Answer:
A)
58/3 = 19.33 hours
B)
84.00 hours
C)
2074.29 miles
Step-by-step explanation:
Under the assumption the earth is a perfect circle, then in a complete rotation ( 24 hours) the earth will rotate through 360 degrees or 2π radians.
A)
In one day or 24 hours the earth rotates through 360 degrees. We are required to determine the duration it takes to rotate through 290 degrees. Let x be the duration it takes the earth to rotate through 290 degrees, then the following proportions hold;
(24/360) = (x/290)
solving for x;
x = (24/360) * 290 = 58/3 = 19.33 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it will takes the Earth to rotate through 7π radians. Let x be the duration it takes the earth to rotate through 7π radians, then the following proportions hold;
(24/2π radians) = (x/7π radians)
Solving for x;
x = (24/2π radians)*7π radians = 84 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:
If they create a 90 degree angle then yes.
Answer:
D) Over $4,000,000
Step-by-step explanation:
On the last day, the worker is paid $0.07*2²⁵ (it's by the power of 25 because it's 0 on the first day), which is $2,348,810.24. That means that the amount of money earned on all other days are $2,348,810.37, since 2⁰ + 2¹ + 2² + 2³... + 2ⁿ⁻² + 2ⁿ⁻¹ = 2ⁿ + 1.
That totals to approximately $4.6 million dollars, which is larger than $4 million.
<h2>
Coordinate Pairs</h2>
Coordinate pairs are organized like (x,y).
- x tells us the location of the point in relation to the x-axis, the axis that is horizontal.
- y tells us the location of the point in relation to the y-axis, the axis that is vertical.
To determine a coordinate pair, we can determine each coordinate individually, then put them together.
<h2>Solving the Question</h2>
Notice how the red point sits on the very edge of the graph.
When we look at the x-axis, we can see that it occurs at the number 0 on the x-axis. In other words, the red point occurs when x=0.
When we look at the y-axis, we can see that it lines up with the number 2. In other words, the red point occurs when y=2.
Therefore, when we put the two coordinates together like (x,y), we get (0,2).
<h2>Answer</h2>
(0,2)
If the smaller number is x, then the larger number has to be 20 - x in order for the arithmetic mean to be 10, as their sum must be 20.
If the geometric mean is 8 the product of the numbers has to be 64 and so the larger number is 64/x
Solving 64/x = 20 - x gives the quadratic x^2 -20x +64 = 0 so x = 4 or 16.
The two numbers are 4 and 16.
