(1b) Given sinx=2/3, then, sin θ = opp/hyp., by pathegoras, 3 raistopower 2 = 2 raisetopower 2 + a raise 2, 9 = 4 + a raise 2,a = square rut 5, tan x-cos x, (2)/(squar rut5)-(squar rut)/(3),=(squar rut5)/(15)
(1b) Given sinx=2/3, then, sin θ=opp/hyp., by pathegoras, 3 raisetopower 2 = 2 raisetopower 2 + a raisetopower 2, 9 = 4 + a raise 2, a = square rut 5, tan x-cos x, (2)/(squar rut5)-(squar rut)/(3),=(squar rut5)/(15)
(2) let son's years be S& wale's years be W, S=2w--- (1),4year's ago, wale*4, S=4* W, (S-4) = (4)(W-4)---(2), S-4=4(W-4),S-4W=4-16, but s=2W, 2W-4W=-12, W=6. therefore, S=12, we have XS + YW= 66, X(12)+Y(6)= 66, at X=3 & Y=5, i.e in 3years'time.
(10) class interval: 60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99. X: 62,67,72,77,82,87,92,97. F: 2,3,6,11,8,7,2,1. FX: 124,201,432,847,656,609,184,97. F(x-x bar) 2: 561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06,
(10a) Mean=3150/40=78.75.
(10b) S.D = square root of 2527.40/40 = square root of 63.185, S.D = 7.949, to 2 decimal places =7.95
USE THIS MATHEMATICAL SYMBOLS: YOU WILL SEE THIS LIKE THIS:
It means X= -b+-square b power2 -4ac/2a
THIS MEANS: Class Limit:5-10,10-15,15-20,20-25,25-30.....
Frequency: 1,2,4,0,3,5,6
Cummulative Frequency: 1,3,7,7,10,15,21.
This means dat Comma(,) is used for next line. If u see comma, then u know itis unda the one it is follow. Eg like above Frequency:- 2 is unda 1,while 4 is unda 2, then 0 is unda 4.,etc
* means MULTIPLY. / means OVER. X or x means Alphabet X not multiplication. Eg 2*2=4 4/2= 2 2x-x= x Or X+2x = 3x.
(3a) let STU = θ,
y = 36 + θ,
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