標題:
數學知識交流 － 數學雜題 (4)
發問:
(11) 變主項： (11a) z(x/y-y/z^2)-7x(v-t) = x/(7y-6) [x] (11b) p(t-uy)(y-pu) + 9pt = t^0 + ut(py^2 + 9uy) [t] (12a) 求正十九邊形的内角。 (12b) 求正十九邊形的外角。 (12c) 求正十九邊形的内角和。 (12d) 求正九邊形的外角和。 (12e) 求十邊形的内角外角和。
最佳解答:
11a. z[(xz^2-y^2)/yz^2] = x/(7y-6) + 7x(v-t) [(xz^2-y^2)/yz] [7y-6] = x [1 + 7(v-t)(7y-6)] [xz^2-y^2] [7y-6] = xyz [1 + 7(v-t)(7y-6)] x(7y-6)z^2 - (7y-6)y^2 = xyz [1 + 7(v-t)(7y-6)] x{[(7y-6)z^2 - yz[1 + 7(v-t)(7y-6)]} = (7y-6)y^2 x = {(7y-6)(y^2)} / {[(7y-6)z^2 - yz[1 + 7(v-t)(7y-6)]} 11b. p(t-uy)(y-pu) + 9pt = 1 + ut(py^2 + 9uy) pt(y-pu) - puy(y-pu) + 9pt = 1 + tupy^2 + 9tyu^2 pt(y-pu) + 9pt - tupy^2 - 9tyu^2 = 1 + puy(y-pu) t[p(y-pu) + 9p - upy^2 - 9yu^2] = 1 + puy(y-pu) t = [1 + puy(y-pu)] / [p(y-pu) + 9p - upy^2 - 9yu^2] sum of interior angle = (n-2) x 180 where n is number of side of polygon sum of exterior angle = 360 for all polygon 12a. sum of interior angle = (19-2) x 180 = 3060 each interior angle = 3060/19 = ~161 12b. each exterior angle = 360/19 = ~19 12c. sum of interior angle = (19-2) x 180 = 3060 12d. sum of exterior angle = 360 12e. sum of exterior angle + sum of exterior angle = 360n = 3600
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