The answer will be 6118.4
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
Answer/Step-by-step explanation:
a. Using two points on the line (0, 2) and (4, 12), find the gradient:
Gradient = ∆y/∆x = (12 - 2) / (4 - 0) = 10/4 = 2.5
Gradient = 2.5
b. The gradient, 2.5, represents the unit rate. That is, the volume of the oil in the tank per second.
i.e. 2.5 litres per second
c. The value, L = 2 represents the y-intercept, which is the starting value or initial volume of oil in the tank at 0 secs.
<span>First of all, F is true because (16 - 16)/(16 - 4) = 0. It just means when you plug in that number (16) you'll get 0. This will NOT happen for 4 because the 0 is in the denominator.
Look what happens if you have x = 4. This gives you 12/0, which is undefined. For some graphs, this is a hole, but let's look closer.
What happens if you have x = 3.9? You'll have 12.1/0.1. 3.9999? 12.0001/0.0001. The closer you get to 4, the closer you'll get to y = infinity.
But what if you have 4.1? 11.9/-0.1. You'll get the same results, but NEGATIVE infinity. So it is NOT a hole in the graph.
If you draw it out, you'll see that there is a vertical asymptote at x = 4.
B and F are true.
As for horizontal asymptotes, look at it like this: y = 16-16/16 - 4 means y = 0. There is no asymptote here. Try subbing in 1 = (x -16)/(x - 4).
Multiply by x - 4 on both sides
x - 4 = x - 16
There is no solution here; there will be an asymptote, so D is also true.
B, D, and F are true. ,"yahoo answers"//////////////////if i get busted at least i put down my main source (you know what I'm saying)</span>
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