Question

College Algebra: a clock reads 10:30, how long after that time will the hands be perpendicular?

Answer 1

Hello, professor :)

Answer 2

^_^ haha

Answer 3

Why do you want this stuff?

Answer 4

its just a math problem, thats all

Answer 5

do you like this question?

Answer 6

it's ok, not hard

Answer 7

so, if 135-90 = 45 degree
each time, the needle goes 6 degree, 45/6 = number of minutes we need to get 90 degree. ( but just approximate because the short hand will move a little bit) if you want accurate number, you need write down the function of both hands. and... I don't think I can solve it accurately. hihihiiu

Answer 8

ya, it sssooounds easy, but is crap hard! both hands are moving..

Answer 9

I gotta log off, but if someone figures this, post it up

Answer 10

The position, in degrees, of the hour hand is x/12*360 and the position of the minute hand is (x-10)*360. The two will be perpendicular when (x-10)*360=x/12*360-90
or: x-10=x/12-.25
11x/12=9.75
x=12*9.75/11
x=10.636
or at 10:38.16

Answer 11

The minute hand moves at 6 deg per min. The hour hand moves at 1/2 degree per minute. That means, since the minute hand is chasing the hour hand, they will come together at 11/2 degrees per minute. As noted in the picture above, the starting position is 45 degrees from the desired position. That means\[45=\frac{11}{2}t \implies \frac{90}{11}=t\]This is a little more than eight minutes. A touch after 10:38.

Answer 12

thanks a bunch,
the Back of book says 8 and 11/2 is the time after 10:30, so you guys are right

Answer 13

No sweat. Do math every day.

Answer 14

Let the clock be set at 10 o'clock or 1000 military time.
Let t be the elapsed time in hours required, for the hands to make a right angle with each other.

Solve the folling equation for t:\[\left(\frac{t}{12}+\frac{10}{12}\right)-t=\frac{3}{12} \]\[t=\frac{7}{11} \]Subtract a half hour from t because the minute hand was pointing at 6, 30 minutes in the problem. The start time was 10:30 in the problem statement. Subtract 1/2 hours from t.\[t=\frac{7}{11}-\frac{1}{2}=\frac{3}{22}=8\min 10.9 \sec \]