All about plane geometry....?

Question

The question goes like this:
Form two times when the hands of a clock form a straight angle...

I just want to be completely sure...

Answer 1

at 6'0 clock and at 3:45.

It can also be at 12:30 , 9:15 and many others.

Answer 2

Find the length of time from 6 o'clock to the next time the hands of the clock form a straight angle.

Let
12 = distance around the clock one time
d = distance hour hand travels
d + 12 = distance minute hand travels
r = rate of hour hand
12r = rate of minute hand

time = distance/rate

t = d/r = (d + 12)/(12r)
12dr = r(d + 12)
12dr = dr + 12r
11dr = 12r
11d = 12
d = 12/11 hour

Every 12/11 hour the hands of the clock return to a straight angle.

So times for this would be:

6 = 6:00:00
7 1/11 ≈ 7:05:27
8 2/11 ≈ 8:10:55
9 3/11 ≈ 9:16:22
etc.

Answer 3

the answer depends on which standard u r in. if u r in middle school, all the above said answers r true.
but if u r not, at 12 am n 12 pm, the hands form a straight angle. to get the other times, calculations need to b done. thats bcos at 3:45 or 9:15, while the minutes hand has transversed 45mins(270 degrees) n 15 mins (90 degrees) respectively, the hour hand has also traversed some distance right?
if u wan the complex calculations :- while the minute hand travels 360 degrees, the hour hand travells 360/12 = 30 degrees. so while min hand travels 90 degrees(15 mins), hour hand travels 7.5 degrees. so at 9 :15, the hands of clock r short of a straight angle = 180 degrees by 7.5 degrees n so is the case wid 3:45 too.

Answer 4

θm = ωmt
θh = ωht
ωm = 360°/3600 s
ωh = 360°/43200 s
θm = θh + 180(2n - 1), n = number of occurance
ωmt - ωht = 180(2n - 1)
(360°/3600 - 360°/43200)t = 180°(2n - 1)
(360°(12/43200 - 1/43200)t = 180°(2n - 1)
(360°(11/43200)t = 180°(2n - 1)
t = 180°(2n - 1)(43200 s)/(11(360°)
t = (2n - 1)(21600 s)/11

. 1, 12:32:44
. 2,.. 1:38:11
. 3,.. 2:43:38
. 4,.. 3:49:05
. 5,.. 4:54:33
. 6,.. 6:00:00
. 7,.. 7:05:27
. 8,.. 8:10:55
. 9,.. 9:16:22
10, 10:21:49
11, 11:27:16
12, 12:32:44

Answer 5

A straight anlge is 180 degrees. So it has to be a stright line. That would be 6 o'clock and 12:30.

Answer 6

6.00 in morning and 6.00 in evening.

Other are 1:38, 2:43 ...
For every 360 turn of minute hand, the hour hand advances by 30 degrees.

Answer 7

go with 6 a.m. and 6 p.m., because those are the only two where it's exactly 180 degrees on the clock

Answer 8

1200
0000
0600
1800

rest r yet to be calculated coz you c

c there cud be many is my guess

Answer 9

3.00, 9.00