Chapter 10

The hour hand of a clock moves from 12 to 5 o'clock. Through how many degrees does it move?

The hour hand of a clock moves from 12 to 4 o'clock. Through how many degrees does it move?

The hour hand of a clock moves from 1 to 4 o'clock. Through how many degrees does it move?

The hour hand of a clock moves from 1 to 7 o'clock. Through how many degrees does it move?

In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(48^{\circ}\)

Find the measure of the complement and the supplement of each angle. \(52^{\circ}\)

Find the measure of the complement and the supplement of each angle. \(89^{\circ}\)

Find the measure of the complement and the supplement of each angle. \(1^{\circ}\)

Draw (or find and describe) an object of genus 4 or more.

Find the measure of the complement and the supplement of each angle. \(37.4^{\circ}\)

In the diagram for Exercises \(17-19\), suppose that you are not told that \(\triangle A B C\) and \(\triangle A D E\) are similar. Instead, you are given that \(\overleftrightarrow{E D}\) and \(\overleftrightarrow{C B}\) are parallel. Under these conditions, explain why the triangles must be similar.

Find the measure of the complement and the supplement of each angle. \(15 \frac{1}{3}^{\circ}\)

In Exercises 21-24, use an algebraic equation to find the measures of the two angles described. Begin by letting \(x\) represent the degree measure of the angle's complement or its supplement. The measure of the angle is \(12^{\circ}\) greater than its complement.

Use an algebraic equation to find the measures of the two angles described. Begin by letting \(x\) represent the degree measure of the angle's complement or its supplement. The measure of the angle is \(56^{\circ}\) greater than its complement.

Use an algebraic equation to find the measures of the two angles described. Begin by letting \(x\) represent the degree measure of the angle's complement or its supplement. The measure of the angle is three times greater than its supplement.

Use an algebraic equation to find the measures of the two angles described. Begin by letting \(x\) represent the degree measure of the angle's complement or its supplement. The measure of the angle is \(81^{\circ}\) more than twice that of its supplement.

Find the sum of the measures of the angles of a five-sided polygon.

What is a graph?

Find the sum of the measures of the angles of a six-sided polygon.

What does it mean if a graph is traversable?

Find the sum of the measures of the angles of a quadrilateral.

How do you determine whether or not a graph is traversable?

Find the sum of the measures of the angles of a heptagon.

Describe one way in which topology is different than Euclidean geometry.

State the assumption that Euclid made about parallel lines that was altered in both hyperbolic and elliptic geometry.

How does hyperbolic geometry differ from Euclidean geometry?

How does elliptic geometry differ from Euclidean geometry?

A machine produces open boxes using square sheets of metal measuring 12 inches on each side. The machine cuts equal-sized squares whose sides measure 2 inches from each corner. Then it shapes the metal into an open box by turning up the sides. Find the volume of the box.

What is self-similarity? Describe an object in nature that has this characteristic.

Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 3 inches to the volume of a sphere with a radius of 6 inches.

Some suggest that nature produces its many forms through a combination of both iteration and a touch of randomness. Describe what this means.

At a certain time of day, the angle of elevation of the Sun is \(40^{\circ}\). To the nearest foot, find the height of a tree whose shadow is 35 feet long.

Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 3 inches to the volume of a sphere with a radius of 9 inches.

Find an Internet site devoted to fractals. Use the site to write a paper on a specific use of fractals.

A plane rises from take-off and flies at an angle of \(10^{\circ}\) with the horizontal runway. When it has gained 500 feet in altitude, find the distance, to the nearest foot, the plane has flown.

A cylinder with radius 3 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder?

What will it cost to carpet a rectangular floor measuring 9 feet by 21 feet if the carpet costs \(\$ 26.50\) per square yard?

Can a tessellation be created using only regular nine-sided polygons? Explain your answer.

Use similar triangles to solve Exercises 37-38. A person who is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86-foot shadow. The person's shadow is 6 feet in length. What is the tree's height?

Did you know that laid end to end, the veins, arteries, and capillaries of your body would reach over 40,000 miles? However, your vascular system occupies a very small fraction of your body's volume. Describe a self-similar object in nature, such as your vascular system, with enormous length but relatively small volume.

A road is inclined at an angle of \(5^{\circ}\). After driving 5000 feet along this road, find the driver's increase in altitude. Round to the nearest foot.

A cylinder with radius 2 inches and height 3 inches has its radius quadrupled. How many times greater is the volume of the larger cylinder than the smaller cylinder?

Can a tessellation be created using only regular ten-sided polygons? Explain your answer.

Use similar triangles to solve. A tree casts a shadow 12 feet long. At the same time, a vertical rod 8 feet high casts a shadow that is 6 feet long. How tall is the tree?

Describe a difference between the shapes of man-made objects and objects that occur in nature.

The tallest television transmitting tower in the world is in North Dakota. From a point on level ground 5280 feet (one mile) from the base of the tower, the angle of elevation to the top of the tower is \(21.3^{\circ}\). Approximate the height of the tower to the nearest foot.

A building contractor is to dig a foundation 12 feet long, 9 feet wide, and 6 feet deep for a toll booth. The contractor pays \(\$ 85\) per load for trucks to remove the dirt. Each truck holds 6 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

In Exercises 39-42, use an algebraic equation to determine each rectangle's dimensions. A rectangular field is four times as long as it is wide. If the perimeter of the field is 500 yards, what are the field's dimensions?

Use the Pythagorean Theorem to solve Exercises 39-46. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. A baseball diamond is actually a square with 90 -foot sides. What is the distance from home plate to second base?

Explain what this short poem by Jonathan Swift has to do with fractal images: So Nat'ralists observe, A Flea Hath Smaller Fleas that on him prey and these have smaller Fleas to bite'em And so proceed, ad infinitum