All Questions
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Jacob 05/03/2018 at 02:37a mile = 5280 feets, an hour = 3600 seconds
30 miles per hour = 30 x 5280 feets per hour = 30 x 5280 / 3600 feets per second = 44 feets per second
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Nguyễn Huy Thắng 28/04/2018 at 15:47We have: \(2^{2018}=\left(2^{1009}\right)^2=\left(2^{979}\cdot2^{30}\right)^2=\left(\left(2^{11}\right)^{89}\cdot2^{30}\right)^2\)
\(\equiv\left(48^{89}\cdot824\right)^2\left(mod1000\right)\)\(=\left(48^3\cdot\left(48^2\right)^{43}\cdot824\right)^2\)
\(\equiv\left(592\cdot304^{43}\cdot824\right)^2\left(mod1000\right)\)
\(\equiv\left(592\cdot\left(304^5\right)^8\cdot464\cdot824\right)^2\left(mod1000\right)\)
\(\equiv\left(912\cdot24^8\right)^2\left(mod1000\right)\)
\(\equiv\left(912\cdot776^2\right)^2\left(mod1000\right)\)
\(\equiv\left(912\cdot176\right)^2\left(mod1000\right)\)
\(\equiv512^2\left(mod1000\right)\equiv144\left(mod1000\right)\)
So the last three-digit numbers of \(M\) is \(144\)
Lê Quốc Trần Anh selected this answer. -
Đỗ Anh 10/05/2018 at 11:00
Theo bài ra ta có: 22018= ( 21009)2= ( 2979⋅ 230)2= ( ( 211)89⋅ 230)222018=(21009)2=(2979⋅230)2=((211)89⋅230)2
≡ ( 4889⋅ 824 )2( m o d1000 )≡(4889⋅824)2(mod1000)= ( 483⋅ ( 482)43⋅ 824 )2=(483⋅(482)43⋅824)2
≡ ( 592 ⋅ 30443⋅ 824 )2( m o d1000 )≡(592⋅30443⋅824)2(mod1000)
≡ ( 592 ⋅ ( 3045)số 8⋅ 464 ⋅ 824 )2( m o d1000 )≡(592⋅(3045)số 8⋅464⋅824)2(mod1000)
≡ ( 912 ⋅ 24số 8)2( m o d1000 )≡(912⋅24số 8)2(mod1000)
≡ ( 912 ⋅ 7762)2( m o d1000 )≡(912⋅7762)2(mod1000)
≡ ( 912 ⋅ 176 )2( m o d1000 )≡(912⋅176)2(mod1000)
≡ 5122( m o d1000 ) ≡144 ( m o d1000 )≡5122(mod1000)≡144(mod1000)
Vì vậy, con số ba chữ số cuối cùng của MM là 144
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Anna 27/02/2018 at 08:262 sons x and y cross; x returns.
Father crosses; y returns.
Two sons cross.
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In Anna's second line: father cross, x or y returns
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I love Math 02/03/2018 at 12:42
Figure 2
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nguyen tuan anh 26/04/2018 at 04:14figure two
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nguyen tuan anh 22/04/2018 at 01:11
figure two
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lehahieu 27/02/2018 at 14:16
The total population in Province A is :
18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )
Answer : 17826 people
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I love Math 27/02/2018 at 04:40
The total population in Province A is :
18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )
Answer : 17826 people
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¤« 04/03/2018 at 14:50
The total population in Province A is :
18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )
Answer : 17826 people
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Hà Minh Hiếu 27/02/2018 at 11:09
A = \(\left(1-\dfrac{4}{a^2}\right)\left(1-\dfrac{4}{b^2}\right)\)
= \(\dfrac{\left(a-2\right)\left(a+2\right)\left(b-2\right)\left(b+2\right)}{a^2b^2}\)
= \(\dfrac{ab\left(a+2\right)\left(b+2\right)}{a^2b^2}\)
= \(\dfrac{ab+2\left(a+b\right)+4}{ab}\)
= \(1+\dfrac{8}{ab}\)
\(\le1+\dfrac{8}{\left(\dfrac{a+b}{2}\right)^2}=1+8=9\)
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Thanh Nguyen 07/02/2018 at 19:18
9 . cá 100%
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Faded 22/01/2018 at 12:33
A= (1-2a)(1-2b)(1+2a)(1+2b
)
A= ( 1-a+ba
)(1-a+bb)(1+a+ba)(1+a+bb
)
A= ba
.ab.(2+ba)(2+ab
)
A= 4 +1 + 2 (ba+ab
) >= 5 +2. 2√ba.ab= 5+4 =9
