What is the frequency of the sinusoidal graph?

Mathematics

1 answer:

FrozenT [24]4 years ago

5 0

Answer:

$\boxed{f=\dfrac{3}{2\pi}}.$

Step-by-step explanation:

Notice that the wave completes 3 oscillations at $x=2\pi$ . This means that the period is:

$T = \dfrac{2\pi}{3}.$

Since the frequency is the reciprocal of the period, we get:

$f= \dfrac{1}{T} = \dfrac{1}{2\pi/3} = \dfrac{3}{2\pi}.$

So the frequency is:

$\boxed{f=\dfrac{3}{2\pi}}.$

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What is the vertex of the graph of y = x^2+ 4x?

xxTIMURxx [149]

Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

y+(4/2)^2 = x^2+4x+(4/2)^2

y+4 = x^2 + 4x + 4

y+4 = (x+2)^2

y = (x+2)^2 - 4

This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)

6 0

2 years ago

How do I do number 14?

luda_lava [24]

Answer:

1/4^3 = 1/64

Step-by-step explanation:

you just basically multiply 1/4 for the first 3 ones, you multiply $\frac{1}{4} x\frac{1}{4} x\frac{1}{4} = \frac{1}{64}$ . then you do the same but twice and then once.