tính:C=29.273+15.49.94/69.220+1210
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\(2C=2+6+12+20+...+2450\)
\(2C=1.2+2.3+3.4+4.5+...+49.50\)
\(6C=1.2.3+2.3.3+3.4.3+...+49.50.3\)\(6C=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)
\(6C=1.2.3+2.3.4-1.2.3+...+49.50.51-49.50.51\)
\(6C=49.50.51\)
\(6C=124950\)
\(C=20825\)
\(c,\dfrac{12}{25}.\dfrac{-5}{24}=\dfrac{-60}{600}=-\dfrac{1}{10}\\ d,\dfrac{8}{15}:\dfrac{-4}{9}=\dfrac{8}{15}.\dfrac{9}{-4}=\dfrac{72}{-60}=-\dfrac{6}{5}\)
\(=\dfrac{27}{5}\cdot\dfrac{30}{7}+\dfrac{40}{7}\cdot\dfrac{37}{7}=\dfrac{2614}{49}\)
\(c)\)
\(5\dfrac{2}{5}\times4\dfrac{2}{7}+5\dfrac{5}{7}\times5\dfrac{2}{7}\)
\(=\dfrac{27}{5}\times\dfrac{30}{7}+\dfrac{40}{7}\times\dfrac{37}{7}\)
\(=\dfrac{162}{7}+\dfrac{40}{7}\times\dfrac{37}{7}\)
\(=\dfrac{162}{7}+\dfrac{1480}{49}\)
\(=\dfrac{1134}{49}+\dfrac{1480}{49}\)
\(=\dfrac{2614}{49}\)
Số viên gạch để lát nền cho 8 phòng là:
1210 8 = 960 (viên)
Đáp số: 960 viên
\(c,\dfrac{5}{18}\times\dfrac{2}{15}:\dfrac{1}{5}\\ =\dfrac{1}{9}\times\dfrac{1}{3}\times5\\ =\dfrac{5}{27}\\ d,\dfrac{4}{13}+\dfrac{2}{11}:\dfrac{4}{33}\\ =\dfrac{4}{13}+\dfrac{2}{11}\times\dfrac{33}{4}\\ =\dfrac{4}{13}+\dfrac{3}{2}=\dfrac{8}{26}+\dfrac{39}{26}\\ =\dfrac{47}{26}\)
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4
=> A=24497550
c, 126 - (126 - 33)=126-126+33=33
d, (-53 - 23) - (567 - 53) =-76-567+53=-590
e, 145 - (23 - 45) - (-23 - 10) =145+22+33=200