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stealth61 [152]
2 years ago
11

Riley makes a mistake in step 2 while doing her homework. what was her mistake? startfraction x over x squared minus 5 x 6 endfr

action startfraction x over x 3 endfraction
Mathematics
1 answer:
Nastasia [14]2 years ago
6 0

She used wrong common denominator.

<h3> Correct solution:</h3>

\frac{x}{{x}^2-5x+6} + \frac{3}{x+3}\\\\=\frac{x}{{x}^2 - 3x - 2x + 6} + \frac{3}{x+3}\\\\=\frac{x}{(x-3)(x-2)} + \frac{3}{x+3}\\\\=\frac{x(x+3) + 3(x-2)(x-3)}{(x-3)(x-2)(x+3)}\\\\=\frac{{x}^2 + 3x + 3{x}^2-15x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{4{x}^2 -12x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{2(2{x}^2 - 6x + 9)}{(x-3)(x-2)(x+3)}

To learn more, visit:

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Answer:

The function touches the damping factor

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Step-by-step explanation:

Given function is f(x)=e^{-3x} sin(x) and damping factor as y=e^{-3x} and y=(-1)e^{-3x}

To find when function touches the damping factor:

For f(x)=e^{-3x} sin(x) and y=e^{-3x}

Equating the both the equation,

e^{-3x} sin(x)=e^{-3x}

sin(x)=1

x=\frac{(4n-3)\pi}{2}

For f(x)=e^{-3x} sin(x) and y=(-1)e^{-3x}

Equating the both the equation,

e^{-3x} sin(x)=(-1)e^{-3x}

sin(x)=(-1)

x=\frac{(4n-1)\pi}{2}

Therefore, The function touches the damping factor x=\frac{(4n-3)\pi}{2} and x=\frac{(4n-1)\pi}{2}

To find x-intercept of f(x):

For x-intercept, y=0

f(x)=e^{-3x} sin(x)

y=e^{-3x} sin(x)

e^{-3x} sin(x)=0

Hence, e^{-3x} is always greater than zero.

Therefore,sin(x)=0

x=n\pi

Thus,

The x-intercept of f(x) is at x=n\pi

7 0
3 years ago
Pls answer! i will mark brainliest!
Volgvan

Answer:

3 inches

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Answer:

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