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
2*2*2*2*2 which is equal to 32
Answer:
Y= X 23
—- + ——
5 5
Step-by-step explanation: solve for Y
by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 2
Step-by-step explanation:
Start by multiplying both sides by 7
Simplify
Subtract both sides by 10
Simplify
Apply exponent rules
Solve
Answer:
The number line that shows x > 8
Step-by-step explanation:
First, subtract 15 from both sides
<em>15 + 2x -15 > 31</em>
<em>2x > 16</em>
Then divide both sides by 2
<em>2x ÷ 2 > 16 ÷ 2</em>
<em>x > 8</em>
