Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. calcPa Operatio Function Symbols (d) Use the given information to write an equation that relates the variables x and y. Relations Sets Vi o! Vectors (e) Use part (d) to write the volume as a function of only x. Trig V) - | x(3— 2х)2 Greek Help (f) Finish solving the problem by finding the largest volume that such a box can have. ft3 미ㄷ
Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. calcPa Operatio Function Symbols (d) Use the given information to write an equation that relates the variables x and y. Relations Sets Vi o! Vectors (e) Use part (d) to write the volume as a function of only x. Trig V) - | x(3— 2х)2 Greek Help (f) Finish solving the problem by finding the largest volume that such a box can have. ft3 미ㄷ
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
Section9.1: Prisms, Area And Volume
Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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parts c, d, and f.
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