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4 years ago

Consider the function g(x) = 10/x

Mathematics

2 answers:

Sati [7]4 years ago

6 0

Answer:

0,0

2. The domain of g(x) is the same as the domain of the parent function.

4. The range is the same as the range of the parent function.

5. The function g(x) increases over the same x-values as the parent function.

6. The function g(x) decreases over the same x-values as the parent function.

Step-by-step explanation:

ss7ja [257]4 years ago

5 0

The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0

Explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.

Rational Function = g(x) = $\frac{10}{x}$ 

Denominator = x = 0

Hence the vertical asymptote is x = 0.

(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:

Given function = g(x) = $\frac{10}{x}$ 

We can write it as:

g(x) = $\frac{10 * x^0}{x^1}$ 

If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.

In above case, 0 < 1, therefore, the horizontal asymptote is y = 0

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3 years ago

Write the value of 4 in 305,444

BigorU [14]

Divide 305444 by 4

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3 years ago

Read 2 more answers

1. Find the sum of the measures of the interior angles of a convex 11-gon.

OleMash [197]

Answer:

The measure of the sum of interior angles of a 11-gon is $1620^{o}$ .

Each interior angle is approximately $147.273^{o}$ .

Step-by-step explanation:

A convex polygon has the measure of each interior angles to be less than $180^{o}$ .

But,

sum of interior angles of polygon = (n - 2) x $180^{o}$

where n is the number of sides of the polygon.

For a convex 11-gon, we have;

sum of angles of a 11-gon = (11 - 2) x $180^{o}$

= 9 x $180^{o}$

= $1620^{o}$

Sum of angles of a 11-gon = $1620^{o}$

To check: convex polygons' interior angles are less than $180^{o}$ .

so that,

each interior angle of 11-gon = $\frac{1620}{11}$

= $147.273^{o}$

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3 years ago

Evaluate the integral by changing to polar coordinatesye^x dA, where R is in the first quadrant enclosed by the circle x^2+y^2=2

34kurt

$\displaystyle\iint_Rye^x\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=5}r^2\sin\theta e^{r\cos\theta}\,\mathrm dr\,\mathrm d\theta$

which follows from the usual change of coordinates via

$\begin{cases}\mathbf x(r,\theta)=r\cos\theta\\\mathbf y(r,\theta)=r\sin\theta\end{cases}$

and Jacobian determinant

$|\det J|=\left|\begin{vmatrix}\mathbf x_r&\mathbf x_\theta\\\mathbf y_r&\mathbf y_\theta\end{vmatrix}\right|=|r|$

Swap the order, so that the integral is

$\displaystyle\int_{r=0}^{r=5}\int_{\theta=0}^{\theta=\pi/2}r^2\sin\theta e^{r\cos\theta}\,\mathrm d\theta\,\mathrm dr$

and now let $\sigma=r\cos\theta$ , so that $\mathrm d\sigma=-r\sin\theta$ . Now, you have

$\displaystyle\int_{r=0}^{r=5}\int_{\sigma=0}^{\sigma=r}re^\sigma\,\mathrm d\sigma\,\mathrm dr=\int_{r=0}^{r=5}r(e^r-1)\,\mathrm dr=4e^5-\dfrac{23}2$

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3 years ago

Estimate the sums and difference of 38.12 + 12.24 and round to the nearest tenth

Alinara [238K]

Answer:

50.4

Step-by-step explanation:

38.12 + 12.24 = 50.36

6 is near 10

50.36 = 50.4

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3 years ago