We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is $\frac{7\pi}{12}$ . The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is $y=A\cos(b(x-c))-d$ , where,

A = Amplitude,

$\frac{2\pi}{b}$ = Period,

c = Horizontal shift,

d = Vertical shift.

The equation of parent cosine function is $y=\cos(x)$ . Since function is reflected about x-axis, so our function will be $y=-\cos(x)$ .

Let us find the value of b.

$\frac{2\pi}{b}=\frac{7\pi}{12}$

$7\pi\cdot b=24\pi$

$\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}$

$b=\frac{24}{7}$

Upon substituting our given values in general cosine function, we will get:

$f(x)=-11\cos(\frac{24}{7}x)-9$

Therefore, our required function would be $f(x)=-11\cos(\frac{24}{7}x)-9$ .

7 0

3 years ago

ine segment XY has endpoints X(–10, –1) and Y(5, 15). To find the y-coordinate of the point that divides the directed line segme

stiks02 [169]

X=(-10,-1)=(Xx,Yx)→Xx=-10, Yx=-1
Y=(5,15)=(Xy,Yy)→Xy=5,Yy=15
y=?
ratio=5:3→r=5/3
y=(Yx+rYy) / (1+r)
y=[-1+(5/3)15] / (1+5/3)
y=[-1+(5*15)/3] / [(3+5)/3]
y=(-1+75/3) / (8/3)
y=(-1+25) / (8/3)
y=(24) / (8/3)
y=24*(3/8)
y=72/8
y=9

Asnwer: T<span>he y-coordinate of the point that divides the directed line segment XY in a 5:3 ratio is y=9</span>

3 0

3 years ago

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