Question

help

Answer 1

whats the radius of each gear.

Answer 2

ok i c sec

Answer 3

well im thinking we could start by finding the circumference of the smaller one

Answer 4

and then find the angle of the arc length = to that, on the bigger one

Answer 5

2piR

Answer 6

so im getting

18.85 or so

Answer 7

the circumference of the bigger one is 43.98

Answer 8

thats what I got.

Answer 9

so how 18.85 is what percentage of 43.98?

Answer 10

huh? i don't understand. sorry im terible at math... :'c

Answer 11

about 42.86 percent

or 0.4286

Answer 12

if you divide the smaller circumference by the larger one

Answer 13

So now that we have that we can find the arc length?

Answer 14

we can take a shortcut i think. if a rotation of 43.98 is 360 degrees on the bigger one

and were only going rotating around 18.85

18.85/43.98 = 0.4286

we rotated around 42.86 percent of 360 degrees.

Answer 15

So thats what part 1 is? :D

Answer 16

yes, thats the shortcut way of doing it i think. to factor in the arc length and all that, id have to think about it a bit more. but its probably basically the same thing

Answer 17

well the arc length is = the circumference of the smaller one

Answer 18

yes thats the arc length on the bigger one.

Answer 19

the angle formed by that arc is what ure trying to find for part 1

Answer 20

hmmm. How would I do that. I'm confused. Would I multiply or divide that by 360?

Answer 21

so arc length = theta times radius

Answer 22

whats the theta?

Answer 23

the angle

Answer 24

\[18.85=\theta \times \frac{ \pi }{ 180 } \times 7\]

Answer 25

thats the formula to find it in degrees

Answer 26

arclength = theta times pi/180 times radius

Answer 27

so were trying to solve for theta (this is stil part 1, minus well do it the right way)

Answer 28

\[18.85= \theta \times \frac{ 7\pi }{ 180 }\]

Answer 29

we wanna solve for theta

Answer 30

ya sounds about right

Answer 31

yep

Answer 32

i dunno how strict your teacher is on rounding

Answer 33

but this is close enough for me

Answer 34

So would that be the answer for Part 1?

Answer 35

yes

Answer 36

for part 2 we can do something quite similar

Answer 37

the circumference of the larger one is 43.98

Answer 38

so

\[43.98 = \theta \times \frac{ \pi }{ 180 } \times 3\]

Answer 39

im getting something like 839.956 degrees ya

Answer 40

one rotation is 360 degrees

Answer 41

so divide by 360

Answer 42

yep so it rotates approx 2 and 1/3 times

Answer 43

but it will only make 2 full rotations

Answer 44

Wow, thank you so much!!! That was a lot of steps lol. Would you mind helping me with one more problem?

Answer 45

ya i explained it lazily so it seemed like more but

Answer 46

http://www.coolmath.com/reference/circles-trigonometry.html

Answer 47

thats the formula

Answer 48

Do you want me to close this question and open a new one? Or want to just put it here? :D

Answer 49

close