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3 years ago

Find the solution of this system of equations. Separate the x- and y-values with a comma. x - 4y = 9 and x - y = -9

1 answer:

4 0

X - 4y = 9 ------- (1)
x - y = -9 ---------(2)

(2) - (1):
-y - (-4y) = -9 - 9
-y + 4y = -18
3y = -18
y = -6 . -------- sub into (2)

x - (-6) = -9
x + 6 = -9
x = -9 - 6
x = -15

Ans: x = -15, y = -6

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We have function,

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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.

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