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anonymous
 one year ago
SIMPLE TRIG PROBLEMS NEED HELP. I WILL GIVE MEDAL AND FAN
anonymous
 one year ago
SIMPLE TRIG PROBLEMS NEED HELP. I WILL GIVE MEDAL AND FAN

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not really sure what the first one is asking for, but I can help you with the second one.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well I mean, it's really simple. The angle \(\theta\) can be found using the formula \[\large \sf \theta~=~\frac{arc~length}{radius}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Here's a nice little cheatsheet for trig formulas: http://learnix.net/wordpress/wpcontent/uploads/TrigCheatSheet1.4.pdf

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i do not have arc lenght

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ugh, this is what I get for trying to do math while sleep deprived. Give me a minute, sorry.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's look at the first problem. You are given an angular velocity, and you asked to find a linear velocity.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1In the formula below, we use \(\omega\) (smallcase Greek letter "omega" is usually used to denote an angular velocity). Point A moves in a circular path around point O with an angular velocity of \(\omega\). If point A is r units from point O, then the linear velocity of point A is \(v = r \omega \). \(\omega\) must be expressed in radians per unit time in this formula.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\ \large v = r\omega\) In your case, you have the angular velocity given in revolutions per minute. You need to convert revolutions into radians.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Since the answer must be in miles per hour, you will also need to convert minutes into hours and inches into miles.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so angular velocity is 6500

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont get it, what do i do next

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We start with this: \(\large v = r \omega = 7.25 ~in. \times ~3250 ~\dfrac{rev}{min}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to apply all the conversion factors.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but isnt angular velocity 6500

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Angular velocity needs to be in radians per minute. You have revolutions per minute. 1 revolution is \(2 \pi\) radians, not 2 radians.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's deal with the conversion of revolutions to radians. It's in red below. \(\large v = r \omega = 7.25 ~in. \times ~3250 ~\dfrac{rev}{min} \color{red}{\times \dfrac{2 \pi ~rad }{1~rev}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Since you guys are still working on the first part, I'll just leave this here so you can work it out after you finish. You can find arc length from sector area and radius with for formula \[\large \sf Area~=~\frac{1}{2} \times r \times Arc \huge \rightarrow \large \frac{2 \times Area}{r}~=~Arc\] from there, you can find \(\large \sf \theta\) with the original formula. \[\large \sf \theta~=~\frac{Arc~length}{Radius}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to deal with the conversion of inches into miles. We can convert using 12 in. = 1 ft, and 5280 ft = 1 mile. This conversion is in green below. \(v = r \omega = 7.25 ~in. \color{green}{\times \dfrac{1~ft}{12~in.} \times \dfrac{1~mile}{5280~ft} } \times ~3250 ~\dfrac{rev}{min} \color{red}{\times \dfrac{2 \pi ~rad }{1~rev}}\) Now we have miles per minute. We need to convert minutes to hours.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The conversion from minutes to hours is in blue below. 60 minutes = 1 hour \(v = r \omega = 7.25 ~in. \color{green}{\times \dfrac{1~ft}{12~in.} \times \dfrac{1~mile}{5280~ft} } \times ~3250 ~\dfrac{rev}{min} \color{red}{\times \dfrac{2 \pi ~rad }{1~rev}} \color{blue} {\times \dfrac{60~min}{1~hour} }\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1What do you get? \(v = \dfrac{7.25 \times 3250 \times 2 \times \pi \times 60}{12 \times 5280} \dfrac{miles}{hour} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That's what I got.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0140.2 miles per hour

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so whats my first step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That would be to find the arc length \[\large \sf Area~=~\frac{1}{2} \times r \times Arc \huge \rightarrow \large \frac{2 \times Area}{r}~=~Arc\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so arc length is 20/3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Correct. Now we can plug that into our other formula to find \(\large \sf \theta\) \[\large \sf \theta~=~\frac{Arc~length}{Radius}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0bit i need theta in radians

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is the solution in radians. That's why I chose this formula instead of the degrees formula.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Second problem: \(\Large A_{sector} = \dfrac{\theta}{2 \pi ~rad}\pi r^2\) \(\Large \theta = \dfrac{2 \pi A}{\pi r^2} = \dfrac{2A}{r^2} = \dfrac{2 \times 30 ft^2}{(9~ft)^2} = \dfrac{60}{81} = \dfrac{20}{27}\)
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