The top of an off-shore wind turbine can be sighted from the deck of your yacht from a point 252 meters from the base of the wind turbine with an angle of elevation that doubles as you sail 172 meters closer to the base of the wind turbine. How tall is the wind turbine?
A special basketball shot is made by James 20% of the time, by Kristy 30% of the time, and by Hannah 40% of the time. A game is played in which the players shoot consecutively and the first player to make the shot wins. If the order of shooting is first James, then Kristy, and then Hannah, which of the following statements are true?
cos21° + cos22° + cos23° + . . . + cos289° + cos290° = ?
A notice goes up on the company bulletin board:
“All those who have not already received their subsistence allowance this week should report to the Deputy Assistant Bursar (D.A.B.) at 9 am next Monday, unless they also failed to get it last week, in which case they should not report to anybody anywhere, unless they are over 21 and/or have a maternal grandmother who is still alive, in which case they should either report to the Substantive Acting Registrar at 10 pm on Tuesday or to the D.A.B. at 12 noon on Wednesday according to whether their surname begins with a letter in the first half of the alphabet or not, unless their paternal grandmother does not have or did not have a passport, in which case they should report to the Warden as soon as possible, unless they have already passed their driving test and/or do not have a bicycle, in which case they should take a couple of aspirins and go quietly home to bed.”
Ms. Zola Hooberry, age 20, has not received her subsistence allowance this week or last. She has a bicycle but has not passed her driving test. Both her grandmothers are still alive and have passports.
What should she do?
A wheel of radius 10 inches rolls inside a wheel of radius 54 inches. Point P1 on the little rolling wheel starts at point P on the fixed wheel. After how many revolutions of the little wheel do points P and P1 coincide once more?
Two parallelograms are drawn at random on a page (i.e., in a plane). Describe how to draw a single line that will divide each parallelogram into two regions having equal area.
A circle and a square have the same area. What is the ratio of the area of a square inscribed in the circle to the area of a circle inscribed in the square? (Draw nice pictures.)
In the figure, AB and CD are parallel, the measure of angle D is twice that of angle B, AD is of length a and CD is of length b. What is the length of AB in terms of a and b?
Find an integer n such that (1 + 2 + 3 + . . . + n)/3n = 36.
Let us take another look at the goldfish pond problem. Just how short could the two boards be to reach across in the way shown here? For purposes of this problem, ignore any width of boards and consider them as two congruent segments. Find the length of these segments.