping with a run of math questions… This problem is on the Internet. You have to provide an answer without going to the Internet.

The large arc is centered at O, The small arc is centered at D. Prove the two shaded areas are equal.

Post  your answer as a comment below.

Update and solution

Mike and Steve have provided correct solutions. See the comments. Steve worked out the math, and Mike stated the path to resolution rather cryptically. Both invoked π, which is not necessary. Try this approach.

The triangle is a right, equilateral triangle. The hypotenuse is √2 times the base and is also the diameter of the small semicircle. You will have no problem from that point concluding the small semicircle’s area is ½ the area of the large semicircle. The area A of the small semicircle is equal to the area of the triangle + the circle segment subtended by the triangle’s hypotenuse. The area of the triangle is A – the area of the segment. The area of the lune outside the large semicircle is A – the area of the segment. Therefore the two areas are the same.

Quiz Question

One of a continuing series

Back to math questions for a change. Full disclosure: I don’t make up all of these. This is from an Internet site. No fair going to the Internet to get the answer.

The triangle is equilateral. Prove the shaded area is equal to the inner circle. Post your answer as a comment below.

Update and solution

Mike is the first and only to provide the correct solution. A reasoning goes like this.

It is easy to demonstrate (exercise left to the reader) that the inner circle is ¼ the area of the outer circle. Then the region between the inner and outer circles is ¾ the area of the outer circle. The blue-shaded regions total 1/3 of this difference or ¼ the area of the outer circle. The inner circle is equal to the blue-shaded area.

Quiz Question

One of a continuing series

More fun with word games…

37 years ago I was taking a course in database design, and the professor got onto the subject of data security. He discussed how contents of a file could be encrypted to protect your information from prying eyes. To illustrate, he wrote two lines of text on the board:

ABTAESBAD

FRSRXRMG

Then he turned to the class, pointed to the board, and asked, “What is this?”

I had been watching as he was writing and had started running some stuff through my head.

“Anybody?” the professor inquired.

I raised my hand.

He said, “Yes?”

I said, “Well the top one is a …,” and here I inserted an encryption technique. “And the second one is …,” and I mentioned another method.

The professor looked a little unsettled. “But what do these mean?”

So I told him.

Today’s question (problem) is, translate the two lines of text. Post your answer as a comment below. I will post a hint tomorrow if nobody has the solution by then.

Update and answer

Greg got it right. I was looking at the words. What had about that many letters? What course was I sitting in? Database Design. Bingo. Then my cruel nature emerged. The professor asked how I did that. I told him I had experience with that sort of thing, and I didn’t say any more.

Another update and correction

Mike has pointed out the obvious. The top line of text has an extra B. My bad. I scanned this line not enough times to spot the error. I apologize for posing a Quiz Question with no answer. Here are the two lines of text that make sense.

ABTAESAD

FRSRXRMG

Quiz Question

One of a continuing series

Airliner crosses Vineland Avenue North Hollywood while landing at Burbank Airport

This is the kind of question that sometimes comes up in engineering.

An engineer is tasked with designing a new airplane, with two requirements. The airplane must be able to carry 8 passengers, and the design must use engine model A3-28, made by the boss’s company.

The engineer completes a design, and then does some calculations. The plane will not fly with a single engine of that model, but it will fly with two engines. The engineer’s boss tells him to modify the design and use two of the engines.

The engineer knows this is a bad idea.

Why?

Post your answer in the comments section below.

Quiz Question

One of a continuing series

I’m taking a few days off, so here is another easy Quiz Question for the week. Name the country in the map above. Post your answer in the comments section  below. John Coombes, you should be able to get this one.

Update and answer

All right! A number of people figured out this was on the west coast of somewhere (see the water off to the left). Helen figured it can’t be Chile or Peru. It must  be Ecuador. Take note, geography students. That horizontal line running into Ecuador’s coast is the equator, after which the country is named.

Quiz Question

One of a continuing series

There’s a lot of stuff out there. Some more than others. On this planet, which is more?

  1. Uranium or lead
  2. Gold or platinum
  3. Sulfur or calcium
  4. Hydrogen or potassium
  5. Sodium or potassium
  6. Copper or zinc
  7. Nickel or aluminum
  8. Silver or nickel
  9. Iodine or fluorine
  10. Oxygen or iron

These are hard. You can use Google. Post your answers on Facebook. It’s interesting which things are more than you expected.