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13 Nov 2019
1. (Based on 3.7) An equilateral triangle is inscribed within a cirele. (An equilateral triangle is a triangle for which all three sides have the same length, and for which the measure of each vertex angle is 60°) The circle's radius begins to increase at a rate of 2 inches per minute, and the equilateral triangle grows at a commensurate rate so that it remains inscribed within the growing circle. From geometry, we know that if the radius ofthe circle is r, then the length of one of the sides of the inscribed triangle is s = r.J3 (a) At what rate (in inches per minute) does the perimeter P-3s of the triangle increase? Express all irrational values in exact form, not as decimal approximations. (b) At what rate in square inches per minute) does the area A of the triangle increase at the instant when the radius of the circle is r = 3 inches? Hints. The area of a triangle is given by A = bh , where b is the base and h is the height. Start with this formula, and note (for the triangle depicted above) that b = s ; you may need to use trigonometry to find an expression for h. Express all irrational values in exact form, not as decimal approximations.
1. (Based on 3.7) An equilateral triangle is inscribed within a cirele. (An equilateral triangle is a triangle for which all three sides have the same length, and for which the measure of each vertex angle is 60°) The circle's radius begins to increase at a rate of 2 inches per minute, and the equilateral triangle grows at a commensurate rate so that it remains inscribed within the growing circle. From geometry, we know that if the radius ofthe circle is r, then the length of one of the sides of the inscribed triangle is s = r.J3 (a) At what rate (in inches per minute) does the perimeter P-3s of the triangle increase? Express all irrational values in exact form, not as decimal approximations. (b) At what rate in square inches per minute) does the area A of the triangle increase at the instant when the radius of the circle is r = 3 inches? Hints. The area of a triangle is given by A = bh , where b is the base and h is the height. Start with this formula, and note (for the triangle depicted above) that b = s ; you may need to use trigonometry to find an expression for h. Express all irrational values in exact form, not as decimal approximations.
Irving HeathcoteLv2
5 Nov 2019