Giải bài 16 từ câu số 15 đến 45 giùm mik nha mọi ng
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Câu 15: (mãi mới nghĩ ra :v)
\(\dfrac{\left(a+b\right)^2}{ab}+\dfrac{\left(b+c\right)^2}{bc}+\dfrac{\left(c+a\right)^2}{ca}\ge9+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow\dfrac{a^2+2ab+b^2}{ab}+\dfrac{b^2+2bc+b^2}{bc}+\dfrac{c^2+2ca+a^2}{ca}\ge9+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow\dfrac{a}{b}+2+\dfrac{b}{a}+\dfrac{b}{c}+2+\dfrac{c}{b}+\dfrac{c}{a}+2+\dfrac{a}{c}\ge9+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow\dfrac{a}{b}+\dfrac{b}{a}+\dfrac{b}{c}+\dfrac{c}{b}+\dfrac{c}{a}+\dfrac{a}{c}\ge3+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow a\left(\dfrac{1}{b}+\dfrac{1}{c}\right)+b\left(\dfrac{1}{c}+\dfrac{1}{a}\right)+c\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\ge3+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
-Áp dụng BĐT Caushy Schwarz ta có:
\(\left\{{}\begin{matrix}\dfrac{1}{b}+\dfrac{1}{c}\ge\dfrac{\left(1+1\right)^2}{b+c}=\dfrac{4}{b+c}\\\dfrac{1}{c}+\dfrac{1}{a}\ge\dfrac{\left(1+1\right)^2}{c+a}=\dfrac{4}{c+a}\\\dfrac{1}{a}+\dfrac{1}{b}\ge\dfrac{\left(1+1\right)^2}{a+b}=\dfrac{4}{a+b}\end{matrix}\right.\)
-Từ đó suy ra: \(a\left(\dfrac{1}{b}+\dfrac{1}{c}\right)+b\left(\dfrac{1}{c}+\dfrac{1}{a}\right)+c\left(\dfrac{1}{a}+\dfrac{1}{b}\right)\ge\dfrac{4a}{b+c}+\dfrac{4b}{c+a}+\dfrac{4c}{a+b}\)
-Ta c/m rằng: \(\dfrac{4a}{b+c}+\dfrac{4b}{c+a}+\dfrac{4c}{a+b}\ge3+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\ge3+2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\)
\(\Leftrightarrow2\left(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\right)\ge3\)
\(\Leftrightarrow2\left(\dfrac{a}{b+c}+1+\dfrac{b}{c+a}+1+\dfrac{c}{a+b}+1-3\right)\ge3\)
\(\Leftrightarrow2\left(\dfrac{a+b+c}{b+c}+\dfrac{b+c+a}{c+a}+\dfrac{c+a+b}{a+b}\right)-6\ge3\)
\(\Leftrightarrow2\left(a+b+c\right)\left(\dfrac{1}{b+c}+\dfrac{1}{c+a}+\dfrac{1}{a+b}\right)\ge9\left(1\right)\)
-Áp dụng BĐT Caushy Schwarz cho VT của BĐT ta được:
\(2\left(a+b+c\right)\left(\dfrac{1}{b+c}+\dfrac{1}{c+a}+\dfrac{1}{a+b}\right)\ge2\left(a+b+c\right)\left(\dfrac{\left(1+1+1\right)^2}{a+b+b+c+c+a}\right)=2\left(a+b+c\right)\dfrac{9}{2\left(a+b+c\right)}=9\)
\(\Rightarrow\)BĐT (1) đúng.
\(\Rightarrowđpcm\)
-Dấu "=" xảy ra khi \(a=b=c\)
52+16<x9<45+25
=>68<x9<70
=>7.9+5<x9<7.9+7 mà 7.9+5<7.9+6<7.9+7
Nên 7.9+6=x9
69=x9
x=69/9=23/3
Vậy x=23/3
Bài 9
Công
\(A=F.s=100.30000=3000000J\)
Công suất
\(P=\dfrac{A}{t}=\dfrac{3000000}{40\cdot60}=1250W\)
Bài 10
Hiệu suất
\(H=\dfrac{A_i}{A_{tp}}=\dfrac{55.10.1,5}{275.5}.100\%=60\%\)
Lực cản
\(F_c=\dfrac{A_{tp}-A_i}{l}=110N\)
Bài 11
Lực kéo
\(F=\dfrac{P}{s}=\dfrac{500000}{10}=50000N\)
Công thực hiện trong 120s
\(A=P.t=500000.120=60000kJ\)
Bài 12)
Nl đun sôi nước là
\(Q=Q_1+Q_2=m_1c_1\Delta t+m_2c_2\Delta t\\ =0,3.880+2,5.4200\left(100-30\right)=753480J\)
Bài 13)
Ta có ptcbn
\(Q_{thu}=Q_{tỏa}\\ =2,5.4200\left(30-t\right)=0,6.380\left(100-30\right)\\ \Rightarrow t=28,48^o\)
--> nước nóng lên 1,52 oC
Bài 14)
Công
\(A=F.s=2000.3000=6000000J\)
Công suất
\(P=\dfrac{A}{t}=\dfrac{6000000}{10.60}=10kW\)
Hồi hôm qua bạn đã làm cho mình bài 1 và bài 10 rồi bây giờ bạn chịu khó làm cho mình những câu còn lại đi nha. Cám ơn bạn.
\(15)2K + 2H_2O \to 2KOH + H_2\\ 16) 2Na + 2H_2O \to 2NaOH + H_2\\ 17) Ca + 2H_2O \to Ca(OH)_2 + H_2\\ 18) Ba + 2H_2O \to Ba(OH)_2 + H_2\\ 19) Mg + 2AgNO_3 \to Mg(NO_3)_2 + 2Ag\\ 20) 2Al + 3CuCl_2 \to 3Cu + 2AlCl_3\\ 21) 2Al + 3H_2SO_4 \to Al_2(SO_4)_3 + 3H_2\\ 22) Zn + 2HCl \to ZnCl_2 + H_2\\ 23) Fe + 2HCl \to FeCl_2 + H_2\\ 24) 2Al + 2H_3PO_4 \to 2AlPO_4 + 3H_2\\ 25) Fe_2O_3 + 6HCl \to 2FeCl_3 + 3H_2O\\ 26) CuO + 2HCl \to CuCl_2 + H_2O\\ 27) 2Fe + 3Cl_2 \xrightarrow{t^o} 2FeCl_3\\\)
\(28) 4Cr + 3O_2 \xrightarrow{t^o} 2Cr_2O_3\\ 29) 2Fe + 3Br_2 \xrightarrow{t^o} 2FeBr_3\\ 30) 2H_2 + O_2 \xrightarrow{t^o} 2H_2O\\ 31) 2C_2H_2 + 5O_2 \xrightarrow{t^o} 4CO_2 + 2H_2O\\ 32) C_2H_4 + 3O_2 \xrightarrow{t^o} 2CO_2 + 2H_2O\\ 33) CH_4 + 2O_2 \xrightarrow{t^o} CO_2 + 2H_2O\\ 34) BaCl_2 + 2AgNO_3 \to 2AgCl + Ba(NO_3)_2\\ 35) 6NaOH + Fe_2(SO_4)_3 \to 2Fe(OH)_3 + 3Na_2SO_4\\ 36) Na_2CO_3 + Ca(OH)_2 \to CaCO_3 + 2NaOH\\ 37) 2HCl +CaCO_3 \to CaCl_2 + CO_2 + H_2O\\ 38) CuCl_2 + 2AgNO_3 \to 2AgCl + Cu(NO_3)_2\\ 39) Na_2SO_4 + BaCl_2 \to BaSO_4 + 2NaCl\\ 40) H_2 + CuO \xrightarrow{t^o} Cu + H_2O\\ 41) 3H_2 + Fe_2O_3 \xrightarrow{t^o} 2Fe + 3H_2O\\ 42) H_2 + FeO \xrightarrow{t^o} Fe + H_2O\\ 43) 4H_2 + Fe_3O_4 \xrightarrow{t^o}3Fe + 4H_2O\\ 44) H_2 + PbO \xrightarrow{t^o} Pb + H_2O\\ 45) 2Al + 3CuO \xrightarrow{t^o} Al_2O_3 + 3Cu\)