Tính nhanh
3476-1999
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IK//EF
=>\(\widehat{IKF}+\widehat{OFE}=180^0\)(hai góc trong cùng phía)
=>\(\widehat{OFE}+140^0=180^0\)
=>\(\widehat{OFE}=40^0\)
\(\widehat{IEF}+\widehat{E_1}=180^0\)(hai góc kề bù)
=>\(\widehat{IEF}+130^0=180^0\)
=>\(\widehat{IEF}=50^0\)
Xét ΔOEF có \(\widehat{EOF}+\widehat{FEO}+\widehat{EFO}=180^0\)
=>\(x+50^0+40^0=180^0\)
=>\(x=90^0\)
Lời giải:
Bổ sung điều kiện: $IK\parallel EF$.
Vì $IK\parallel EF$ nên:
$\widehat{OIK}=\widehat{OEF}$ (2 góc đồng vị)
$=180^0-130^0=50^0$
$\widehat{OKI}=180^0-\widehat{IKF}=180^0-140^0=40^0$
Xét tam giác $OIK$ thì:
$x=180^0-(\widehat{OIK}+\widehat{OKI})=180^0-(50^0+40^0)=90^0$
\(1.4.7+4.7.10+...+n\left(n+3\right)\left(n+6\right)\\ =\dfrac{n^2\left(n+1\right)^2}{4}+9\cdot\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}+18\cdot\dfrac{n\left(n+1\right)}{2}\)
\(=\dfrac{n\left(n+1\right)\left(n^2+13n+42\right)}{4}=\dfrac{n\left(n+1\right)\left(n+6\right)\left(n+7\right)}{4}\)
Áp dụng vào bài toán:
\(P=\dfrac{2021.2022.2027.2028}{4}=...\)
CM:
Với \(n=1\Leftrightarrow1.4.7=28\)
\(\dfrac{n\left(n+1\right)\left(n+6\right)\left(n+7\right)}{4}=\dfrac{2.7.8}{4}=28\)
Giả sử \(n=k\Leftrightarrow1.4.7+4.7.10+...+k\left(k+3\right)\left(k+6\right)=\dfrac{k\left(k+1\right)\left(k+6\right)\left(k+7\right)}{4}\)
Với \(n=k+1\), cần cm:
\(1.4.7+4.7.10+...+k\left(k+3\right)\left(k+6\right)+\left(k+1\right)\left(k+4\right)\left(k+7\right)=\dfrac{\left(k+1\right)\left(k+2\right)\left(k+7\right)\left(k+8\right)}{4}\)
Ta có \(VT=\dfrac{k\left(k+1\right)\left(k+6\right)\left(k+7\right)}{4}+\left(k+1\right)\left(k+4\right)\left(k+7\right)\)
\(=\left(k+1\right)\left(k+7\right)\left[\dfrac{k\left(k+6\right)}{4}+k+4\right]=\left(k+1\right)\left(k+7\right)\left(\dfrac{k^2+10k+16}{4}\right)\\ =\dfrac{\left(k+1\right)\left(k+7\right)\left(k+2\right)\left(k+8\right)}{4}=VP\)
Do đó theo pp quy nạp ta đc đpcm
85 x 65 + 65 x 35
= 65 x (85 + 35)
= 65 x 120
= 7800
85 x 65 + 65 x 35
= 5525 + 2275
= 7800
\(\dfrac{14}{9}-\dfrac{1}{6}-\dfrac{1}{3}-\dfrac{1}{2}+\dfrac{4}{9}\\ =\left(\dfrac{14}{9}+\dfrac{4}{9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)\\ =\dfrac{18}{9}-\left(\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}\right)\\ =2-\dfrac{6}{6}\\ =2-1\\ =1\)
3476 - 1999 = ( 3476 - 1 ) - ( 1999 + 1 ) = 3475 - 2000 = 1475
tk mk nha
3476 - 1999
= (3476 - 1) - (1999 + 1)
= 3475 - 2000
= 1475