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1 year ago

Write a rational function with the given characteristics.

1 answer:

6 0

According to the question, to express the rational function for the vertical asymptote whose equation is $x=8$ and horizontal asymptote whose equation is at $y=0.$

As per the question, the function 'f(x)' is vertical at $x=8$ . Therefore, the denominator be $(x-8)$

$f(x)=\frac{g(x)}{(x-8)}$

The function 'g(x)' should have same degree as the denominator function has and it is defined as $y=0$

The rational function can be written as:

Rational function = $\frac{y}{(X-8)}$

What is rational function?

Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.

To learn more about rational function from the given link:

brainly.com/question/19044037

#SPJ4

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A chemical flows into a storage tank at a rate of (180+3t) liters per minute, where t is the time in minutes and 0<=t<=60

Yuliya22 [10]

Answer:

The amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.

Step-by-step explanation:

Consider the provided information.

A chemical flows into a storage tank at a rate of (180+3t) liters per minute,

Let $c(t)$ is the amount of chemical in the take at t time.

Now find the rate of change of chemical flow during the first 20 minutes.

$\int\limits^{20}_{0} {c'(t)} \, dt =\int\limits^{20}_0 {(180+3t)} \, dt$

$\int\limits^{20}_{0} {c'(t)} \, dt =\left[180t+\dfrac{3}{2}t^2\right]^{20}_0$

$\int\limits^{20}_{0} {c'(t)} \, dt =3600+600$

$\int\limits^{20}_{0} {c'(t)} \, dt =4200$

So, the amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.

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2 years ago

Which of the following are true

Eva8 [605]

I cannot see the question

6 0

2 years ago

8/20 greater than or less than 2/10

kumpel [21]

8/20 is greater than 2/10. If you were to make the denominators the same, by mulipling 2x2 and 10x2, you would get 4/20, which is less than 8/20.

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3 years ago

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Brian draws a triangle on the coordinate plane and names it AMNB. The dilation

Shkiper50 [21]

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2 years ago

Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an av

Nesterboy [21]

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using: distance = speed x time

$\implies t=\dfrac{d}{v}$

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

$\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}$

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

$\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1$

Now all we have to do is solve the equation for v:

$\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1$

$\implies \dfrac{18(v+15)+18v}{v(v+15)}=1$

$\implies 18(v+15)+18v=v(v+15)$

$\implies 18v+270+18v=v^2+15v$

$\implies v^2-21v-270=0$

$\implies (v-30)(v+9)=0$

$\implies v=30, v=-9$

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

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1 year ago

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