What is the correct equation for the function whose graph is shown?

y = -5 cos 3x
y = -3 cos 5x
y = 3 cos 5x
y = 5 cos 3x

y = -3 cos 5x

Step-by-step explanation:

First, let's start by defining the standard form of a cosine function:

Where:

The angular frequency is:

So:

Frequency is a quantity that measures the number of repetitions per unit of time of any phenomenon or periodic event. In other words, for the cosine function, it is the number of cycles during its period of oscillation.

From one of the equations provided:

You can extract the angular frequency, so:

This tells you that the number of cycles during the period of oscillation (which is 2π) is 5. As you can see from the graph provided, the number of cycles of the function is 5.

Now, why -3. Well, as you may know, for x=0:

Thus, for x=0, this functions is always equal to 1. But from the graph you may note that the function for x=0 is equal to -3, hence,  

Therefore the answer is:

I attached you the graph, so you can corroborate the answer.  

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: