1.5.5. Write an equation to represent the following statements:
(a) At Mindy's restaurant, for every four people who ordered cheesecake,
there were five who ordered strudel.
(b) There are six times as many students as professors at this college.
1.5.6. Guy wires are strung from the top of each of two poles to the base
of the other. What is the height from the ground where the two wires cross?
1.5.7. A piece of paper 8 inches wide is folded as in Figure 1.17 so that one
corner is placed on the opposite side. Express the length of the crease, L, in
terms of the angle 0 alone.
1.5.8. Let P1, P2,
P12 be the successive vertices of a regular dodeca-
gon (twelve sides). Are the diagonals concurrent?
1.5.9. Use algebra to support your answers to each of the following.
(a) A car travels from A to B at the rate of 40 miles per hour and then
returns from B to A at the rate of 60 miles per hour. Is the average rate
for the round trip more or less than 50 miles per hour?
(b) You are given a cup of coffee and a cup of cream, each containing the
same amount of liquid. A spoonful of cream is taken from the cup and
put into the coffee cup, then a spoonful of the mixture is put back into
the cream cup. Is there now more or less cream in the coffee cup than
coffee in the cream cup? (This problem has an elegant nonalgebraic
solution based on the observation that the coffee in the cream cup has
displaced an equal amount of cream which must be in the coffee cup.)
Imagine that the earth is a smooth sphere and that a string is wrapped
around it at the equator. Now suppose that the string is lengthened by
six feet and the new length is evenly pushed out to form a larger circle
just over the equator. Is the distance between the string and the surface
of the earth more or less than one inch?
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