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3 years ago

Find the vertical and horizontal asymptote if they exist

Mathematics

1 answer:

tresset_1 [31]3 years ago

7 0

Hello!

Vertical asymptotes are determined by setting the denominator of a rational function to zero and then by solving for x.

Horizontal asymptotes are determined by:

1. If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

2. If the degree of the numerator = degree of denominator, then y = leading coefficient of numerator / leading coefficient of denominator is the horizontal asymptote.

3. If degree of numerator > degree of denominator, then there is an oblique asymptote, but no horizontal asymptote.

To find the vertical asymptote:

2x² - 10 = 0

2(x² - 5) = 0

(x - √5)(x + √5) = 0

x = √5 and x = -√5

Graphing the equation, we realize that x = -√5 is not a vertical asymptote, so therefore, the only vertical asymptote is x = √5.

To find the horizontal asymptote:

If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

Therefore, the horizontal asymptote of this function is y = 0.

Short answer: Vertical asymptote: x = √5 and horizontal asymptote: y = 0

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A random sample of 100 automobile owners in thestate of Virginia shows that an automobile is driven onaverage 23,500 kilometers

Anastaziya [24]

Answer:

a) 22497.7 < μ< 24502.3

b) With 99% confidence the possible error will not exceed 1002.3

Step-by-step explanation:

Given that:

Mean (μ) = 23500 kilometers per year

Standard deviation (σ) = 3900 kilometers

Confidence level (c) = 99% = 0.99

number of samples (n) = 100

a) α = 1 - c = 1 - 0.99 = 0.01

$\frac{\alpha }{2} =\frac{0.01}{2}=0.005\\ z_{\frac{\alpha }{2}}=z_{0.005}=2.57$

Using normal distribution table, $z_{0.005$ is the z value of 1 - 0.005 = 0.995 of the area to the right which is 2.57.

The margin of error (e) is given as:

$e= z_{0.005}\frac{\sigma}{\sqrt{n} } = 2.57*\frac{3900}{\sqrt{100} } =1002.3$

The 99% confidence interval = (μ - e, μ + e) = (23500 - 1002.3, 23500 + 1002.3) = (22497.7, 24502.3)

Confidence interval = 22497.7 < μ< 24502.3

b) With 99% confidence the possible error will not exceed 1002.3

5 0

4 years ago

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum are

kifflom [539]

Garden
max area is if the sides are as equal as possible
so he should try to make a square (ideal is a circle, but barn walls are normally straight)
squaer perimiter=4 times legnth of 1 side
perimiter=amount of fencing=80
80=4s
divide 4
20=s
one sides=20

area=legnth times width
in squaer, legnth=width

20=legnth
20=width
area=20 times 20=400

dimetions are 20ft by 20ft to give 400ft^2
(fun fact, if it were a circle, the area would be about 509.5ft^2)

answer is 20ft by 20ft and area=400ft^2

7 0

3 years ago

If you change the sign of a point’s x<br> -coordinate, how will the location of the point change?

Umnica [9.8K]

By changing the sign of x coordinates the point would be reflected along "y" axis.

Step-by-step explanation:

Let us plot a hypothetical point (x, y) where both x and y are positive integer. Since both the number sets are positive integer, hence the points lie in 1st quadrant.

Now we change the sign of the x coordinates i.e. x=-x

The new coordinates are (-x, y)

since x is negative and y is positive hence this set would lie in 2nd quadrant.

Comparing the above two pointset (x, y) and (-x, y)

We find that 2nd set is the reflection of the 1st set along y axis (“y” remains constant and sign of “x” coordinates change)

Hence if the original point is in 1st quadrant then the after changing the sign points would lie in 2nd quadrant and vice-versa.

Similarly, if both the values of “x” and “y” are negative i.e. points lie in 3rd quadrant, then the points would lie in 4th quadrant after changing and vice-versa

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3 years ago

A product cost $48.50 for 75 feet. how much does it cost per inch?

Ivahew [28]

The answer is: $ 0.0538888888888889 / in.
______________________________
Round to: $0.05388 per inch.
________________________________
Explanation:
________________________________
Note the exact conversion: 1 feet (ft) = 12 inch (in.) .
______________________________________________
$\frac{48.50}{75 ft}$ * $\frac{1 ft}{12in}$ =

$ { $\frac{48.50}{75*12}$ } / in. =

$ { $\frac{48.50}{900}$ } / in =

<span>$ 0.0538888888888889 / in. .

→ Round to: $ 0.05388 / in.
__________________________________

</span>

8 0

3 years ago

Help me pls need help

alexira [117]

Answer:

9s+11

Step-by-step explanation:

Combine like terms → (7s+2s and 2+9 = 9s and 11) and boom

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3 years ago

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