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A right circular cylinder and a hemisphere with equal base radii and equal heights. If the total surface area of the cylinder is A, then the total surface area of the heimsphere isA. 3A/4B. AC. 5A/4D. 3A/2In the figure, ABCD is a //gram. EF and AC intersect at P. If AE:ED=3:1 and BF:FC=1:4, then... 顯示更多 A right circular cylinder and a hemisphere with equal base radii and equal heights. If the total surface area of the cylinder is A, then the total surface area of the heimsphere is A. 3A/4 B. A C. 5A/4 D. 3A/2 In the figure, ABCD is a //gram. EF and AC intersect at P. If AE:ED=3:1 and BF:FC=1:4, then AP:PC= https://www.flickr.com/photos/130230543@N06/15632131 A. 1:1 B. 3:4 C. 4:5 D. 15:16 In the figure, ABCD is a //gram. Find the slope of AC https://www.flickr.com/photos/130230543@N06/16252008865/ A. 1 B. 5/3 C. 5/7 D. -7/5 Two perpendicular lines x+y-1=0 and bx+y+3=0 intersect at the point (a,b). Find a and b A. a=0 b=1 B. a=-2 b=1 C. a=2 b=-1 D. a=3 b=-1 The % of the graduates entering the local u of a school is 90% this year and was 85% last year. Which of the follow is/are correct? 1. Compare with last year, the % of graduates entering the local u this year is increased by 5% 2. Compare with last year, the % of graduates entering the local u this year rises by 5 percentage points 3. The number of graduates entering the local u is 5 more than last year Find the maximum area of the rectangle shown in the figure https://www.flickr.com/photos/130230543@N06/16252017155/ A. 11/2 cm2 B. 11/4 cm2 C. 1/8 cm2 D. 1/4 cm2
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A = 2πrh + 2πr^2 = 2πr^2 + 2πr^2 = 4πr^2 (as h = r) Total surface area of the hemisphere = πr^2 + 2πr^2 = 3πr^2 = 3A/4 Triangle AGE ~ Triangle CFG (AAA) AE:FC = 3/4 : 4:5 = 15 : 16 i.e. AG : GC = 15 : 16 L1: x + y - 1 = 0 L2: bx + y + 3 = 0 L1 perpendicular to L2 => Slope of L2 = -1/Slope of L1 -b = -1/-1, b = -1 L2: -x + y + 3 = 0 When L1 and L2 intersect at (a,b) a + b - 1 = -a + b + 3 2a = 4 a = 2 Hence, a = 2, b = -1 Compare with last year, the % of graduates entering the local u this year rises by 5 percentage points. It rises by (90% - 85%)/85% x 100% = 0.0588%. Since the number of graduates are not given, we could not find out the exact number of graduates, as well as the difference between these 2 years. Area of rectangle = (3 - x)(2x - 5) = -2x^2 + 11x - 15) = -2(x - 11/4)^2 + 121/8 - 15 = -2(x - 11/4)^2 + 1/8 Maximum area = 1/8 cm^2 2015-01-11 18:41:12 補充： Oops... I've skipped one question. In the figure, ABCD is a //gram. Find the slope of AC Let A be (a, b), 4 - a = 6 - (-1) and -1 - b = 7 - 6 we have A(-3, -2) slope of AC = [7 - (-2)]/[6 - (-3)] = 1
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