Alex 發問於 科學及數學數學 · 5 年 前

HYC_Mock_1112_P2

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@N06/156321...

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@N06/162520...

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@N06/162520...

A. 11/2 cm2

B. 11/4 cm2

C. 1/8 cm2

D. 1/4 cm2

1 個解答

評分
  • 5 年 前
    最佳解答

    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

    資料來源: Myself, Myself
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