How do you want this solved?
Given data
<span>sin (x+pi/2)=cos x
</span>now using sin law
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
now using above values
sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x)
as we know that
sin(pi/2)=1
cos(pi/2)=0
now putting these values
sin(pi/2+x)=1*cosx+0*1
sin(pi/2+x)=cosx
hence proved that
<span>sin (x+pi/2)=cos x</span>
Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
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The mean = 2,000
s = Sigma ( standard deviation ) = 300
M - 2 s = 2,000- 2 * 300 = 2,000 - 600 = 1,400
M + 2 s = 2,000 + 2 * 300 = 2,000 + 600 = 2,600
Answer.
Useful life of light bulbs within 2 standard deviations of the mean is:
A ) Between 1,400 and 2,600 hours