4. An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by cutting out equal squares from each corner and folding up the flaps to form the sides. Find the dimensions of the largest box that can be constructed in this way? 5. A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr. Meanwhile, the car is going north at a constant speed of 60 km/hr. (a) At what rate are they separating or approaching after 2 hours? (b) At what time are they closest to each other 6. A window is in the form of an equilateral triangle surmounted on a rectangle. The rectangle is of clear glass and transmit twice as much light as does the triangle which is made of stained glass. If the entire window has a perimeter of 20 feet, find the dimensions of the window that will admit the most light. 7. A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet above ground. At what rate is the length of his shadow changing when he is 20 feet away from the base of the light? At what rate is the tip of his shadow moving? 8. Water is running out of a conical funnel at the rate of 2 cubic inches per second. Th radius at the top of the funnel is 6 inches and the height of the funnel is 12 inches. How fast is the water level dropping when the water is 4 inches deep?
4. An open box is to be made from a square piece of cardboard, 18 inches by 18 inches, by cutting out equal squares from each corner and folding up the flaps to form the sides. Find the dimensions of the largest box that can be constructed in this way? 5. A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr. Meanwhile, the car is going north at a constant speed of 60 km/hr. (a) At what rate are they separating or approaching after 2 hours? (b) At what time are they closest to each other 6. A window is in the form of an equilateral triangle surmounted on a rectangle. The rectangle is of clear glass and transmit twice as much light as does the triangle which is made of stained glass. If the entire window has a perimeter of 20 feet, find the dimensions of the window that will admit the most light. 7. A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet above ground. At what rate is the length of his shadow changing when he is 20 feet away from the base of the light? At what rate is the tip of his shadow moving? 8. Water is running out of a conical funnel at the rate of 2 cubic inches per second. Th radius at the top of the funnel is 6 inches and the height of the funnel is 12 inches. How fast is the water level dropping when the water is 4 inches deep?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.4: Polyhedrons And Spheres
Problem 24E: A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:4. An open box is to be made from a square piece of cardboard, 18 inches by 18
inches, by cutting out equal squares from each corner and folding up the flaps to form
the sides. Find the dimensions of the largest box that can be constructed in this way?
5. A truck is 300 kilometers due east of a car and is traveling west at a constant speed
of 30km/hr. Meanwhile, the car is going north at a constant speed of 60 km/hr. (a) At
what rate are they separating or approaching after 2 hours? (b) At what time are they
closest to each other
6. A window is in the form of an equilateral triangle surmounted on a rectangle. The
rectangle is of clear glass and transmit twice as much light as does the triangle which
is made of stained glass. If the entire window has a perimeter of 20 feet, find the
dimensions of the window that will admit the most light.
7. A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12
feet above ground. At what rate is the length of his shadow changing when he is 20
feet away from the base of the light? At what rate is the tip of his shadow moving?
8. Water is running out of a conical funnel at the rate of 2 cubic inches per second. Th
radius at the top of the funnel is 6 inches and the height of the funnel is 12 inches.
How fast is the water level dropping when the water is 4 inches deep?
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