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Gọi quãng đường AB là x
Ta có:
Thời gian xe máy đi từ A đến B là \(\dfrac{x}{50}\)
Thời gian xe máy đi trở về là \(\dfrac{x}{40}\)
Thời gian đi là: 4h30=4,5h
Theo đề bài ta có pt:
\(\dfrac{x}{50}+\dfrac{x}{40}=4,5\)
\(\Leftrightarrow\dfrac{4x+5x}{200}=\dfrac{900}{200}\)
\(\Leftrightarrow9x=900\)
\(\Leftrightarrow x=100km\)
Vậy quãng đường từ A đến B là 100km
II
1 C
2 B
3 C
4 D
5 A
6 A
7 D
8 C
III
1 is getting
2 is - is visited
3 selling
4 were you doing - phoned
IV
1 This road isn't used very often
2 A lot of trees will be grown in the park
3 The living-room is being painted light blue
4 Many different paper products have been developed
5 We were asked many difficult questions by the examier
V
1 It's is coffee "black" without cream or sugar
2 They are China, Japan and other Oriental countries
3 They drink tea with sugar
4 Yes, it is
VI
1 drive => driving
2 That => the
3 meets => has met
4 getting => to get
Thay m=2 vào HPT ta có:
\(\left\{{}\begin{matrix}2x+y=1\\x+2y=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}4x+2y=2\\x+2y=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}4x+2y=2\\3x=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=\dfrac{1}{3}\\y=\dfrac{1}{3}\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}mx+y=1\\x+my=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}y=1-mx\\x+m\left(1-mx\right)=1\left(1\right)\end{matrix}\right.\)
(1) ⇔x+m-m2x=1
⇔x(1-m2)=1-m (2)
TH1: 1-m2 = 0
⇔m = +- 1
Thay m=1 vào (2) ta có: 0x=0 (Luôn đúng) ⇒m=1 (chọn)
Thay m=-1 vào (2) ta có: 0x=2 (Vô lí) ⇒m=-1 (loại)
TH2: 1-m2 ≠0
⇔m≠ +-1
⇒HPT có nghiệm duy nhất:
x= \(\dfrac{1-m}{1-m^2}\)
⇒y= \(1-m.\dfrac{1-m}{1-m^2}\)
⇔y=\(\dfrac{1-m}{1-m^2}\)
Dễ thấy x=y nên:
\(\dfrac{1-m}{1-m^2}>0\)
⇔1-m>0
⇔m<1
Vậy m <1 thì Thỏa mãn yêu cầu đề bài.
1 We are having a wonderful time at the moment in Sa Pa
2 It is necessary to cool the burn imediately
V
1 will be watching
2 will make
3 is going to rain
4 will become - won't get
5 will change
6 to call
7 will be lying
8 had come - had been
9 arrived - had been waiting
10 are not
11 pollution
12 were destroyed
13 would do
14 had left - came
15 didn't go - stayed
16 Has - learnt , has learnt
17 Did - wear , didn't wear
18 Does - read , watch
19 would save
20 will have
21 will be being painted
22 smoked
23 came - had left
24 had finished
25 was built
VI
1
a)
1 T
2 F
3 T
4 T
5 T
6 F
b)
1 It is a device which is used to send multiple messages over a single wire
2 It is a device which is used to draw the shape of the sound waves
3 It happened in 1876, while bell was at one end of ........
Để hàm bậc 3 có 2 cực trị nằm về 2 phía trục hoành
\(\Leftrightarrow y=0\) có 3 nghiệm pb
\(\Leftrightarrow x^3-\left(2m+1\right)x^2+\left(m+1\right)x+m-1=0\) có 3 nghiệm pb
\(\Leftrightarrow\left(x-1\right)\left(x^2-2mx-m+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2-2mx-m+1=0\left(1\right)\end{matrix}\right.\)
Bài toán thỏa mãn khi (1) có 2 nghiệm pb khác 1
\(\Leftrightarrow\left\{{}\begin{matrix}a+b+c=1-2m-m+1\ne0\\\Delta'=m^2+m-1>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne\dfrac{2}{3}\\\left[{}\begin{matrix}m< \dfrac{-1-\sqrt{5}}{2}\\m>\dfrac{-1+\sqrt{5}}{2}\end{matrix}\right.\end{matrix}\right.\)
Có 19 số tự nhiên nhỏ hơn 20 thỏa mãn
\(\left\{{}\begin{matrix}P=U.I\Rightarrow I=\dfrac{P}{U}=\dfrac{100}{220}=\dfrac{5}{11}\left(A\right)\\R=\dfrac{U}{I}=\dfrac{220}{\dfrac{5}{11}}=484\left(\Omega\right)\end{matrix}\right.\)
\(R_Đ=\dfrac{U_Đ^2}{P_Đ}=\dfrac{220^2}{100}=484\Omega\)
a)Cường độ dòng điện:
\(I_m=\dfrac{U_m}{R}=\dfrac{220}{484}=\dfrac{5}{11}A\)
b)Cường độ dòng điện khi đặt 1 hđt 200V vào hai đầu đèn:
\(I'=\dfrac{200}{484}=\dfrac{50}{121}A\)
Điện năng đèn tiêu thụ trong 10' :
\(A=UIt=200\cdot\dfrac{50}{121}\cdot10\cdot60=49586,8J\)