giúp mik bài 2 nha !
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Bài 3:
\(\widehat{A_1}=110^0;\widehat{A_2}=70^0;\widehat{A_3}=70^0\)
\(\widehat{B_3}=55^0;\widehat{B_4}=125^0;\widehat{B_1}=125^0\)
a)\(x\left(x-3\right)-2x+6=0\)
\(\Leftrightarrow x\left(x-3\right)-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=3\end{cases}}\)
b)\(\left(3x-5\right)\left(5x-7\right)+\left(5x+1\right)\left(2-3x\right)=4\)
\(\Leftrightarrow15x^2-46x+35-15x^2+7x+2-4=0\)
\(\Leftrightarrow33-39x=0\Leftrightarrow33=39x\Leftrightarrow x=\frac{33}{39}\)
a) \(x\left(x-3\right)-2x+6=0\)
\(x\left(x-3\right)-2\left(x-3\right)=0\)
\(\left(x-3\right)\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=2\end{cases}}}\)
b) \((3x-5)(5x-7)+(5x+1)(2-3x)=4\)
\(15x^2-46x+35+10x-15x^2+2-3x-4=0\)
\(33-39x=0\)
\(3\left(11-13x\right)=0\)
\(11-13x=0\)
\(13x=11\)
\(x=\frac{11}{13}\)
Nữa chu vi là
100:2=50 (cm)
CHiều dài là
50 : ( 2+3) x 3 = 30 (cm)
Chiều rộng là
50-30 = 20 (cm)
Diện tích hình chữ nhật là
20x30= 600 (cm2)
1. Gọi số mol Fe trong hỗn hợp là a
m = mNa + mFe
+) Hỗn hợp tác dụng hết với HCl:
2Na + 2HCl → 2NaCl + H2↑
Fe + 2HCl → FeCl2 + H2↑
a----------------->a
Dung dịch thu được gồm: NaCl, FeCl2, HCl (có thể còn dư)
+) Dung dịch thu được tác dụng với Ba(OH)2 dư:
2HCl + Ba(OH)2 → BaCl2 + 2H2O
FeCl2 + Ba(OH)2 → BaCl2 + Fe(OH)2↓
a--------------------------------------->a
Kết tủa: Fe(OH)2
+) Nung kết tủa đến khối lượng không đổi:
4Fe(OH)2 + O2 → 2Fe2O3 + 4H2O
a---------------------------a/2
mcr = m = mFe2O3 = a/2 . 160 = 80a
\(m_{Fe}=\dfrac{56a}{80a}.100=70\%\)
%mNa=100%−70%=30%
2/
CaCO3 ---to--> CaO + CO2
x----------------------x
MgCO3 ---to--> MgO + CO2
y----------------------y
mban đầu= 2.msau nung
=> 100x+84y = 2 .(56x+40y)
=> 12x = 4y
=> \(\dfrac{n_{CaCO_3}}{n_{MgCO_3}}=\dfrac{1}{3}\)
Đặt n CaCO3 = 1mol => n MgCO3 = 3mol
%CaCO3=\(\dfrac{100}{100+84.3}.100\)=28,41%
%MgCO3=100-28,41=71,59%
a) \(\sqrt{4x}+\sqrt{\dfrac{x}{4}}+\dfrac{1}{2}\sqrt{49x}=6\left(x\ge0\right)\)
\(\Rightarrow2\sqrt{x}+\dfrac{1}{2}\sqrt{x}+\dfrac{7}{2}\sqrt{x}=6\Rightarrow6\sqrt{x}=6\Rightarrow\sqrt{x}=1\Rightarrow x=1\)
b) ĐKXĐ: \(x\ge\dfrac{1}{2}\)
\(\sqrt{18x-9}-0,5\sqrt{2x-1}+\dfrac{1}{2}\sqrt{25\left(2x-1\right)}+\sqrt{49\left(2x-1\right)}=24\)
\(\Rightarrow\sqrt{9\left(2x-1\right)}-0,5\sqrt{2x-1}+\dfrac{5}{2}\sqrt{2x-1}+7\sqrt{2x-1}=24\)
\(\Rightarrow3\sqrt{2x-1}-0,5\sqrt{2x-1}+\dfrac{5}{2}\sqrt{2x-1}+7\sqrt{2x-1}=24\)
\(\Rightarrow12\sqrt{2x-1}=24\Rightarrow\sqrt{2x-1}=2\Rightarrow2x-1=4\Rightarrow x=\dfrac{5}{2}\)
c) \(\sqrt{x^2-2x+1}-7=0\Rightarrow\sqrt{\left(x-1\right)^2}=7\Rightarrow\left|x-1\right|=7\)
\(\Rightarrow\left[{}\begin{matrix}x-1=7\\x-1=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\x=-6\end{matrix}\right.\)
d) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-2\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\left(\dfrac{x}{x+2}\ge0,x\ne-2\right)\)
\(\Rightarrow\dfrac{7}{2}\sqrt{\dfrac{x}{x+2}}-3\sqrt{\dfrac{x}{4\left(x+2\right)}}-2\sqrt{\dfrac{x}{x+2}}=\sqrt{5}\)
\(\Rightarrow\dfrac{7}{2}\sqrt{\dfrac{x}{x+2}}-\dfrac{3}{2}\sqrt{\dfrac{x}{x+2}}-2\sqrt{\dfrac{x}{x+2}}=\sqrt{5}\)
\(\Rightarrow0=\sqrt{5}\) (vô lý) \(\Rightarrow\) pt vô nghiệm
a) \(\sqrt{4x}+\sqrt{\dfrac{x}{4}}+\dfrac{1}{2}\sqrt{49x}=6\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\2\sqrt{x}+\dfrac{\sqrt{x}}{2}+\dfrac{7}{2}\sqrt{x}=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\left(2+\dfrac{1}{2}+\dfrac{7}{2}\right)=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\6\sqrt{x}=6\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x=1\end{matrix}\right.\) \(\Leftrightarrow x=1\)
Vậy \(S=\left\{1\right\}\)
b) \(\sqrt{18x-9}-0.5\sqrt{2x-1}+\dfrac{1}{2}\sqrt{25\left(2x-1\right)}+\sqrt{49\left(2x-1\right)}=24\)
\(\Leftrightarrow3\sqrt{2x-1}-0,5\sqrt{2x-1}+\dfrac{5}{2}\sqrt{2x-1}+7\sqrt{2x-1}=24\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-1\ge0\\\sqrt{2x-1}\left(3-0.5+\dfrac{5}{2}+7\right)=49\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\12\sqrt{2x-1}=24\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\\sqrt{2x-1}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\2x-1=4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\) \(\Leftrightarrow x=\dfrac{5}{2}\)
Vậy \(S=\left\{\dfrac{5}{2}\right\}\)
c) \(\sqrt{x^2-2x+1}-7=0\) (*)
Ta có \(x^2-2x+1=\left(x-1\right)^2\ge0\forall x\) \(\Rightarrow\sqrt{x^2-2x+1}\ge0\forall x\)
(*) \(\Leftrightarrow\sqrt{\left(x-1\right)^2}-7=0\)
\(\Leftrightarrow\left|x-1\right|-7=0\)
\(\Leftrightarrow x-1-7=0\)
\(\Leftrightarrow x=8\)
Vậy \(S=\left\{8\right\}\)
\(\)d) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-2\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\) (**)
\(\Leftrightarrow\dfrac{7}{2}\sqrt{\dfrac{x}{x+2}}-\dfrac{3}{2}\sqrt{\dfrac{x}{x+2}}-2\sqrt{\dfrac{x}{x+2}}=\sqrt{5}\)
ĐKXĐ: \(\dfrac{x}{x+2}\ge0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x\le0\\x+2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x>-2\end{matrix}\right.\\\left\{{}\begin{matrix}x\le0\\x< -2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge0\\x< -2\end{matrix}\right.\)
(**) \(\Leftrightarrow\sqrt{\dfrac{x}{x+2}}\left(\dfrac{7}{2}-\dfrac{3}{2}-2\right)=\sqrt{5}\)
\(\Leftrightarrow0\sqrt{\dfrac{x}{x+2}}=\sqrt{5}\)
\(\Leftrightarrow0=\sqrt{5}\) ( vô lý )
Vậy phương trình trên vô nghiệm
Độ dài quãng đường BD:
\(BD=\dfrac{CD}{sin\widehat{CBD}}=\dfrac{10}{sin3^050'}\approx150\left(m\right)=0,15\left(km\right)\)
Thời gian đi hết đoạn AB:
\(t_1=\dfrac{0,4}{4}=0,1\left(h\right)\)
Thời gian đi hết đoạn BD:
\(t_2=\dfrac{0,15}{3}=0,05\left(h\right)\)
Tổng thời gian:
\(t=t_1+t_2=0,15\left(h\right)=9\left(ph\right)\)