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3 years ago

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For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f(x)=2x^m/x+a {a =

–1, m = 1}

1 answer:

iVinArrow [24]3 years ago

3 0

Answer:

See below

Step-by-step explanation:

$f(x)=\frac{2x^{m} }{x+a}$

$f(x)=\frac{2x^{1} }{x-1}$

If x=1, then 1-1=0, which implies a vertical asymptote at x=1 since dividing by 0 is undefined.

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A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as

mamaluj [8]

Answer:

The farmer have at first <u>202</u> chickens.

Step-by-step explanation:

Given:

A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.

Now, to find the chickens farmer have at first.

Let the chickens be $x.$

And, the ducks be $y.$

<em>As, the farmer had twice as many chickens as ducks on his farm.</em>

So, $x=2y$ ......(1)

<em>As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.</em>

According to question:

$x-166=(y-29)\times \frac{1}{2}$

$x-166=\frac{y-29}{2}$

Substituting the value of $x$ from equation (1) we get:

$2y-166=\frac{y-29}{2}$

<em>By cross multiplying we get:</em>

$4y-332=y-29$

<em>Adding both sides 332 we get:</em>

$4y=y+303$

<em>Subtracting both sides by </em> $y$ <em> we get:</em>

$3y=303$

<em>Dividing both sides by 3 we get:</em>

$y=101.$

Now, to get the number of chickens substituting the value of $y$ in equation (1):

$x=2y\\\\x=2\times 101\\\\x=202.$

Therefore, the farmer have at first 202 chickens.

7 0

3 years ago

State the domain restriction(s) in interval notation of \displaystyle f\left(g\left(x\right)\right)f(g(x)) given: \displaystyle

DENIUS [597]

Answer:

The interval notation for the domain is $[\frac{23}{3},\infty ]$ .

Step-by-step explanation:

Consider the provided information.

It is given that $\:f\left(x\right)=\sqrt{3x-2},\:\text{ and }\:g\left(x\right)=x-7$

We need to find the value of $f\left(g\left(x\right)\right)$ .

Put the value of g(x) in $f\left(g\left(x\right)\right)$ .

$f\left(g\left(x\right)\right)=f(x-7)$ ....(1)

Now, put x=x-7 in $\:f\left(x\right)=\sqrt{3x-2}$

$\:f\left(x-7\right)= \sqrt{3(x-7)-2}$

$\:f\left(x-7\right)= \sqrt{3x-21-2}$

$\:f\left(x-7\right)= \sqrt{3x-23}$

From equation 1.

$f\left(g\left(x\right)\right)=\:f\left(x-7\right)= \sqrt{3x-23}$

The domain of the function is the set of input values for which a function is defined.

Here, the value of $3x-23$ should be greater or equal to 0 as the square root of a negative number is not real.

Domain= $3x-23\geq0$

$x\geq\frac{23}{3}$

The value of x is all real number greater than $\frac{23}{3}$ .

Hence, the interval notation for the domain is $[\frac{23}{3},\infty ]$ .

7 0

2 years ago

Need help with this please

Katarina [22]

For the first one, since she earns $17 per hour, & she tutored for 12 hrs this month, all you have to do is multiply the amount she makes per hour by the hours she’s tutored for. so 12x17=$204 so she made $204 this month. For the second one, it’d be the same thing, just multiply 19.5 by 17, which would give you 331.5.

& For the second question, all you have to do is plug in the numbers to the equation above. so it’d be 540 gallons / 1 minute multiplied by 42 since that is the time the pool needs to be filled by. So, if you do that, you will get 22,680, so the answer will be : yes it will fill up on time.

3 0

3 years ago

3.. please help!!!!!!!!!!!

mario62 [17]

Answer: lalala

Step-by-step explanation:

7 0

3 years ago

I need to know the answer for my test pls help

DochEvi [55]

3= -1 + 7y x 10 to the second power

5 0

2 years ago

Read 2 more answers