Trig: Questions involving revolutions, how many radians turned?

[Naturalistjf]

The restaurant at the top of a very tall building in Seattle rotates 0.98 revolutions every hour. Dana sits 21.2 meters from the center of the restaurant near a window.

(a1) Through how many radians does Dana turn in 106 minutes?
(exact) angle:
Enter the exact answer; use pi for

.

(a2) Now, report the answer accurate to 3 decimal places:
(approximate) angle:

(b1) How far does Dana move in 106 minutes?
(exact) distance:
Enter the exact answer; use pi for

.

(b2) Now, report the answer accurate to 1 decimal place:
(approximate) distance:

I'm really lost. I'm not even sure how to get started- although I converted .98 of a revolution to 352.8 degrees. And I did 352.8pi/180/60 to give me .103 of a revolution per minute... yes? Usually I get clarification at the math lab at my college, but this is an online class with homework due on weekends. I work Saturday and there are no math lab hours on Sunday. Any guidance would be greatly appreciated!

 

[Steven G]

The restaurant at the top of a very tall building in Seattle rotates 0.98 revolutions every hour. Dana sits 21.2 meters from the center of the restaurant near a window.

(a1) Through how many radians does Dana turn in 106 minutes?
(exact) angle:
Enter the exact answer; use pi for

.

(a2) Now, report the answer accurate to 3 decimal places:
(approximate) angle:

(b1) How far does Dana move in 106 minutes?
(exact) distance:
Enter the exact answer; use pi for

.

(b2) Now, report the answer accurate to 1 decimal place:
(approximate) distance:

I'm really lost. I'm not even sure how to get started- although I converted .98 of a revolution to 352.8 degrees. And I did 352.8pi/180/60 to give me .103 of a revolution per minute... yepi =ually I get clarification at the math lab at my college, but this is an online class with homework due on weekends. I work Saturday and there are no math lab hours on Sunday. Any guidance would be greatly appreciated!

I converted .98 of a revolution to 352.8 degrees.This is correct but I would convert to radians as a1 asks for the answer in radians. Now .98*2*pi rads =6.158rads. So 6.158rads in 60 min. To me that means 6.158rads = 60 min. So 6.158rads / 60 min = 1 and 60 min / 6.158rads = 1

Now we want to convert 106 minutes to radians. That is we want to change the way 106 minutes looks like => we want to multiply it by 1 !!!!

106 minutes = 106 minutes * (6.158rads / 60 min)= 10.8782881618 rads----ans to A1


B1) How far does Dana travel in 1 revolution? What formula do you use? Get a result like x meters/60 min and for this problem both x meters/ 60 min and its reciprocal equals 1. We want to change (ie multiply by 1) 106 minutes to meters. Now 106 min =106 min * (x meters/ 60 min) =....

 

[Naturalistjf]

Thank you so much. This is due tonight- I've been at it awhile and had started to panic. How do I form the answer including pi?

 

[Steven G]

Thank you so much. This is due tonight- I've been at it awhile and had started to panic. How do I form the answer including pi?

I gave you big hints. You really need to do some of this work yourself. If you have a number of radians and it does not have pi in it this means you want to change the way it looks which means you want to multiply by 1. Now 1 = pi/3.14159265 (about). ......
Good luck

 

[Naturalistjf]

Thank you so much. I'll keep working at it! In the future, I'll cram on weekdays so the math lab is available to me- I'll plan to have upcoming weekend homework finished the Friday prior.

 

[Steven G]

Thank you so much. I'll keep working at it! In the future, I'll cram on weekdays so the math lab is available to me- I'll plan to have upcoming weekend homework finished the Friday prior.

OK, good luck.

 

[stapel]

The restaurant at the top of a very tall building in Seattle rotates 0.98 revolutions every hour. Dana sits 21.2 meters from the center of the restaurant near a window.

(a1) Through how many radians does Dana turn in 106 minutes? (exact) angle:

How many radians is "one revolution"? How many hours is "106 minutes"? Set up the units so, when they've cancelled, you're left with "radians":

. . . . .[(how many?) radians / revolution] * [0.98 revolutions / hour] * [1 hour / (how many?) minutes] * [106 minutes / 1] = ...?

(a2) Now, report the answer accurate to 3 decimal places: (approximate) angle:

Plug (a1) into your calculator.

(b1) How far does Dana move in 106 minutes? (exact) distance:

You have the angle (from a1) and the radius (from the exercise). Now find the arc-length, using the formula they gave you.

(b2) Now, report the answer accurate to 1 decimal place: (approximate) distance:

Plug (b1) into your calculator.