The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
9x+4=5x+20
——————
9x-5x=20-4
—————-
4x=16
————-
X=4
————
My deepest apologies if my answer turned out to be wrong but i tried my best so best of wishes!!
9514 1404 393
Answer:
(-1, -2)
Step-by-step explanation:
The difference between the coordinates of the image and the coordinates of the original is the same for both points.
X - (0, 2) = (5, 2) -(6, 6)
X = (5, 2) -(6, 6) +(0, 2) = (5-6+0, 2-6+2)
X = (-1, -2)
The image of the point after translation is (-1, -2).
Answer:
(4, 2) the formula for 270 rotation counterclockwise is (y,-x)
Step-by-step explanation:
