Answer:
1.
Step-by-step explanation:
sec 16° cosec 74° - cot 74° tan 16°
= 1/ cos 16 * 1/ sin 74 - 1/tan 74 * tan16
= 1/ cos16 sin 74 - cos74/ sin74 * sin 16 / cos 16
Now cos 16 = sin 74 and sin 16 = cos 74 (supplementary angles) so:
= 1 / cos^2 16 - sin 16/cos 16 * sin 16 / cos 16
=( 1 - sin ^2 16 )/ cos^2 16
= cos^2 16 / cos^2 16
= 1.
Trains depart after every 4 minutes.
Total time train takes to complete a circuit= 24 minutes
Evan sets off at 8:30 am, so he will be back at 8:54 am.
So time of trains coming in opposite direction:
8: 34 am
8:38 am
8:42 am
8:46 am
and 8:50 am
5 trains coming in opposite directions.
Now the trains started at 8:06 am from the stations are:
8:06 am
8:10 am
8:14 am
8:18 am
8:22 am
and 8:26 am.
So there are 6 trains started the circuit at 8:06 am.
Now total number of trains=6+5=11 trains
Answer: 11 trains will pass on complete circuit.
Answer:
Step-by-step explanation:
The first equation is the weights of the rabbit and the ferret together which is
r + f = 7.
The second equation puts the weight of the ferret in terms of the rabbit. If the ferret's weight is 2 pounds more than the rabbit, then
f = r + 2 (the word "is" means equals). Since we know what f is equal to, we will sub it into the first equation and solve for r:
r + (r + 2) = 7 and
2r + 2 = 7 and
2r = 5 so
r = 2.5 pounds.
A rabbit weights 2.5 pounds and the ferret weights 7 - 2.5 which is 4.5 pounds.
The lcm of 120 and 20 is 120!
20 = 2 x 2 x 5
120 = 2 x 2 x 2 x 3 x 5
LCM = 2 x 2 x 2 x 3 x 5
