Wikipedia:Reference desk/Archives/Mathematics/2016 January 23

= January 23 =

Trigonometry problem
(sin a+cosec a)2+(cos a+sec a)2=7+tan2 a+cot2 a — Preceding unsigned comment added by 116.202.251.201 (talk) 04:41, 23 January 2016 (UTC)


 * True if the 2s are powers rather than multiples. Follows from expanding each bracket and using sin^2 + cos^2 =1←86.139.120.76 (talk) 16:27, 23 January 2016 (UTC)

Turtle racing
My question is a basic math problem. I would appreciate some help in answering this basic math problem, as I am trying t help a neighbour who has learning disabilities. Two turtles (Eddie and Matilda) are in a 100 metre race. Eddie begins at the starting line. Eddie travels 9 metres a minute. Matilda begins at the 11 metre mark. Matilda travels at 8 metres a minute. I have made a chart that shows the distance travelled every minute, but that as far as I can get. What I am trying to explain (and figure out) is which turtle gets to the 100 meter line first? (I figure that both reach the 99 metre mark at 12 min.) How long does it take matilda to get to 100 metre line, and how long does it take eddie to get to the 100 metre line? I would say that Eddie gets to the finish line at 12 and half minutes, but what about matilda who got an 11 metre head start? — Preceding unsigned comment added by 65.95.242.137 (talk) 17:22, 23 January 2016 (UTC)
 * You are correct that they meet at the 99 meter mark, but this happens at 11 min (that is, 11 minutes after the race starts), not 12 min.
 * After that, they both have 1 meter to go, and obviously Eddie will do it first because he's faster. It will take him an extra 0.1111 minutes (6.666 seconds), not half a minute as you suggested. It will take Matilda 0.125 minutes (7.5 seconds).
 * You can use the formula $$x=x_0+v(t-t_0)$$. -- Meni Rosenfeld (talk) 17:47, 23 January 2016 (UTC)
 * As an addendum I would like to point of that the number ".1111 minutes" really means "1/9 minutes": if Eddie travels at a constant rate of 9 meters per minute then it takes one ninth of one minute for him to travel one meter. Meni Rosenfeld then converted this number to decimal. --JBL (talk) 15:55, 24 January 2016 (UTC)