Maths解答區／交流區

飛機場^_^

事緣在這區看見許多會員對有關Maths的課業難題百思不解。

本人特此在此開一個集中帖，希望形成一個數學集聚地，作互相分享和交流，同時使彼此的數學有所進步。

不論誰也可以發問，也可以解答，僅以交流，絕對歡迎參與！

Ar文'

我會幫手答架啦中5以下既我多數都識-_-

壺一v一

I have a question

A point P(x,y) is ok the curve y=X^2+1

a) Express the distance from P to the origin as a function of x.
b) In part (a), you expressed the length of a certain line segment as a function of x. Now exoress the slope of that line segment in terms of x.

the answer is....
a)  D(x)= 平方x^4+3x^2+1
b)  m(x)= (x^2+1)／x

Who knows how can do it....think you

飛機場^_^

(a)
We had already learnt how to find the distance between two points in form4.

There is one important formula have been provided in order to make us to find distance become easy as following:
S = √{(y2-y1)^2 + (x2-x1)^2}

So, let me to put the existing information into this formula, we know the origin is (0,0), and P is (x,y), which is on the curve x^2+1.
S = √{(y-0)^2 + (x-0)^2}
　= √{(x^2+1-0)^2 + (x)^2}
　= √{(x^2+1)^2 + (x)^2}
　= √(x^4+2x^2+1+x^2)
　= √(x^4+3x^2+1)

Therefore, we find the distance between any point on curve y=x^+1 and (0,0) is  √(x^4+3x^2+1).

(b)
This time we need to find the slope of the line that we had find in part(a).
The formula of slope is (y2-y1)/(x2-x1)
So, let me put the existing information into this formula,

let M be the slope of line.
M=(y-0)/(x-0)
　=(x^2+1-0)/(x-0)
　=(x^2+1)/x

[ 本帖最後由 飛機場^_^ 於 10-9-16 08:22 PM 編輯 ]

壺一v一

Think you. it was so clearly.
But can you explain what means is S and M and D
because the answer is D(x) m(x), I have no idea when i need to write D(X) M(X)

i have the another question>.< the exam is coming>.<S_O_S

Q: Let 2s denote the length of the side of an equilateral triangle.
a) Express the height of the triangle as a function of s.
b)exoress the area of the triangle as a function of s.
c) Use the function you found in part(a) to determine the height of an equilateral triangle, each side of which is 8cm long.
~~~~~~~~~~~~~~~~~~~~~
my answer:
　　／＼　　　　　　　a) (2s)^2= H^2+(2s/2)2
　／　　＼　２Ｓ　　          4s^2  = h^2+s^2
／＿＿＿＿＼                           3s^2 = h^2
　２ｓ／２                                     s^2= (h^2)/3
                                            s   =  √{(h^2)/3}
                                 b) (1/2) (√{(h^2)/3}) (2S)
just i guess..but very strange

Q2) The volume V and the surface area S of a  sphere of radius r are given by the formulas
V= (4/3派r^3) and S=4派r^2. Express V as a function of S
P.S派=3.14=.=
佢係問圓球體 但之後點=[

Q2 答案) V(S) = (S√S派) / 6派

Q3) A piece of wire 4m long is cut into two pieces, then each is bent in to a square.
Express the combined area of the two ssquares in terms of one variable.

my answer) 設第1條=Xm  第2條= 4-Xm
x/4 = 第1個正方形邊    (4-X) / 4=第2個正方形邊
(X/4)^2 + {(4-x)/4}^2 = area
x^2/16 + 16-x^2 / 16 = area
area =  (x^2 - x^2 + 16) / 16
area = 1m  
isn't it= =???

飛機場^_^

Well, S and M is just like D(x) and M(x), it's just a defintion which is maybe people like to use them and think them is easy to express the notion. Anyway, don't mind it, it'd not make your answer become wrongly.   

But you have better to used D(x) and M(x) express the notion, it can show the curve is a function of x. Besides, I think D(x) is mean distance, and M(x) is mean slope. People who learn Maths is always use M to instead of slope, so this show the reason why the answer call it M(x).

I suspect that you have do a right answer of these question. But I don't know what detail you want to understand, i'm sorry. You may think it by yourself and also believe youself.^^

[ 本帖最後由 飛機場^_^ 於 10-9-17 04:54 PM 編輯 ]

一筆一劃去繪畫

probability 問題,
Q23
請幫手

bens

月球被太陽照射的一面,其表面溫度最高可達127度;在沒有被太陽照射的一面,其表面溫度最低為-183 度。求月球表面最高和最低溫度之差。

Naozumi

Q23
(b) P[E and (F or G)] = P[(E and F) or ( E and G)]
                                 = P(E and F) + P(E and G) - P(E and F and E and G)
                                 = P(E)P(F) + P(E)P(G) - P(E and F and G)
                                 = P(E)P(F) + P(E)P(G)
                                 = P(E) [P(F) + P(G)]
                                 = P(E) [P(F or G)]
Hence E is independent of (F or G)
(c) P[G and (E and F)] = P(E and (F and G)]
                                   = P(E) P(F and G)
                                    = P(E) P(F) P(G)
                                   = P(E and F)P(G)
Hence, G, E and F are independent

一筆一劃去繪畫

原帖由 Naozumi 於 10-9-20 11:34 PM 發表
Q23
(b) P[E and (F or G)] = P[(E and F) or ( E and G)]
                                 = P(E and F) + P(E and G) - P(E and F and E and G)
                                 = P(E)P(F) + P(E)P(G) - P ...

Thanks!
請問有冇人識PART A AND D???

36661124

原帖由 bens 於 10-9-20 09:29 PM 發表
月球被太陽照射的一面,其表面溫度最高可達127度;在沒有被太陽照射的一面,其表面溫度最低為-183 度。求月球表面最高和最低溫度之差。

唔係加減數咩-,-?

sky333

1+1=?
1ax9993s=9g

二陵

我有一題關於Arithmetic Sequence ge數唔多識做T^T 有冇人可以解答下o_o

In an arithmetic sequence ,the product of the 1st term and the 2nd term is 150. The sum of the 5th term and the 6th term is 15. Suppose the first term is a negative number.
(a)  Find the first term and the common difference. <--用聯合方程計?
(b)  Find the general term T(n) of the sequence.
(c)  Determine whether 200 is a term of the sequence.

THX><

36661124

原帖由 二陵 於 10-9-28 10:26 PM 發表
我有一題關於Arithmetic Sequence ge數唔多識做T^T 有冇人可以解答下o_o

In an arithmetic sequence ,the product of the 1st term and the 2nd term is 150. The sum of the 5th term and the 6th term is 15. S ...

yes

二陵

咁我想問..c點做

R-H-Y

Q3.等差級數32,25,18,11,...的總和為-12,903,求該數的總項數

[ 本帖最後由 R-H-Y 於 10-10-16 03:56 PM 編輯 ]