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A=(992-982)+(972-962)+.....+(32-22)+1=((98+1)2-982)+......+((2+1)2-22)+1
=(2.98+1)+(2.96+1)+....+(2.2+1)+1=50+4.(1+2+...+48+49)=50.4.(49.50/2)=50.4.49.25=245000
3,
Ta có
\(\tan\widehat{ABH}=\tan41,5^0=\dfrac{AH}{BH}\approx1\Leftrightarrow AH\approx BH\)
\(\tan\widehat{ACH}=\tan32^0=\dfrac{AH}{CH}\approx1\Leftrightarrow AH\approx CH\)
Vậy \(AH\approx\dfrac{BH+CH}{2}=\dfrac{BC}{2}=150\left(m\right)\)
4, Bài này mình làm tròn đến hàng đơn vị nhé
\(\tan\widehat{B}=\tan30^0=\dfrac{AH}{BH}=\dfrac{\sqrt{3}}{3}\Leftrightarrow AH=\dfrac{\sqrt{3}BH}{3}\)
\(\tan\widehat{ACH}=\tan35^0=\dfrac{AH}{CH}\approx1\Leftrightarrow AH\approx CH\)
\(\Leftrightarrow\dfrac{\sqrt{3}}{3}BH\approx CH\)
Mà \(BH-CH=BC=1500\Leftrightarrow BH-\dfrac{\sqrt{3}}{3}BH=1500\)
\(\Leftrightarrow\dfrac{3-\sqrt{3}}{3}BH=1500\\ \Leftrightarrow\left(3-\sqrt{3}\right)BH=4500\\ \Leftrightarrow BH=\dfrac{4500}{3-\sqrt{3}}=\dfrac{4500\left(3+\sqrt{3}\right)}{6}=750\left(3+\sqrt{3}\right)\left(cm\right)\)
\(\Leftrightarrow AH=\dfrac{\sqrt{3}}{3}BH=\dfrac{\sqrt{3}}{3}\cdot750\left(3+\sqrt{3}\right)=250\sqrt{3}\left(3+\sqrt{3}\right)\\ AH=750\sqrt{3}+750\left(cm\right)\)
Vậy ...
2:
a: \(A=\dfrac{x_1+x_2}{x_1x_2}=\dfrac{-6}{3}=-2\)
b: \(B=\dfrac{\left(x_1+x_2\right)^2-3x_1x_2}{1-x_1x_2}=\dfrac{36-3\cdot3}{1-3}=\dfrac{36-9}{-2}=-\dfrac{27}{2}\)
c: \(C=\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}\)
\(=\sqrt{\left(-6\right)^2-4\cdot3}=2\sqrt{6}\)
d: \(D=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)-3x_1x_2\)
\(=\left(-6\right)^3-3\cdot3\cdot\left(-6\right)-3\cdot3\)
=261