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Fed [463]
4 years ago
12

Find the dicontinuities of the function.

Mathematics
1 answer:
elena-s [515]4 years ago
5 0

Answer:

Step-by-step explanation:

I'm assuming you meant to type in

f(x)=\frac{x^2+12x+27}{x^2+4x+3} because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to

f(x)=\frac{(x+3)(x+9)}{(x+1)(x+3)} and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.

The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!

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1/36

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Express the following division in the form of a + bi: (-9 - 8i)/(7 + 2i)
hodyreva [135]

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-79/53 - 38i/53

Step-by-step explanation:

6 0
3 years ago
Use cosine to find the missing value round to 2 decimal places #trigonometry
Naddika [18.5K]

Answer:

1. 17.27 cm

2. 19.32 cm

3. 24.07°

4. 36.87°

Step-by-step explanation:

1. Determination of the value of x.

Angle θ = 46°

Adjacent = 12 cm

Hypothenus = x

Using cosine ratio, the value of x can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos 46 = 12/x

Cross multiply

x × Cos 46 = 12

Divide both side by Cos 46

x = 12/Cos 46

x = 17.27 cm

2. Determination of the value of x.

Angle θ = 42°

Adjacent = x

Hypothenus = 26 cm

Using cosine ratio, the value of x can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos 42 = x/26

Cross multiply

x = 26 × Cos 42

x = 19.32 cm

3. Determination of angle θ

Adjacent = 21 cm

Hypothenus = 23 cm

Angle θ =?

Using cosine ratio, the value of θ can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos θ = 21/23

Take the inverse of Cos

θ = Cos¯¹(21/23)

θ = 24.07°

4. Determination of angle θ

Adjacent = 12 cm

Hypothenus = 15cm

Angle θ =?

Using cosine ratio, the value of θ can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos θ = 12/15

Take the inverse of Cos

θ = Cos¯¹(12/15)

θ = 36.87°

8 0
3 years ago
Darla found that the least common denominator needed to subtract \frac{x}{x^2+4x-12}-\frac{3}{x+6}is (x + 6)(x – 2). Which is th
Leona [35]
<h3>Answer: Choice B</h3>

\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}

which is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

=====================================

Explanation:

The LCD is (x+6)(x-2) which is the factorization of x^2+4x-12, and that is the denominator of the first fraction. The first fraction has the LCD already. The second fraction does not. It has (x+6) but it is missing (x-2).

We multiply top and bottom of the second fraction by (x-2) to get the second fraction to have the LCD.

\frac{3}{x+6} turns into \frac{3}{x+6}*\frac{x-2}{x-2} = \frac{3(x-2)}{(x+6)(x-2)}

------

So,

\frac{x}{x^2+4x-12} - \frac{3}{x+6}

\frac{x}{(x+6)(x-2)} - \frac{3}{x+6}

\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}

This is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

Note the parenthesis around "(x+6)(x-2)"

Instead of x/(x+6)(x-2) you should write x/( (x+6)(x-2) ) to ensure that all of "(x+6)(x-2)" is in the denominator.

4 0
3 years ago
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