Answer:
it will take her family 12 minutes
Step-by-step explanation:
i hope this helps
Answer:
4 cups
Step-by-step explanation:
No, Rays go one way only since a point block te other way. Otherwise it wont be a ray :)
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:
Check below, please
Step-by-step explanation:
Step-by-step explanation:
1.For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.)
When the derivative of a function is equal to zero, then it occurs when we have either a local minimum or a local maximum point. So for our x-coordinates we can say

2. For which values of x is f '(x) positive?
Whenever we have

then function is increasing. Since if we could start tracing tangent lines over that graph, those tangent lines would point up.

3. For which values of x is f '(x) negative?
On the other hand, every time the function is decreasing its derivative would be negative. The opposite case of the previous explanation. So

4.What do these values mean?

5.(b) For which values of x is f ''(x) zero?
In its inflection points, i.e. when the concavity of the curve changes. Since the function was not provided. There's no way to be precise, but roughly
at x=-4 and x=4