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Magazine Problem 36
Some suggest that nature produces its many forms through a combination of both iteration and a touch of randomness. Describe what this means.
Problem 36
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.
Problem 36
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.
Problem 37
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?
Problem 37
What will it cost to carpet a rectangular floor measuring 9 feet by 21 feet if the carpet costs \(\$ 26.50\) per square yard?
Problem 37
Find an Internet site devoted to fractals. Use the site to write a paper on a specific use of fractals.
Problem 37
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.
Problem 37
Can a tessellation be created using only regular nine-sided polygons? Explain your answer.
Problem 37
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?
Problem 38
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.
