HOC24
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Gọi muối đó là:\(M_2CO_3\)
\(M_2CO_3+2HCl\rightarrow2MCl+H_2O+CO_2\) (1)
Từ (1)\(\Rightarrow n_{M_2CO_3}=n_{CO_2}\)
\(\Leftrightarrow2.\dfrac{2,12}{2M+60}=\dfrac{0,38}{12+2.16}\)
\(\Leftrightarrow M=216\)(ko có M thỏa mãn)
Vậy sai đề :v.
\(n_M=\dfrac{11,2}{M}\left(mol\right),n_{HCl}=0,4\left(mol\right)\)
\(M+2HCl\rightarrow MCl_2+H_2\) (1)
Từ (1)\(\Rightarrow2n_M=n_{HCl}\Leftrightarrow2.\dfrac{11,2}{M}=0,4\)
\(\Leftrightarrow M=56\)
Vậy M là Fe
Ý B
\(g_h=\dfrac{1}{2}g_{MĐ}\)
\(\Leftrightarrow\dfrac{GM}{\left(R+h\right)^2}=\dfrac{1}{2}\dfrac{GM}{R^2}\)
\(\Leftrightarrow h\simeq2651\left(km\right)\)
B8)
Tiết diện của dây: \(S=\dfrac{\rho.l}{R}=\dfrac{0,4.10^{-6}.3}{2}=6.10^{-7}\left(m^2\right)=0,6\left(mm^2\right)\)
Bán kính thiết diện dây:\(S=\pi R^2\Rightarrow R=\sqrt{\dfrac{S}{\pi}}\simeq0,4\left(mm\right)\)
Ý A
B9)\(R_1=R_2\Leftrightarrow\rho_1.\dfrac{l}{S_1}=\rho_2.\dfrac{l}{S_2}\)
\(\Leftrightarrow\rho_1.\dfrac{l}{\dfrac{\pi d_1^2}{4}}=\rho_2.\dfrac{l}{\dfrac{\pi d^2_2}{4}}\)
\(\Leftrightarrow d_2^2=\dfrac{\rho_2.d_1^2}{\rho_1}\simeq6.10^{-7}\left(m\right)\Rightarrow d_2\simeq7,861.10^{-4}\left(m\right)=0,786\left(mm\right)\)
Ý D
\(3x^2-6x+3=0\Leftrightarrow x^2-2x+1=0\Leftrightarrow\left(x-1\right)^2=0\Leftrightarrow x=1\)
\(y=7-2|cos2x|\)
Có \(0\le\left|cos2x\right|\le1\)
\(\Rightarrow0\ge-2\left|cos2x\right|\ge-2\)
\(\Leftrightarrow7\ge7-2\left|cos2x\right|\ge5\)
hay \(7\ge y\ge5\) \(\Rightarrow M=7,m=5\Rightarrow M^3-m^3=218\)
\(C^n_n+C^{n-1}_n+C^{n-2}_n=37\)
\(\Leftrightarrow1+\dfrac{n!}{\left(n-1\right)!}+\dfrac{n!}{\left(n-2\right)!2!}=37\)
\(\Leftrightarrow1+n+\dfrac{n\left(n-1\right)}{2}=37\)
\(\Rightarrow n=8\)
\(P=\left(2+5x\right)\left(1-\dfrac{x}{2}\right)^8=\left(2+5x\right).\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{x}{2}\right)^k\right)\)
\(=\left(2+5x\right).\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\)
\(=2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)+5x\)\(\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\)
\(=2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)+5\)\(\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^{k+1}\right)\)
Số hạng chứa \(x^3\) trong \(2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\) là \(2C^3_8.\left(-\dfrac{1}{2}\right)^3x^3\)
Số hạng chứa \(x^3\) trong \(5\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^{k+1}\right)\) là \(5C^2_8.\left(-\dfrac{1}{2}\right)^2x^3\)
Vậy số hạng chứa x3 trong P là:\(\left[2.C^3_8\left(-\dfrac{1}{2}\right)^3+5C^2_8\left(-\dfrac{1}{2}\right)^2\right]x^3\)
\(a=\dfrac{v^2-v_0^2}{2s}=\dfrac{0-\left(2,5\right)^2}{2.0,01}=-312,5\)(m/s2)
\(E=\dfrac{F}{q}=\dfrac{a.m}{q}=\dfrac{-312,5.9,1.10^{-31}}{1,6.10^{-19}}=1,8.10^{-9}\left(V\right)\)
\(u_{n+1}=\sqrt{1+u_n^2}\left(1\right)\)
\(u_1=3=\sqrt{9}\)
\(u_2=\sqrt{1+u_1^2}=\sqrt{10}\)
\(u_3=\sqrt{1+u_2^2}=\sqrt{11}\)
...
Dự đoán công thức:\(u_n=\sqrt{n+8}\),\(n\ge1\) (*)
Thật vậy
+)\(n=1,(*)\)\(\Leftrightarrow u_1=3\) (lđ)
+)Giả sử (*) đúng với mọi \(n=k,k>1\)
\((*)\Leftrightarrow u_k=\sqrt{k+8}\)
+)\(n=k+1,\) thay vào (1) có: \(u_{k+2}=\sqrt{1+u^2_{k+1}}=\sqrt{1+\left(\sqrt{1+u_k^2}\right)^2}=\sqrt{2+u^2_k}=\sqrt{2+k+8}=\sqrt{10+k}\)
\(\Rightarrow\)(*) đúng với n=k+1
Vậy CTSHTQ: \(u_n=\sqrt{n+8}\), \(n\ge1\)
\(D=R\)
Để hàm số f(x) là hàm số lẻ
\(\Leftrightarrow f\left(-x\right)=-f\left(x\right),\forall x\in D\)
\(\Leftrightarrow\left(m^2-3\right)cos\left(-10x\right)+sin\left(-2021x\right)=-\left(m^2-3\right)cos10x-sin2021x,\forall x\)
\(\Leftrightarrow\left(m^2-3\right)cos10x-sin2021x=-\left(m^2-3\right)cos10x-sin2021x,\forall x\)
\(\Leftrightarrow\left(m^2-3\right)cos10x=0,\forall x\)
\(\Leftrightarrow m^2-3=0\)
\(\Leftrightarrow m=\pm\sqrt{3}\)
Vậy...