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10, the base by x, and the altitude by x 2 3, and the altitude by x 3 (9.3)

Shifting, reversal, and time-scaling operations are order-dependent. Therefore, one needs to be careful in evaluating compositions of these operations. For example, Fig. 1-3 shows two systems, one that consists of a delay followed by a reversal and one that is a reversal followed by a delay. As indicated. the outputs of these two systems are not the same.

(a) The base if the area is 40 and the altitude has length 15 (b) The length of the altitude if the area is 22 and the base has length 1.1

x(n)

16.9 Use implicit differentiation to nd the slope of the tangent line to the graph of y = the radicals by squaring twice.]

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(c) The length of the base if the area is 27 and the base is three times the altitude (d) The length of the altitude if the area is 21 and the base has length four more than the altitude (e) The base if the area is 90 and the ratio of the base to the altitude is 5:2 (f) The length of the altitude to a side of length 20 if the altitude to a side of length 15 is 16 (g) The length of the base if the area is 48, the base is represented by x by x 1 (h) The length of the base if the area is represented by x2 3, and the altitude is represented 1

x ( n - no)

9.14. Find the area of a triangle if the lengths of the base and altitude are, respectively, (a) 6 in and 32 in; (b) 1 yd and 3 2 ft; (c) 8 and x 7; (d) 5x and 4x; (e) 4x and x 9; ( f ) x 4 and x 4; (g) 2x 6 and x 3. (9.4)

x ( - n - no)

x(n)

9.15. Find the area of (a) A triangle if two sides have lengths 13 and 15 and the altitude to the third side has length 12 (b) A triangle whose sides have lengths 10, 10, and 16 (c) A triangle whose sides have lengths 5, 12, and 13 (d) An isosceles triangle whose base has length 30 and whose legs each have length 17 (e) An isosceles triangle whose base has length 20 and whose vertex angle measures 68 (f) An isosceles triangle whose base has length 30 and whose base angle measures 62

25 + 25 = 50 [ 1 ( 3)]2 + (2 6)2 = (2)2 + ( 4)2 = 4 + 16 = 20 [4 ( 3)]2 + (7 6)2 = 72 + 12 = 49 + 1 = 50 ( 1 4)2 + (2 7)2 = ( 5)2 + ( 5)2 =

x(-n)

(9.4)

+ no)

(g) A triangle inscribed in a circle of radius 4 if one side is a diameter and another side makes an angle measuring 30 with the diameter (h) A triangle cut off by a line parallel to the base of a triangle if the base and altitude of the larger triangle have lengths 10 and 5, respectively, and the line parallel to the base is 6 9.16. Find the altitude of a triangle if (9.4)

(b)A time-reversal Tr followed by a delay T",,

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