This problem is taken from a Chinese mathematics textbook called Chui-chang suan-shu, or Nine Chapters on the Mathematical Art, which was written about $250$ B.C.

A $10$-ft-long stem of bamboo is broken in such a way that its tip touches the ground $3 \mathrm{ft}$ from the base of the stem, as shown in the figure. What is the height of the break? [Hint: Use the Pythagorean Theorem.]

Fluid Flow The velocity $v$ of a fluid flowing in a conduit is inversely proportional to the cross-sectional area of the conduit. (Assume that the volume of the flow per unit of time is held constant.) Determine the change in the velocity of water flowing from a hose when a person places a finger over the end of the hose to decrease its cross-sectional area by $25 \%$.

Fluid Flow The velocity $v$ of a fluid flowing in a conduit is inversely proportional to the cross-sectional area of the conduit. (Assume that the volume of the flow per unit of time is held constant.)

(a) Determine the change in the velocity of water flowing from a hose when a person places a finger over the end of the hose to decrease its cross-sectional area by $25 \%$.

Fluid Flow The velocity $v$ of a fluid flowing in a conduit is inversely proportional to the cross-sectional area of the conduit. (Assume that the volume of the flow per unit of time is held constant.)

(b) Use the fluid velocity model in part (a) to determine the effect on the velocity of a stream when it is dredged to increase its cross-sectional area by one-third.

A movie star, unwilling to give his age, posed the following riddle to a gossip columnist. "Seven years ago, I was eleven times as old as my daughter. Now I am four times as old as she is." How old is the star?

A movie star, unwilling to give his age, posed the following riddle to a gossip columnist: "Seven years ago, I was eleven times as old as my daughter. Now I am four times as old as she is." How old is the movie star?

A movie star, unwilling to give his age, posed the following riddle to a gossip columnist: "Seven years ago, I was eleven times as old as my daughter. Now I am four times as old as she is." How old is the movie star?

Jack invests $\$ 1000$ at a certain annual interest rate, and he invests another $\$ 2000$ at an annual rate that is one-half percent higher. If he receives a total of $\$ 190$ interest in $1$ year, at what rate is the $\$ 1000$ invested?

Jack invests $1000 at a certain annual interest rate, and he invests another$2000 at an annual rate that is one-half percent higher. If he receives a total of $190 interest in 1 year, at what rate is the$1000 invested?

Jack invests $1000 at a certain annual interest rate, and he invests another$2000 at an annual rate that is one-half percent higher. If he receives a total of $190 interest in 1 year, at what rate is the$1000 invested?

If Ben invests $\$ 4000$ at $4 \%$ interest per year, how much additional money must he invest at $5 \frac{1}{2} \%$ annual interest to ensure that the interest he receives each year is $4 \frac{1}{2} \%$ of the total amount invested ?

Phyllis invested $12,000, a portion earning a simple interest rate of$4 $\frac{1}{2}$ %$per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these investments was$525. How much money did she invest at each rate?

Mary has $3.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and five more nickels than dimes, how many coins of each type does she have?

Wendy took a trip from Davenport to Omaha, a distance of $300 \mathrm{}$ mi. She traveled part of the way by bus, which arrived at the train station