Question

nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north

280

likes
1402 views

Answer to a math question nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north

Expert avatar
Lurline
4.6
47 Answers
To find the distance between the North Pole (latitude 90° north) and Springfield, Illinois (latitude 40° north), we can use the arc length formula in terms of degrees.

The arc length formula in terms of degrees is given by:

\text{{arc length}} = \left(\frac{{2\pi\text{{r}}}}{{360}}\right)\theta

where r is the radius of the sphere and θ is the central angle (in degrees).

Given that the radius of the Earth is 4000 miles and the latitudes of the two cities, we can substitute these values into the formula:

For the North Pole:

\text{{arc length}}_{\text{{North Pole}}} = \left(\frac{{2\pi\text{{(4000)}}}}{{360}}\right)(90) \approx 6,283.19 \text{{ miles}}

For Springfield, Illinois:

\text{{\text{arc length}}}_{\text{{\text{Springfield, Illinois}}}}=\left(\frac{{2\pi\text{{(4000)}}}}{{360}}\right)(40)\approx2,792.53\text{{\text{ miles}}}

To find the distance between the two cities, we subtract the arc length of Springfield, Illinois from the arc length of the North Pole:

\text{{Distance between the cities}} = \text{{arc length}}_{\text{{North Pole}}} - \text{{arc length}}_{\text{{Springfield, Illinois}}}

=6,283.19\text{{\text{ miles}}}-2,792.53\text{{\text{ miles}}}

=3490.66\text{{\text{ miles}}}

Answer: The distance between the North Pole and Springfield, Illinois is approximately 3490.66 miles.

Frequently asked questions (FAQs)
Find the roots of the cubic equation x^3 - 5x^2 + 4x - 2 = 0.
+
What is the equation for the logarithmic function whose graph passes through the points (1,2) and (10,5)?
+
What is the equation of an ellipse with center (2, 3), major axis length 10, and minor axis length 6?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
(x^2+3x)/(x^2-9)=
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
Derivative of x squared
Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic. At the 0.05 level of significance, would you conclude they are similar?
If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.
(24, -7) is on the terminal arm of an angle in standard position. Determine the exact values of the primary trigonometric functions.
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
-1%2F2x-4%3D18
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
A block slides across the floor with a force of 20N, which has an angle of 30°. The mass of the block is 2kg and the coefficient of friction is 0.1. Calculate the value of all the forces involved in this system and finally the value of the acceleration.
An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?
An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?