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AnnZ [28]
3 years ago
5

Find Horizontal and Vertical Asymptotes for y=(1)/((x+2)^3)

Mathematics
1 answer:
Usimov [2.4K]3 years ago
3 0

Answer:

Vertical asymptote: x = -2

Horizontal asymptote: y = 0 or x axis.

Step-by-step explanation:

The rational function is given as:

y=\frac{1}{(x+2)^3}

Vertical asymptotes are those values of x for which the function is undefined or the graph moves towards infinity.

For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of x.

Here, the denominator is (x+2)^3

Setting the denominator equal to zero, we get

(x+2)^3=0\\(x+2)=0\\x=-2

Therefore, the vertical asymptote occur at x=-2.

Horizontal asymptotes are the horizontal lines when x tends towards infinity.

For a rational function, if the degree of numerator is less than that of the denominator, then the horizontal asymptote is given as y=0.

Here, there is no x term in the numerator. So, degree is 0. The degree of the denominator is 3. So, the degree of numerator is less than that of denominator.

Therefore, the horizontal asymptote is at y=0 or x axis.

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1 2/3 divided by (-2 3/4)
nydimaria [60]

Answer:

-0.606

Step-by-step explanation:

:)

3 0
2 years ago
A country is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30
kondaur [170]

Answer:

We conclude that speed is greater than 30 miles per hour.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ =  30 miles per hour

Sample mean, \bar{x} = 35 miles per hour

Sample size, n = 15

Alpha, α = 0.01

Sample standard deviation, s = 4.7 miles per hour

First, we design the null and the alternate hypothesis

H_{0}: \mu = 30\text{ miles per hour}\\H_A: \mu > 30\text{ miles per hour}

We use one-tailed(right) t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{35 - 30}{\frac{4.7}{\sqrt{15}} } = 4.120

Now, t_{critical} \text{ at 0.01 level of significance, 14 degree of freedom } = 2.624

Since,                  

t_{stat} > t_{critical}

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis and conclude that speed is greater than 30 miles per hour.

We calculate the p-value.

P-value = 0.00052

Since p value is lower than the significance level, we reject the null hypothesis and accept the alternate hypothesis. We conclude that speed is greater than 30 miles per hour.

6 0
2 years ago
What does -43.7 + 9.06 equal?
MrMuchimi
-43.7 + 9.06 = -34.64
4 0
3 years ago
Read 2 more answers
Please help me if you can. please show how you got the answer.
fomenos

Answer:

Step-by-step explanation:

The area of a circle is A = πr², where r is the radius. That means in order to solve this we have to find the value of x, which is the diameter of the lake, and then divide it in half to get the radius. To find x we will use similar triangles and proportions. x is the height of the big triangle and 4.5 is the height of the smaller triangle; 15.3 + 7.4 is the hypotenuse of the big triangle and 7.4 is the hypotenuse of the smaller triangle. Setting up our proportion:

\frac{x}{4.5}=\frac{15.3+7.4}{7.4} which simplifies a bit to

\frac{x}{4.5}=\frac{22.7}{7.4} and cross multiply to solve for x:

7.4x = 102.15 so

x = 13.8  That is the diameter of the lake. Divide it in half to get 6.9, the radius. Applying the area formula for a circle:

A = (3.14)(6.9)² and

A = 3.14(47.61) so

A = 149.5 which rounds to 150, Choice C

5 0
3 years ago
26=4v+3v+12 can anyone help?
motikmotik

Answer:

Step-by-step explanation:

Combine like terms

3v + 4v

26=7v+12

Subtract    12  from both sides of the equation

26-12

12-12

14=7v

Simplify

so subtract the 12's

Divide both sides of the equation by the same term

14 divided by 7

7 divided by 7

Simplify

do the division and move the term on the other side and it would be

v=2

Solution

 

v=2

4 0
3 years ago
Read 2 more answers
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