1)The minute hand of a clock is 10 cm long...How far does the tip of the hand move in 20 minutes?
2)THe no. of sides in 2 regular polygans are 5:4 and the difference between their angles is 6 degrees, find the no. of sides in the polygons??
3)The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius:express the angle of the sector in degrees,min and sec
111)∩ is 30 minutes
Therefore 20*∩/30 = 2∩/3
R = S/L
2∩/3 = S/10
Distance is 20∩/3
112)
For the first polygon
Interior Angle = 180(5x-2)/5x
For the second polygon
Interior Angle = 180(4x-2)/4x
180(5x-2)/5x-180(4x-2)/4x = 6
720(5x-2) - 900(4x-2) = 120x
3600x - 1440 - 3600x + 1800 = 120x
360 = 120x
x = 3
The sides of the polygon are 15,12
113)
A angle of the sector
Perimeter of the sector = 2r + A*r
Length of the arc of the semicircle = ∩*r
∩r = 2r + A*r
A = ∩ - 2
180 ∩
? ∩-2
180 - 360/∩
180 - 114.5454
65.4546
65 degree, 27 minutes , 17 seconds
1For each natural no. k,let Ck denote the circle with radius k,centimeters and centre at the origin. On the circle Ck ,a particle moves k centimetres in the counter-clock wise direction.After completing its motion on Ck,the particle moves to Ck+1 in the radial direction.The motion of the particle continues in this manner.The particle starts at (1,0).If the particle crosses the positive direction of the x- axis for the first time on the circle Cn then n = ?
62http://targetiit.com/iit_jee_forum/posts/long_one_3685.html
oh damn.. no one had solved! :P
11See as the particle moves k in k circle therefore the Radian = 1
2∩ is required for the particle to come back
Therefore the radians to be covered is 7.28
Therefore 7 circles will cover 7 radians
Therefore in the 8th circle it will cross the Circle . Therefore it is 8
But i donot understand the meaning of the particle moving in radial direction
24on every circle particle travels one radian.
the particle crosses X axis(+) on Cn such that n≥2π
=> n=7
