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Dvinal [7]
2 years ago
9

How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) a

t x, rather than a vertical asymptote? Give an example​
Mathematics
1 answer:
Eva8 [605]2 years ago
5 0

Consider that,

x^2+4x+4 = (x+2)(x+2)

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.

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Answer:

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Step-by-step explanation:

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2 years ago
A digital camera for 249.99 at 4% sales tax
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2 years ago
p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.
Margarita [4]

Step-by-step explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

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where k is a constant

First, let find k. Substitute p= 200

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\frac{200}{2(3) {}^{2} }  = k

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Now, since we know our constant, let find p.

\frac{p}{q {r}^{2} }  =  \frac{100}{9}

Q is 5, and r is 2.

\frac{p}{5( {2}^{2}) }  =  \frac{100}{9}

\frac{p}{20}  =  \frac{100}{9}

p =  \frac{2000}{9}

3 0
1 year ago
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