Question

# 1. Use a calulator to find a decimal approximation for each value. sec(-216 degrees 13')= (round...

1. Use a calulator to find a decimal approximation for each value.

sec(-216 degrees 13')=

(round to seven decimal places)

2. A space vechile is orbiting Earth in a circular orbit. What radian measure corresponds to (a) 2.5 orbits? (b) 5/4 orbits?

(a) the radian measure corresponding to 2.5 orbits is ___. (Type an axact answer in terms of pi. Type an interger or a simplified fraction)

b) the radian measure corresponding to 5/4 orbits is ___. (Type an exact answer in terms of pi. Type an interger or a simplified fraction. )

3. Find the length to three significant digits of the arc intercepted by a central angle θ in a circle of radius r.

The length of the intercepted arc is approximately ____ cm.

​(Round to one decimal place as​ needed.)

4.Find the length to three significant digits of the arc intercepted by a central angle

The length of the intercepted arc is approximately ___ ft. (Round to two decimal places)

How long is an arc intercepted by the given central angle in a circle of radius

16.58km? 120°

The length of the intercepted arc is approximately ___ km. ​(Round to the nearest​ hundredth.)

5. Two cities have nearly the same​ north-south line of

95° W. The latitude of the first city is 22° N, and

the latitude of the second city is .28° N.

Approximate the distance between the cities if the average radius of Earth is 6400 km.

The cities are approximately ___ kilometers apart. ​(Round to the nearest integer as​ needed.)

6.

 Refer to the figure to the right. ​(a) How many inches will the weight in the figure rise if the pulley is rotated through an angle of 78°40​'? ​(b)  Through what​ angle, to the nearest​ minute, must the pulley be rotated to raise the weight 5 ​in.? A rope attaches a weight to a pulley with radius 9.78 in

​(a) The weight in the figure will rise __ inches. ​(Do not round until the final answer. Then round to the nearest tenth as​ needed.)

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