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the two groups Z / 2 x Z / 2 x Z / 2 x Z/2og Z / 2 ^ 4 both have order 2 ^ 4 = 16 Here denotes as usual Z / m the cyclic group of order m. The argument that these two groups are not isomorphic.
a cuboidmetal block of dimensions 20*16*12 weight 6 kilogram . find the weight of the block of the same metal of size 10*8*8.
A and B are two fixed points of a circle C(O,R) m is a variable point of the circle (C) .
[MI] and [AR] are two heights of the triangle AMB .
H is the orthocenter of the triangle AMB
the line (MH) cuts the circle (c) again at E
prove that the triangles BIM , HAL and AIE are similar .
verify that the line (AB) is perpendicular bisector OF [HE].
designate by o' the point so that (AB) is the perpendicular bisector of [OO'] .
verify that OHEO' is an isosceles trapezoid and that O'H equal to the radius r .
what is the geometric locus of H when M describes the circle (C) ?
Two lanes of a motorway are being resurfaced.Each lane is 4 metres wide.The speed limit through the road works is 80 km/h.It takes 15 minutes to drive through the road works at this speed.Calculate the area being resurfaced
a boy jumps 1.95 m the winning jump is 17 cm higher what is the height of the winning jump
a mine shaft which slopes at an angle of 19 degrees to the horizontal is driven into a hillside for 400 meters. How much lower, to the nearest meter, is the end of the shaft than the beginning?
sin3A+sin2A-sinA = 4sinAcosA/2cos3A/2
Prove that
tan2A = (sec2A+1)√sec²A-1
cos(5theta - pie/6) = -square root 2/ 2
sin((theta divided by 3) + (pie divided by 4)) = one half
