【纪念当年的帖子（2010）】Add Maths功课讨论区

Enceladus

1)Given the quadratic function f(x)=2x^2 - 6x +9, find the coordinates of the minimum point of the graph of the quadratic function.

2)Find the range the of values of p such that the quadratic function f(x)=3x^2 -4x +p is always positive

以上这两题我不会解答，请救救我。谢谢

数学神

1)Given the quadratic function f(x)=2x^2 - 6x +9, find the coordinates of the minimum point of the g ...
Enceladus 发表于 25-7-2010 21:34

有答案提供吗？
我需要答案来增强我对我答案的自信心

Enceladus

回复 642# 数学神


   1)minimum point= (3/2,9/2)   2)p>4/3

谢谢你。

数学神

Enceladus 发表于 26-7-2010 21:05

OK... 很好.. 谢谢~

1)Given the quadratic function f(x)=2x^2 - 6x +9, find the coordinates of the minimum point of the graph of the quadratic function.

f(x)= 2x^2 - 6x +9
     = 2 ( x^2 - 3x ) + 9
     = 2 [ x^2 - 3x + (-3/2)^2 - (-3/2)^2 ] + 9
     = 2 [ (x - 3/2)^2 - (9/4) ] + 9
     = 2(x - 3/2)^2 - (9/2) + 9
     = 2(x - 3/2)^2 + (9/2)

x = 3/2 , minimum value =  9/2
therefore , minimum point = (3/2 , 9/2)



2)Find the range the of values of p such that the quadratic function f(x)=3x^2 -4x +p is always positive

b^2 - 4ac < 0
(-4)^2 - 4(3)(p) < 0
16 - 12p < 0
16 < 12p
12p > 16
p > 16/12
p > 4/3

Enceladus

请帮帮我，快要把头发拔光了！！！

The above diagram shows two concentric circles such that the radius of the smaller shaded circle is 2/3 of the radius of the larger circle. If an arrow is thrown at the circles, calculate the probability that the arrow strikes the shaded circle.

那个图片是一个黑色的小圆圈在一个白色的大圆圈里面（正中间）

谢谢！

Enceladus

还有不会的，请帮帮我，谢谢。
A box contains 80 beads of colors red and green . A bead is drawn at random from the box and the probability that it is green is 3/8. Calculate the number of red beads that have to be taken out from the box so that the probability of drawing a green bead now becomes 3/7.

这题的答案是10，答案我懂可是算式不会。

Gundam

数学神,可以帮我算这题吗？
Given that -1<x<0 and x+(x^-1) = -3 , find the value of x-(x^-1)
Ans : Square root 5
想到脑快爆了

dollyeye

1)Solve each of these equations for 0°《 x《360°.
(a) 2 sinx cosx= cosx
(b) 4 cos^2 x = 1
(C) 2 tan^2 x +tanx-3=0
怎样做？？请帮帮忙～～～

Gundam

回复 648# dollyeye



１）2sinxcosx - cosx = 0
     cosx ( 2sinx - 1 ) = 0
     cosx = 0                        or     2sinx -1 = 0
         x = 90 , 270 degree            sinx = 1/2  
                                          corresponding angle = 30 degree
                                                    x = 30 , 150 degree

           Therefore , x = 30 , 90 , 150 , 270

2) & 3) 也还蛮简单的，不妨自己试试吧！

Allmaths

数学神,可以帮我算这题吗？
Given that -1
Gundam 发表于 3-8-2010 11:07 PM

Gundam

回复 650# Allmaths


    谢谢 ！！！

5643

刚刚复习..不明白这问题要怎样开始做..请帮帮我解决这几题问题...

1.Three fair coins are tosses simultaneusly 10times.This experiment is considered to be successful if all the three coins show the same face.Caldulate

(a)the probability of success,
(b)the probability of obtaining at most one success,

2.In a game,the probability that erene wins is 3/4

(a)An experiment is carried out where Serene plays the game N times.If found that the probability that she losses every time.Find the value of N

peaceboy

刚刚复习..不明白这问题要怎样开始做..请帮帮我解决这几题问题...

1.Three fair coins are tosses simul ...
5643 发表于 7-8-2010 10:04 AM

    1.a) P(S) = (1/2 * 1/2 * 1/2 ) + (1/2 * 1/2 * 1/2 )
               = 1/4
      
         b)P(S <=1) = P(S=0) + P (S=1)
                      =10C0 (1/4)^0 (3/4)^10 + 10C1 (1/4) (3/4)^9

2. An experiment is carried out where Serene plays the game N times.If found that the probability that she losses every time.Find the value of N〈 题目不完整

5643

回复 653# peaceboy


    谢谢你...我明白第一题了....另一题的题目应该是2. An experiment is carried out where Serene plays the game N times.If found that the probability that she wins 1 times 18 times the she losses every time.Find the value of N

peaceboy

回复  peaceboy


    谢谢你...我明白第一题了....另一题的题目应该是2. An experiment is carried ou ...
5643 发表于 7-8-2010 11:11 PM

     P(S=1) = 18 P(S=0)
nC1 (3/4)^1 (1/4)^(n-1) = 18 nC0 (3/4)^0 (1/4)^n
n (3/4) (1/4)^n/(1/4) =  18 (1/4)^n
3n= 18
n=6

宝贝允儿55

在下有一个想请问大家是permutations and combinations
How many two digit numbers can be made from the set (2,3,4,5,6,7,8,9) each number containing two different digits ? ANSWER=56

angelineang

8p2=56
用p的因为p的意思是位子很重要，c的意思是出现过就可以了，不在乎位子

数学神

在下有一个想请问大家是permutations and combinations
How many two digit numbers can be made from the ...
宝贝允儿55 发表于 28-9-2010 19:51

8P2 吧
因为你有8个numbers，要排2个numbers，所以就是这个咯

如果是8C2
就是8个numbers里random choose 2个而已

5643

slove the equation log3 x=log9 (2x+8)

请问怎样做？？

peaceboy

回复 659# 5643


    log3 x=log9 (2x+8)
             = log3  (2x+8) / log3 9
             = log3  (2x+8) /2
2log3 x = log3 (2x+8)
log3 x^2 = log3 (2x+8)
by comparison
x^2 = 2x+8
x^2-2x-8=0
(x-4)(x+2)=0
x=4 , x=-2(rejected)<<< log3 x ,<<x cant take any negative value