Answer:
A)
62/3 = 20.67 hours
B)
60.00 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 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 we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
I'm gonna hazard a guess at 309.
121+121=242
242-224=18
224-121=103
103-18=85
224+85=309
FYI, that L in the denominator is factorial.
This is some pretty serious stuff for high school.
My inclination is that the answer is A, which is the definition of <em>e. </em> Let's see if we can show this.
Let's write
Let's expand this with the binomial expansion
Let's focus on when n is really big and on the ks that are relatively small, which make up the bulk of the sum as the terms get small rapidly.
Then that numerator n(n-1)···(n-k+1) ≈ n^k as all the factors are about n.
OK, we showed for large n this is approximately true, and it will be exactly true in the limit, so we choose
Answer: A
