Question

What angle is formed by the hands of the clock at 12:05, 7:43, 3:37 MEDALS

Answer 1

@Ashleyisakitty Help

Answer 2

ok the way i would do this is find the angle the minute hand makes with top of clock or 12:00
then find angle the hour hand makes
Finally subtract the two to get angle between the two hands


Minute hand:
clock is divided into 60 min ---> 360/60 = 6
1 min = 6 degrees
whatever number representing minutes, you multiply by 6 to get angle
example:
4:30 ----> 30 is the minutes, 30*6 = 180, minute hand has angle of 180 degrees

Hour hand:
clock is divided into 12 hours --> 360/12 = 30
1 hr = 30 degrees
Also we must consider that the hour hand is slowly moving to next hour based on where the minute hand is..... 1 hr is split into 60 min intervals
--> 30/60 = 1/2
each minute = 1/2 degree
example:
4:30 ---> 4 is hour, 4*30=120 --> 30*1/2 = 15
120 + 15 = 135
hour hand has angle of 135 degrees

Using my example of 4:30
min hand = 180 degrees
hour hand = 135

subtract ---> 180 - 135 = 45 degrees
Also note that if angle is more than 180, subtract from 360 to get correct answer

Answer 3

So for 12:05, the minute hand angle is 30 and the hour hand angle is 360???

Answer 4

I mean 180

Answer 5

But that would mean 180-30=150 and there's no way 12:05 is 150 degrees...

Answer 6

Oh wait I forgot it goes from 360 to 180 to 90 and then I subtract 30 from 90 ro get 60 but that still isn't... right.

Answer 7

lets look at hour hand again
12:05

12*30 = 360 = 0 (360 means we are back where we started)
5*1/2 = 2.5

0+2.5 = 2.5

hour hand has angle of 2.5 degrees

Answer 8

oh, well then. Wait but why is it addition now?

Answer 9

??

Answer 10

But the angle formed by the hands of the clock at 12:05 can't be 2.5 degrees, the minute and the hour hand form at least a 30 degree angle right?

Answer 11

Before you said subtract the minute from the hour or something like that

Answer 12

oh no thats just for the hour hand
minute hand is still 30 degrees

to get angle between them, you still subtract
---> 30 - 2.5 = 27.5

Answer 13

But if the hour hand was 360=0 how is it 30?

Answer 14

er minute

Answer 15

ok at 12:00 both hands are straight up ... angle is 0

as time ticks the minute hand moves faster than hour hand
minute hand moves at 6 degrees per minute

hour hand only moves at 1/2 degree per minute or 30 degrees per hour

Answer 16

Literally can't click Post because of notifications at the bottom -_-

Answer 17

But, the 5 minutes in 12:05 accounts for the 2.5 in terms of hour and the 30 in terms of minutes...

Answer 18

yes

Answer 19

Isn't that like saying x = y but also z but z and y aren't the same??

Answer 20

hmm no because there are 2 different hands moving at different speeds

Answer 21

Ok I think I get it

Answer 22

Let me try another example

Answer 23

Clock forms 4:55

Answer 24

err Clock is 4:55

Answer 25

if the concept is a bit confusing to you i can sum it up in a nice formula

given --> H:m
\[angl e = |(30H+\frac{1}{2}m) - 6m|\]

Answer 26

So 4x30 = 120/2 = 60

Answer 27

55/60 = 11/12

Answer 28

11/12x30=...

Answer 29

dammit

Answer 30

Using your formula [(30(4) + 1/2(55) - 6m]

Answer 31

or 6(55)?

Answer 32

yes, what will that give you?

Answer 33

120 + 27.5 - 330 = 147.5 -330

Answer 34

I don't even understand

Answer 35

dont stop...what is |147.5 -330|?

Answer 36

-182.5

Answer 37

good, notice i used absolute value to force it to be positive

182.5

the 2 hands cant be more than 180 so in this case we will subtract from 360
360 - 182.5 = 177.5

Answer 38

So after the formula if it is - use absolute value and if it's over 180 subtract from 360?

Answer 39

correct

Answer 40

Okay thanks, let me try one more. See if I can do it on my own. Mind giving me a random time?

Answer 41

lets do the ones in your original post
7:43

Answer 42

My gosh I can't scroll down to press Post because of the notifications...

Answer 43

(30(7) + 1/2(43) - 6(43)
210 + 21.5 - 258
-26.5

Answer 44

26.5 is the answer?

Answer 45

very good

now do 3:37

Answer 46

oh yeah its been doing that to me too....press "tab" then "enter" to post without clicking

Answer 47

(30(3) + 1/2(37)) - 6(37)
90 + 18.5 -222
108.5-222
-113.5 = 113.5

Answer 48

yes looks like you got it, just use the formula i gave you

if you want to understand it better you can reread my first post i guess, it may sink in after awhile

Answer 49

Yea, it's definitely sinking in

Answer 50

Although, I do have one more question but I don't know if I should start a new post for it

Answer 51

It has to do with factoring

Answer 52

go ahead and just ask me here...i can do a couple more before i log off

Answer 53

I know x^2+x-30 is (x-5)(x+6) or something like that but I don't know how to figure it out quickly, like I had a quiz today and the question was x^2 + 11x + 172 = 0 and I blanked :p

Answer 54

ok i can give some tips but sometimes, especially with big numbers it can be hard to find the right factors quickly

so want 2 numbers that add to middle coefficient
and multiply to get last coefficient

since 172 is big and have a lot of factors, i would start with the 11
1+10
2+9
3+8
4+7
5+6
and see if any of these multiply to get 172 ... they dont so this is actually not factorable

Answer 55

So what would an example with a big number be that would be factorable?

Answer 56

x^2 + 32x +240 = 0

Answer 57

So I start with 32? Like
31x1
30x2
29x3
etc

Answer 58

yeah but some are obviously not going to work like 31 and 1
start in middle
16 +16
17+15
18+14
...

Answer 59

wait 16+16 not 16x16?

Answer 60

Jeez I've literally forgotten everything about factoring haha

Answer 61

both ... you want it to add to 32 but multiply to 240

Answer 62

ok

Answer 63

so 16+16 = 32 and 16x16 = 256

Answer 64

17+15 = 32 but 17x15 = 255

Answer 65

20+12 = 32 but 20x12 = 240

Answer 66

ok not what do I do

Answer 67

now*

Answer 68

yep so its (x+12)(x+20)

Answer 69

My God I feel stupid hahahahahaha

Answer 70

Silly large numbers

Answer 71

What about another example like x^2 +x -30 = 0 where it's (x-5)(x+6) dealing with negatives

Answer 72

Are those only for 1x or do I use them for other _x's

Answer 73

oh no it could be anything

x^2 -5x-14

Answer 74

Using my battlefield case to kill mosquitos haha

Answer 75

x^2 -5x -14 = 0...
(x - 7)(x + 2)?

Answer 76

correct

Answer 77

yay, I would link an achievement song but I don't know the thread rules on this

Answer 78

most links are ok as far as i know....no spam or porn

Answer 79

https://www.youtube.com/watch?v=ZOJCmPKaYN8 Murica haha

Answer 80

Learned more in one openstudy session than 1 week in Geo, seems legit

Answer 81

Alright well I'm definitely done for the night. Thanks for all your help!

Answer 82

hey yw feel free to tag me if im on if you need more help

Answer 83

ok cool