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3.Have you finished your homework yet?
5.I have never donated blood before
tớ biết mỗi 2 câu này thôi
\(\lim\dfrac{3^n+2.6^n}{6^{n-1}+5.4^n}=\lim\dfrac{6^n\left[\left(\dfrac{3}{6}\right)^n+2\right]}{6^n\left[\dfrac{1}{6}+5\left(\dfrac{4}{6}\right)^n\right]}=\lim\dfrac{\left(\dfrac{3}{6}\right)^n+2}{\dfrac{1}{6}+5\left(\dfrac{4}{6}\right)^n}=\dfrac{0+2}{\dfrac{1}{6}+0}=12\)
\(\lim\left(\sqrt{n^2+9}-n\right)=\lim\dfrac{\left(\sqrt{n^2+9}-n\right)\left(\sqrt{n^2+9}+n\right)}{\sqrt{n^2+9}+n}=\lim\dfrac{9}{\sqrt{n^2+9}+n}\)
\(=\lim\dfrac{n\left(\dfrac{9}{n}\right)}{n\left(\sqrt{1+\dfrac{9}{n^2}}+1\right)}=\lim\dfrac{\dfrac{9}{n}}{\sqrt{1+\dfrac{9}{n^2}}+1}=\dfrac{0}{1+1}=0\)
\(\lim\dfrac{\sqrt{15+9n^2}-3}{5-n}=\lim\dfrac{n\sqrt{\dfrac{15}{n^2}+9}-3}{5-n}=\lim\dfrac{n\left(\sqrt{\dfrac{15}{n^2}+9}-\dfrac{3}{n}\right)}{n\left(\dfrac{5}{n}-1\right)}\)
\(=\lim\dfrac{\sqrt{\dfrac{15}{n^2}+9}-\dfrac{3}{n}}{\dfrac{5}{n}-1}=\dfrac{\sqrt{9}-0}{0-1}=-3\)
2. It is thought that he stole the money.
He is thought to have stolen the money.
3. It is said that she is going to study abroad.
She is said to be going to study abroad.
4. It is thought that the house was broken into last night.
The house was thought to be broken into last night.
Đặt trọng tâm của thanh AB là M
Trọng lượng các vật lần lượt: \(\hept{\begin{cases}P_A=10m_A=10.12=120N\\P=10m=10.0,5=5N\\P_B=10m_BN\end{cases}}\)
Cách tay đòn của \(\hept{\begin{cases}P:OM=\frac{1}{2}.AB\\P_A:OA=\frac{2}{3}.AB\\P_B:OB=\frac{1}{3}.AB\end{cases}}\)
Hệ thống cân bằng khi \(P_A.OA=P.OM+P_B.OB\)
\(\rightarrow120.\frac{2}{3}.AB=5.\frac{1}{6}.AB+P_B.\frac{1}{3}.AB\)
\(\rightarrow120.\frac{2}{3}=5.\frac{1}{6}+P_B.\frac{1}{3}\)
\(\rightarrow80=\frac{5}{6}+P_B.\frac{1}{3}\)
\(\rightarrow\frac{475}{6}=P_B.\frac{2}{3}\)
\(\rightarrow P_B=118,75N\)
Trọng lượng của vật B là: \(m_B=\frac{P_B}{10}=\frac{118,75}{10}=11,875kg\)