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How formal mathematics should be learned by an enthusiast? Are there any prerequisites for learning that?
p(1) : 1/52
p(2) : 1/4
p(3) : 1/52
This displacement is in 1d motion.
(a) : p(a) = 2/7.
(b) : p(ā) = 5/7.
Probably he's a scammer I think.
P(winning) = 4/5 .
Sp#613: a= 4 & d=6.
A#92: y = ( ( -3±√(15) )/2 ).
CG#111: the coordinates of third vertex are ( 0, ±3√(3) ).
p(AUB) = (31/35).
x = 2√3 or x= -2/√3 .
(a) : s₂₀ = 210.
(b) : s₂₀ = 1360.
CG#110: the value of a = 1.
CG#109: the vertices are (0, ±√(3) ) , (-a,0) , (a,0) respectively.
A#90: M = 2 or M= (-7/2)
SP#611 (a) : sₙ = ( n^2) + (10/7)n.
(b) : no,
CG#108: ABCD is quadrilateral
where , A = (-3,-2)
B = (-1,-2)
C = (0,0)
D = (-3,1)
AC & BD are diagonals
Now, using distance formula = √( (x₂-x₁)^2 + (y₂-y₁)^2 ), we get
Distance of AB = √( (-1+3)^2 +(-2+2) ^2)
AB = 2 units.
Distance of BC = √( (0+1)^2 + (0+2)^2)
BC = √(5) units.
distance of CD = √( (-3+0)^2 +(1-0)^2)
CD = √(10) units.
distance of AD = √( (-3+3)^2 + (1+2) ^2)
AD = 3 units.
Distance of diagonal AC = √( (0+3)^2 + (0+2)^2)
AC = √(13) units.
distance of diagonal BD = √( (-3+1)^2+(1+2)^2)
BD = √(13) units.
Sp#610 the sequences are:
(1) : 10, 20, 30 , 40 where
a = 10 & d = 10.
(2) :25, 25, 25,25 where
a = 25 & d = 0.
These jokes are very hilarious.
CG#107: the coordinates are (2, 0) (0, 2) .
The value of k = 6.
My favorite is green
Concrete concepts are those concepts which requires deep understanding of basic topics that are linked to them
For example: if I'm learning some topic about straight lines there's a concept for parallel lines that " two lines are parallel if their slopes are equal ". So, what I do is that I'll take an graph paper , plot linear graphs which are parallel to each other and I'll find their slopes and conclude myself. Actually I wanted to tell something about me but, here it would be an off -topic so, where should we start talking?
Will miscellaneous exercises of matrices in ncert maths textbook helps us for understanding concrete concepts?