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konstantin123 [22]
2 years ago
13

Im lazy dont ask please-

Mathematics
1 answer:
Helen [10]2 years ago
5 0

Answer:

0.75

or 3/4ths

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%
Llana [10]

a) The given function is

f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}

The domain refers to all values of x for which the function is defined.

The function is defined for

x^4+x^3-4x^2-4\ne0

This implies that;

x\ne -2.69,x\ne 1.83

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

x^4+x^3-4x^2-4=0

This implies that;

x= -2.69,x=1.83

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

\frac{x^2-4}{x^4+x^3-4x^2-4}=0

\Rightarrow x^2-4=0

x^2=4

x=\pm \sqrt{4}

x=\pm2

The roots are x=-2,x=2

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

x=0 into the function

f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}

f(0)=\frac{-4}{-4}=1

e) to find the horizontal asypmtote, we take limit to infinity

lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0

The horizontal asymtote is y=0

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is  at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0
3 years ago
Which equation represents the sentence?
Sunny_sXe [5.5K]
<span>4x + 7 = 32
...................</span>
7 0
3 years ago
Adding and subtracing linear wxpressions 12(−4x+8)−14(8x−12)
Delicious77 [7]

Answer:

-160x+264

Step-by-step explanation:

-48+96x-112x+168

-160+264

3 0
3 years ago
George is drafting his dissertation paper for his doctoral program. The graph below shows the line of best fit for the data reco
sweet [91]

a. \: y =  \frac{3}{2} x + 4 \\  \\ 1. \:  \frac{3}{2} x + 4 = y \\ \\  2. \:  \frac{3}{2} x = y - 4 \\  \\ 3. \:  \frac{ \frac{3}{2} x}{\frac{3}{2} }  =  \frac{y - 4}{2}   \\  \\ x =  \frac{2y - 8}{3}

3 0
3 years ago
Read 2 more answers
Help question attached multiple choice
Rina8888 [55]

ANSWER

x =  \frac{\pi}{2} , \frac{7\pi}{6} , \frac{3\pi}{2} , \frac{11\pi}{6}

EXPLANATION

The given trigonometric equation is

\cos(x)  + 2 \cos(x)  \sin(x)  = 0

We factor cos(x) to get:

\cos(x) (1 + 2 \sin(x) ) = 0

Apply the zero product property to obtain:

\cos(x)  = 0 \: or \: 1 + 2 \sin(x)  =  0

\cos(x)  = 0 \: or \: \sin(x)  =   -  \frac{1}{2}

Using the unit circle,

\cos(x)  = 0

when

x =  \frac{\pi}{2}

and

x =  \frac{3\pi}{2}

We know

\sin(y)  =  \frac{1}{2}

when

y=  \frac{\pi}{6}

The sine function is negative in the third and fourth quadrants.

x = \pi +  \frac{\pi}{6}  =  \frac{7\pi}{6}

x = 2\pi  -   \frac{\pi}{6}  =  \frac{11\pi}{6}

Hence the solutions are:

x =  \frac{\pi}{2} , \frac{7\pi}{6} , \frac{3\pi}{2} , \frac{11\pi}{6}

6 0
3 years ago
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