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Aleonysh [2.5K]
2 years ago
11

100 points!!! Pre calculus. I need helpppppppppp

Mathematics
1 answer:
Fantom [35]2 years ago
6 0

Answer:

We have function,

y = 3 - 6 \sin {}^{} (2x +  \frac{\pi}{2} )

Standard Form of Sinusoid is

y =  - 6 \sin(2x +  \frac{\pi}{2} )  + 3

Which corresponds to

y = a \sin(b(x + c))  + d

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

y =  - 6(2(x +  \frac{\pi}{4} )) + 3

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

\frac{2\pi}{ |b| }

\frac{2\pi}{ |2| }  = \pi

So the period is pi radians.

b. Amplitude is

| - 6|  = 6

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

3 - 6 \sin((2(0) +  \frac{\pi}{2} )

3 - 6 \sin( \frac{\pi}{2} )

3 - 6(1)

3 - 6

=  - 3

So the y intercept is (0,-3)

E. To find phase shift, set x-c=0 to solve for phase shift.

x +  \frac{\pi}{4}  = 0

x =  -  \frac{\pi}{4}

Negative means to the left, so the phase shift is pi/4 units to the left.

f. Period is PI, so use interval [0,2pi].

Look at the graph above,

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Help please :))) thank u
Gnom [1K]

Answer:

The distance between A and B is 8.5 after rounded to the nearest tenth

Step-by-step explanation:

The formula you always use for distance between points is as pictured.

Point A is (-6, 4), this is x1 and y1

Point B is (2, 1), this is x2 and y2

(2-[-6])^2 + (1-4)^2

since 2 negatives make a positive, 2 - -6 = 8

1 - 4 = -3

This makes 8 squared and -3 squared

8x8 = 64

-3x-3 = 9

64 + 9 = 73

the square root of 73 = 8.544003745

After rounding to the nearest tenth, it is 8.5

I hope this helps you! Good luck :)

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Step-by-step explanation:

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