In a given circle a central angle of 40° intercepts a chord of 6 cm. What is the circumference of the circle?
Set 10
Circular Lawn with Path
A circular grass plot 12 feet in diameter is cut by a straight gravel path 3 feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grassy area is:
- 36
– 34 - 30 – 15
- 36 – 33
- 35 – 9√3
- 30 – 9√3
Overlapping Parallelograms
At left we have intersecting parallelograms ABCD and AFCE. Which of the sixteen numbered angles are necessarily the same size as angle #1?
Diagonals of Two Regular Polygons
The total number of angles in two regular polygons is 13, and the total number of diagonals is 25. How many angles are in each polygon?
Six Sequences to Continue
Continue these sequences. Explain how each one works.
| a. | 0 | 1 | 3 | 6 | 7 | 9 | 12 | 13 | ___ | ___ | ___ |
| b. | 1 | 2 | 3 | 4 | 9 | 8 | 27 | 16 | ___ | ___ | ___ |
| c. | 0 | 4 | 8 | 4 | 8 | 12 | 6 | 10 | ___ | ___ | ___ |
| d. | 1 | 2 | 3 | 3 | 6 | 9 | 9 | ___ | ___ | ___ | ___ |
| e. | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | ___ | ___ | ___ |
| f. | 0 | 1 | 1 | 2 | 4 | 7 | 13 | 24 | ___ | ___ | ___ |
Kumquat House Numbers
A new housing development, Mango Manors, is being built outside of town. It costs five cents to buy a single digit house number, but two digits can be bought for nine cents. If each home owner on Kumquat Street, a street with only single digit and 2-digit house numbers, buys the numbers for his own house, the total amount paid is $2.15. If one person buys them all, then the total amount paid is $2.12. How many single digit house numbers are on Kumquat Street?
- 3
- 4
- 5
- 6
- 7
Kite Strings
Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?
Cows, Horses, Sheep in Pasture
Kurt, Chris, and David paid a total of $100 to buy a pasture. They split up the cost according to the amount of grass their animals would eat. Kurt put in 9 horses; David put in 12 cows for twice the time; and Chris put in some sheep for 2.5 times as long as David’s cows. If Chris paid half the cost of the pasture, how many sheep did Chris have, and how much did Kurt and David each pay, if 6 cows eat as much as 4 horses and 10 sheep eat as much as 3 cows in a given amount of time?
Fly Between Trains
Due to an extremely unfortunate error involving a train that was behind schedule and a watch that may have been four minutes slow, there was a head-on collision of two trains in the town of Kipton in 1891. The plan was that the slow westbound passenger train, traveling at 8 miles per hour, would be able to get onto a siding in time to get out of the way of the fast eastbound mail train, traveling at 45 miles per hour. But it didn’t work out that way. (You can Google Kipton Train Wreck to find out the details.) Our concern here is with a fly. When the two trains were exactly 10 miles apart, the fly, sitting on the front of the westbound engine, flew down the tracks to the eastbound train at 60 miles per hour. When it got there, it turned around immediately and flew back to the westbound train, thence to the eastbound, thence to the westbound, back and forth, over and over, going a shorter distance each time. The question, of course, is how far did the fly fly before being crushed between the two engines as they collided?
Parking
Baxter has received a grant to run an environmentally sensitive parking lot downtown. To encourage carpooling, he charges $20 per day per vehicle with only the driver in it and $10 per day for each carpool vehicle with two or more people. On one Monday, 115 vehicles were parked in his lot, and he took in $1990. How many of each kind of vehicle used the lot that day?