Since the students are to be selected at random, the concept used is Combination. The combination is 20C7 which means that "combination of 20 taken 7". The numerical value of the combination is 77520. Thus, there are 77520 ways of choosing the members of the student council.
Answer:
See explanation and proof below.
Step-by-step explanation:
For this case we want to proof this identity:
And we need to us the double angle formula given by:
If we use a substitution for example we see that the double angle formila is given by:
And we got:
And if we apply sqaure root on both sides we got:
And that complete the proof
Answer:
12.61 miles
Step-by-step explanation:
The distance of lighthouse B from lighthouse A, the distance from lighthouse A to the boat and the distance of lighthouse B from the boat all form a triangle. Since lighthouse B is west of lighthouse A, and at a distance of 9 miles form lighthouse A, light house A is at a bearing of North 90° East of lighthouse B. The distance from lighthouse A to the boat is 6 miles, and the bearing of the boat from lighthouse B is North 64° East.
So, the angle between the distance from lighthouse B to the boat and lighthouse B to lighthouse A is 90° - 64° = 26°
Since we have two sides and an angle, we use the sine rule
a/sinA = b/sinB where a = 6, A = 26°, b = 9, B = unknown
So, sinB = bsinA/a
= 9sin26/6
= 3(0.4384)/2
= 1.3151/2
= 0.6576
B = sin⁻¹(0.6576)
= 41.11°
≅ 41.1°
We now find the third angle in the triangle, C(the angle facing the distance from lighthouse B to the boat) from
26° + 41.1° + C = 180° (sum of angles in a triangle)
67.1° + C = 180°
C = 180° - 67.1° = 112.9°
Using the sine rule again to find the third side, c(the distance from lighthouse B to the boat), we have
a/sinA = c/sinC
c = asinC/sinA
= 6sin112.9°/sin26°
= 6(0.9212)/0.4384
= 5.5271/0.4384
= 12.61 miles