Answer:
3
Step-by-step explanation:
9 x (N + 2) = 45
9N + 18 = 45
9N = 27
N = 3
Let's forget for the tie being the cost ($3.5)of the 1st fifth of a mile:
Taxi charge excluding $3.5, is $13.95 - $3.5 = $10.45.
If each of the 5th (1/5) of a mile costs $0.55, then with $10.45 we can drive:
10.45/0.55 = 19 fifth of a mile. Add to that the 1st fifth = 20 fifth of a mile
20 fifth = 20 x 1/5 = 4 miles (answer)
Actually, this has little to do with mathematics and geometry but has to do more with logical reasoning. You have two clauses to get a conclusion from. The reasoning is as follows:
Clause 1: <span>Three noncollinear points determine a plane
Clause 2: </span><span>Points S, O, N are noncollinear
</span>Conclusion: Therefore, points S, O and N form a plane.
The identity in question is
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
so that
cos(a - b) = 12/37 cos(a) + 3/5 sin(b)
Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,
cos²(x) + sin²(x) = 1,
that
cos(a) = √(1 - sin²(a)) = 4/5
and
sin(b) = √(1 - cos²(b)) = 35/37
So,
cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185
