If the radius of the earth is approximately 3960 miles, what is the linear speed of a point on the equator in miles per hour. Round your answer to the nearest mph. A. 1681 mph
B. 2073 mph
C. 840 mph
D. 1037

Pls show work

Section 6.1

Solutions and Hints

by Brent M. Dingle

for the book:

Precalculus, Mathematics for Calculus 4

th Edition

by James Stewart, Lothar Redlin and Saleem Watson.

If you remember nothing else from this section remember:

arc length = radius * angle

s = r * q

where the angle, q, is measured in radians.

There are other formulas, but that one is pretty important.

48. A circular arc of length 3 feet subtends a central angle of 25.

Find the radius of the circle.

Start with s = r*q , s = 3 feet, q = 25 = 25*(p/180) = (5/36)p radians

3 = r * (5/36)p Å 3*(36/5) = r*p Å 21.6 = p*r Å r = 21.6/p feet

52. Memphis, Tennessee and New Orleans Louisiana lie approximately on

the same meridian. Memphis has latitude 35 N and New Orleans 30 N.

Find the distance between the cities, given the radius of the earth is

3960 miles.

Again start with s = r*q,

with r = 3960 miles and q = 35 – 30 = 5 = 5*(p/180) = (1/36)p.

and we need to find s = arc length = distance between the cities.

s = 3960*(1/36)p = 110p miles.

60. A sector of a circle of radius 24 miles has an area of 288 square miles.

Find the central angle of the sector.

For this you need a new formula.

The area of a sector of circle = A = ½*r

2

*q ,

where q is the central angle of the sector measured in radians

and r of course is the radius of the circle.

For this problem r = 24 miles, A = 288 sq. miles and we need to find q.

288 = (½)*24

2

*q Å 288 = 288*q Å 1 radian = q (or about 57.3)

62. Three circles with radii 1, 2 and 3 feet are externally tangent to one

another. Find the area of the sector of the circle of radius 1 that is

cut off by the line segments joining the center of that circle to the

centers of the other two circles.

So you start out with:

Notice you know the length of ALL the sides of the triangle, because you know

the radius of each circle. From this you might discern that: 5

2

= 3

2

+ 4

2

. Thus you

have the (length of the hypotenuse)

2

= (length of side A)

2

+ (length of side B)

2

.

And from that you may conclude the triangle is a right triangle, or rather the angle

we are interested in is 90. Thus we use the area formula given in the text:

The area of a sector of circle = A = ½*r

2

*q ,

For this problem r = 1 foot, q = 90 = p/2, and we need to find A

A = ½ * 1

2

* p/2 = p/4 square feet.

Step-by-step explanation: