Answer:
A)
15 hours
B)
108 hours
C)
2074.29 miles
Step-by-step explanation:
Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.
A)
In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;
(24/360) = (x/225)
solving for x;
x = (24/360) * 225 = 15 hours
B)
In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;
(24/2π radians) = (x/9π radians)
Solving for x;
x = (24/2π radians)*9π radians = 108 hours
C)
If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;
circumference = 2*π*R = π*D
= 7920*3.142
= 24891.43 miles
Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;
(24891.43miles)/(24 hours) = 1037.14 miles/hr
The distance covered by the point in 2 hours will thus be;
1037.14 * 2 = 2074.29 miles
Answer:
14/5
Step-by-step explanation:
I'd suggest rewriting both mixed numbers as improper fractions. Then we'd have:
14/3 and 5/3
Dividing 14/3 by 5/3 is equivalent to dividing 14 by 5, since the denominators are the same (3).
Quotient is 14/5.
Number 7 is a. 0.013
number 8 is c.3
_
5
Answer:
D
Step-by-step explanation:
x^2-12x+36
type into desmos and see where it touches the the line
Normal-travel DATA:
distance = 240 km
rate = x km/h
time = d/r
= 240/x hrs
_______________________
Bad weather DATA:
distance = 240 km
rate = (x-20) km/h
time = 240/(x-20) hrs
______________________
Bad time - normal time = 2 hrs
240/(x-20) - 240/x = 2
120/(x-20) - 120/x = 1
120x -120(x-20) = x(x-20)
20 = x^2 -20x
x^2 - 20x - 20 = 0
x = [20 +- sqrt(20^2 - 4*1*-20)]/2
x = [20 +- sqrt(480)]/2
x = [20 +- 4sqrt(30)]/2
x = 10 +- 2sqrt(30)
