Answer:
(0,5)
Step-by-step explanation:
(1) y = -x² + 5
(2) y = x² + 5
2y =10 Added (1) and (2)
(3) y = 5 Divided each side by 2
5 = x² + 5 Substituted (3)into (2)
0 = x² Subtracted 5 from each side
x = 0 Took the square root of each side
The only ordered pair that represents a solution to both functions is (0, 5).
The graph of the second function is an upward-opening parabola (y = x²) translated up five units.
The graph of the first function is a downward-opening parabola (y = -x²) translated up five units.
The two graphs meet at their common vertex, (0, 5).
Recall the Maclaurin expansion for cos(x), valid for all real x :
Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives
The first 3 terms of the series are
and the general n-th term is as shown in the series.
In case you did mean cos(√(5x)), we would instead end up with
which amounts to replacing the x with √x in the expansion of cos(√5 x) :