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Crank
3 years ago
6

What is the equation of the graph below?

Mathematics
2 answers:
nadezda [96]3 years ago
7 0

Answer:  The correct option is (A) y=\sin(x+90^\circ).

Step-by-step explanation:  We are to select the correct equation of the given graph.

From the graph, we can see that

y (x = 0) = 1,

y (x = 90°) = 0,

y (x = -90°) = 0,

y (x = 180°) = -1,

y (x = -180°) = -1, etc.

Option (A) is

y=\sin(x+90^\circ).

We have

y(x=0)=\sin(0+90^\circ)=\sin90^\circ=1,\\\\y(x=90^\circ)=\sin(90^\circ+90^\circ)=\cos90^\circ=0,\\\\y(x=-90^\circ)=\sin(-90^\circ+90^\circ)=\sin0^\circ=0,\\\\y(x=180^\circ)=\sin(180^\circ+90^\circ)=-\sin90^\circ=-1,\\\\y(x=-180^\circ)=\sin(-180^\circ+90^\circ)=-\sin90^\circ=-1,~etc.

So, this option is correct.

Option (B) is

y=\cos(x+90^\circ).

We have

y(x=0)=\cos(0+90^\circ)=\cos90^\circ=0\neq 1.

So, this option is not correct.

Option (C) is

y=\sin(x+45^\circ).

We have

y(x=0)=\sin(0+45^\circ)=\sin45^\circ=\dfrac{1}{\sqrt2}\neq 1.

So, this option is not correct.

Option (D) is y=\sin(x+90^\circ).

y=\cos(x+45^\circ).

We have

y(x=0)=\cos(0+45^\circ)=\cos45^\circ=\dfrac{1}{\sqrt2}\neq 1.

So, this option is also not correct.

Thus, the correct option is (A)

Molodets [167]3 years ago
6 0

Answer:A

Step-by-step explanation:

look at the graph and u will find the same answer

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Answer:

C. The balloon starts at a height of 500 ft  and rises at a rate of 150 ft.

Step-by-step explanation:

We have been given a graph which represents the height of the balloon over time.

We can see from our graph that y-intercept, which represents the height of the balloon (in thousand feet) at time equals zero, is 0.5. To find the correct y-intercept we will multiply 0.5 by 1000 as height of the balloon is given in thousand feet.

Therefore, y-intercept represents that the balloon starts at a height of 500 feet.  

Now let us find slope of our given line using slope formula.

is vertical change or rise.

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Upon substituting given values in above formula we will get,

Now let us multiply 0.15 by 1000 as height of balloon is given in thousand feet.

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1.5/10=3/20=0.15. Since it's based off of 1000 feet, we multiply 0.15 by 1000 to get 150 as the rate of change for every x value. In addition, since we start at 0.5, 1000*0.5=500 and we therefore start at 500 ft. Using the information we have, we therefore have C as our answer

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