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1 answer:
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Answer:
A) 15 hours
B) 108 hours
C) 2073.45 miles
Step-by-step explanation:
The earth rotates fully 1 time in 24 hours. Fully rotate means that it goes through 360 degrees in 24 hours.
A)
For this, we can set up unit ratio to solve.
<em>"If earth rotates 360 degrees in 24 hours, 225 degrees take how much time (let it be x)?"</em>
So , it takes 15 hours.
B)
Here, the rotation is given in radian, NOT degrees. We know that 2π radians is 360 degrees, thus we can say:
<em>"If earth rotates 2π radians in 24 hours, 9π radians take how much time (let it be y)?"</em>
So, it take 108 hours.
C)
The point on the equator is on the "outside" of the earth. So we need to figure out the circumference of the earth, given diameter is approximately 7920.
Circumference formula is C = 2πr, where C is the circumference, r is the radius (half of diameter, which is 7920/2 = 3960)
Hence
C = 2πr = 2π(3960) = 7920π
Hence, is 24 hours, a point travels 7920π miles. 2 hours is 1/12th of 24 hours, so in 2 hours the point will travel 1/12th the distance is travels in 24 hours. So:
Thus, it will travel 2073.45 miles in 2 hours.
Cosecant (csc) is defined as the reciprocal of sine, therefore:
.
1/sinx will be undefined when the denominator sinx = 0.
Recalling the unit circle, sinx = 0 at x = 0 ± πn, where n is an integer.
Since the domain x is restricted from (0, 2π), we only consider the values x = 0, x = π, and x = 2π.
Therefore in the domain 0 ≤ x ≤ 2π, y = csc(x) will be undefined at x = 0, x = π, and x = 2π.
1/sinx will be undefined when the denominator sinx = 0.
Recalling the unit circle, sinx = 0 at x = 0 ± πn, where n is an integer.
Since the domain x is restricted from (0, 2π), we only consider the values x = 0, x = π, and x = 2π.
Therefore in the domain 0 ≤ x ≤ 2π, y = csc(x) will be undefined at x = 0, x = π, and x = 2π.