Answer:
a) D(t) = ![\[20*\sqrt{5} * t\]](https://tex.z-dn.net/?f=%5C%5B20%2A%5Csqrt%7B5%7D%20%2A%20t%5C%5D)
b) 178.885 miles
Step-by-step explanation:
Ship A travels north at the rate of 20 mph.
Ship B travels east at the rate of 40 mph.
After t hours, Ship A is at a distance of 20t miles from the origin.
Similarly, Ship B is at a distance of 40t miles from the origin.
(a) Distance D(t) = ![\[\sqrt{(20t)^{2}+(40t)^{2}}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B%2820t%29%5E%7B2%7D%2B%2840t%29%5E%7B2%7D%7D%5C%5D)
= ![\[\sqrt{400*t^{2}+1600 * (t)^{2}}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B400%2At%5E%7B2%7D%2B1600%20%2A%20%28t%29%5E%7B2%7D%7D%5C%5D)
= ![\[\sqrt{2000*t^{2}}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B2000%2At%5E%7B2%7D%7D%5C%5D)
= ![\[20*\sqrt{5} * t\]](https://tex.z-dn.net/?f=%5C%5B20%2A%5Csqrt%7B5%7D%20%2A%20t%5C%5D)
(b) Distance between the two ships when t = 4,
= ![\[20*\sqrt{5} * 4\]](https://tex.z-dn.net/?f=%5C%5B20%2A%5Csqrt%7B5%7D%20%2A%204%5C%5D)
=
miles
= 80 * 2.236
= 178.885 miles
Well when x is -1, y = 0, then when x is 0, y = 3 so it is increasing there...then when x is 1, y = 6, so it is still increasing, but then it goes back down to 3 when x is 2
Therefore, the largest interval would be from -1 to positive 1 (-1,1)
Hope this helps
Brian
Answer:
1320
Step-by-step explanation:
This is a simple permutation.
Since you start with 12 people and there are 3 winners, after every winner the number pf people available to win decrease.
First, there are 12 people, then after the first win there are 11 people, and after the 2nd win, for the third win the there are 10 people.
Thus, to find the total number of combinations, you multiply:
12*11*10=1320
Thus, there are 1320 possible combinations
Answer: This is what I have tried --
5 gallons : 3 weeks = x gallons : 52 weeks
5/3 = x/52 (cross multiply)
3x = 260 (divide by 3)
x = 86.6 or 87 gallons
Step-by-step explanation: hope this is right