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
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
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13 Answers
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
11
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
