Please show all clear steps.
1) Which of the following expressions have a factor of x+2?
I. x^2-4
II. 2x^2-x-10
III. 5x+10
Multiple Choice
2) Which of the following expressions represents the volume of the cylinder?(height: 3x-1, diameter: 2x+4)
A. V= 派(6x^2+10x-4)
B. V= 派(3x^3-x^2+12x-4)
C. V= 派(3x^3+11x^2+8x-4)
D. V= 派(12x^3+32x-16)
3) Calculate the volume of the cone.(slant height: 25cm, top of the cone: 40degree)
A. 210cm^3
B. 1799cm^3
C. 1914cm^3
D. 2168cm^3
Please show all clear steps for all the questions, thank you :)
數學 Factors And Measurement
2013-05-27 2:45 pm
回答 (3)
2013-05-27 3:38 pm
✔ 最佳答案
1) III. 5x+105x+10=5(x+2)
2) C. V= 派(3x^3+11x^2+8x-4)
Volume of the cylinder
= π(radius)^2(height)
= π((2x+4)/2)^2(3x-1)
= π(x+2)^2(3x-1)
= π(x^2+4x+4)(3x-1)
= π(3x³+11x²+8x-4)
3) B. 1799cm^3
Radius of the base = 25sin20°
Height of the cone = 25cos20°
Volume of cone
= (1/3)π(radius)^2(height)
= (1/3)π(25sin20°)^2(25cos20°)
= 1798.6cm³
2013-05-27 07:48:00 補充：
On Question 3, radius of the base, height and slant height of the cone form a right triangle.
Therefore the angle between height and slant height = 40°/2 = 20°
Base radius and height are obtained by trigonometric ratios
sinθ= opposite/hypotenuse and cosθ = adjacent / hypotenuse
參考: , me
2013-06-03 12:03 pm
Thanks for correcting the first answer^^
2013-05-28 3:05 am
(1) All I, II, III contains the factor (x+2)
I.
x^2 - 4
= x^2 - 2^2 <-- a^2 - b^2 = (a+b)(a-b)
= (x+2)(x-2)
II.
2x^2 - x - 10
=(2x-5)(x+2) <-- ax^2 + bx + c = (px +q)(rx + s)
III.
5x + 10
= 5(x+2)
Therefore all I, II, III contain the factor (x+2)
The other two question, the answer given by the first anwserer is correct. 我就唔再重覆打以免浪費網絡資原了。
I.
x^2 - 4
= x^2 - 2^2 <-- a^2 - b^2 = (a+b)(a-b)
= (x+2)(x-2)
II.
2x^2 - x - 10
=(2x-5)(x+2) <-- ax^2 + bx + c = (px +q)(rx + s)
III.
5x + 10
= 5(x+2)
Therefore all I, II, III contain the factor (x+2)
The other two question, the answer given by the first anwserer is correct. 我就唔再重覆打以免浪費網絡資原了。
參考: 自己 + first answerer for question 2 and 3.
收錄日期: 2021-04-13 19:29:08
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