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Sedbober [7]
3 years ago
14

Find the domain of the function. (Enter your answer using interval notation.)

Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0

Answer:

(-\infty,-9)\cup(-9,\infty)

Step-by-step explanation:

The domain of a rational function is all real numbers <em>except </em>for when the denominator equals 0.

So, to find the domain restrictions, set the denominator to 0 and solve for x.

We have the rational function:

s(y)=\frac{7y}{y+9}

Set the denominator to 0:

y+9=0

Subtract 9:

y\neq-9

So, the domain is all real numbers except for -9.

In other words, our domain is all values to the left of negative 9 and to the right of negative 9.

In interval notation, this is:

(-\infty,-9)\cup(-9,\infty)

And we're done :)

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Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48
Oksana_A [137]

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is x= \frac{1}{12}\cdot y^{2}.

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

x - h = 4\cdot p \cdot (y-k)^{2}

Where:

h, k - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

p - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

p = x_{D} - x_{V}

p = \frac{1}{48}-0

p = \frac{1}{48}

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is x= \frac{1}{12}\cdot y^{2}.

6 0
3 years ago
Rewrite 3/35 and 1/10 so they have common denominators
Aleks [24]

Answer:

\frac{6}{70} and \frac{7}{70}

Step-by-step explanation:

The LCM of 35 and 10 is 70.

35×2=70

10×7=70

You got to multiply 3 with 2 and 1 with 7 to make 6/70 and 7/70.

5 0
3 years ago
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Step-by-step explanation:

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3 years ago
I need the to <br> 572 divided by 10
Hitman42 [59]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
You have to fill in the blank for this one 4/9 divided by blank equals 12
photoshop1234 [79]

For this case, the first thing we must do is define a variable.

We have then:

x: unknown number

We now write the expression that models the problem:

\frac{\frac{4}{9}}{x} = 12

From here, we clear the value of x.

We have then:

\frac{4}{9}=12x

\frac{4}{9(12)}=x

x=\frac{4}{108}

x=\frac{1}{27}

Answer:

4/9 divided by 1/27 equals 12

6 0
3 years ago
Read 2 more answers
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