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nadya68 [22]
3 years ago
15

Where are the vertical asymptote(s) f(x) = x2 + 12x + 27/ x2 + 4x + 3 .

Mathematics
1 answer:
kari74 [83]3 years ago
5 0

Answer:

x = -1

Step-by-step explanation:

f(x) = (x² + 12x + 27) / (x² + 4x + 3)

f(x) = ((x + 3) (x + 9)) / ((x + 3) (x + 1))

f(x) = (x + 9) / (x + 1)

The vertical asymptote is at x = -1.

Graph: desmos.com/calculator/r2x0inxmad

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You are correct. You multiply both sides of the second equation by -9 so that the y turns into -9y. That way you add it to the +9y in the first equation to get 0y (the y terms cancel afterward). Nice work.
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How many different digits are needed for the base 6 system?​
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0, 1, 2, 3, 4 and 5

Step-by-step explanation:

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Is 3 by 3=9 rational or inrational and why
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KCC off KCC off off egg LLC

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Answer:

? > 4x+36

Where x is the number of hour of parking

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5 0
3 years ago
Telephone calls arrive at a doctor’s office according to a Poisson process on the average of two every 3 minutes. Let X denote t
Liono4ka [1.6K]

Answer:

a) f(x)=\frac{2}{3}e^{-\frac{2}{3}x} when x\geq 0

f(x)=0 otherwise

b) P(X

Step-by-step explanation:

First of all we have a Poisson process with a mean equal to :

μ = λ = \frac{2}{3} (Two phone calls every 3 minutes)

Let's define the random variable X.

X : ''The waiting time until the first call that arrives after 10 a.m.''

a) The waiting time between successes of a Poisson process is modeled with a exponential distribution :

X ~ ε (λ)    Where λ is the mean of the Poisson process

The exponential distribution follows the next probability density function :

I replace λ = a for the equation.

f(x)=a(e)^{-ax}

With

x\geq 0

and

a>0

f(x)=0 Otherwise

In this exercise λ= a = \frac{2}{3} ⇒

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

x\geq 0

f(x)=0 Otherwise

That's incise a)

For b) P(X>2) We must integrate between 2 and ∞ to obtain the probability or either use the cumulative probability function of the exponential

P(X\leq x)=0

when x

and

P(X\leq x)=1-e^{-ax} when x\geq 0

For this exercise

P(X\leq x)=1-e^{-\frac{2}{3}x}

Therefore

P(X>2)=1-P(X\leq 2)

P(X>2)=1-(1-e^{-\frac{2}{3}.2})=e^{-\frac{4}{3}}=0.2636

5 0
3 years ago
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