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3 years ago

Find any points of discontinuity for the rational function. y=x-5/x^2-7x-8

Mathematics

2 answers:

Crazy boy [7]3 years ago

4 0

Answer:

The function is not continuous at x= -1 and x= 8

Step-by-step explanation:

The given function is,

$y=\dfrac{x-5}{x^2-7x-8}$

Factoring the denominator,

$=x^2-7x-8$

$=x^2-8x+x-8$

$=x(x-8)+1(x-8)$

$=(x+1)(x-8)$

Now the function becomes,

$y=\dfrac{x-5}{(x+1)(x-8)}$

The function is not defined (it does not exist) for x= -1 and for x= 8, because the denominator is zero for those values of x.

To be continuous, the function has to be defined. So at those points the function is not continuous.

*At x= -1 and at x= 8 , the function has a vertical asymptote.

kotegsom [21]3 years ago

3 0

For discontinuity of the function:
x² - 7 x - 8 ≠ 0
x² - 8 x + x - 8 = 0
x ( x - 8 ) + ( x - 8 ) ≠ 0
( x - 8 ) ( x + 1 ) ≠ 0
The points of discontinuity are: x = - 1 and x = 8.
As for the Domain of the function:
x ∈ ( - ∞, - 1 ) ∪ ( - 1 , 8 ) ∪ ( 8, +∞ ).

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3 years ago

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What is the value of the following expression?2 x [(12 + 2) x 5] + 32 divided by 2 number on top right 3

a_sh-v [17]

The value of the expression is $141.5$

Explanation:

The expression is $2 \times[(12+2) \times 5]+\frac{3}{2}$

The value of the expression can be determined using the rule PEMDAS.

According to the PEMDAS rule, first we need to perform the operation which is within the parenthesis.

Thus, the expression becomes,

$2 \times(14 \times 5)+\frac{3}{2}$

Multiplying the values within parenthesis, we have,

$2 \times70+\frac{3}{2}$

Using PEMDAS, we need to multiply the numbers.

$140+\frac{3}{2}$

Again using PEMDAS rule, divide the number,

$140+1.5$

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$141.5$

Thus, the value of the expression is $141.5$

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2 years ago

An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence

Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error for this case is given by this formula:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

For the first case the confidence was 68% so then $\alpha =1-0.68 =0.32$ and $\alpha/2 =0.16$ we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is $z=\pm 0.994$ , because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

$ME = z_{\alpha/2} SE$

We can solve for the standard error on this case and we got:

$SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207$

And then for the new confidence interval we need to calculate the new $z_{\alpha}$ . For the first case the confidence was 95% so then $\alpha =1-0.95 =0.05$ and $\alpha/2 =0.025$ we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is $z=\pm 1.96$ , because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be:

$ME = z_{\alpha/2} SE = 1.96*201.207=394.366$

The estimation for the mean not changes and from the before and new case is 1000 years. So then the best option for this case would be:

B. 10000 years old, with a margin of error of 400 years

And makes sense since a larger confidence interval means a wider interval.

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3 years ago

7x < 10 please solve

Anvisha [2.4K]

Answer: The answer would be x < 10/7

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

7*x (10)>0

Step by step solution :

STEP

Pulling out like terms

1.1 Pull out like factors :

7x - 10 = -1 • (7x + 10)

Equation at the end of step

STEP 2

2.1 Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

7x+10 < 0

2.2 Divide both sides by 7

x+(10/7) < 0

Solve Basic Inequality :

2.3 Subtract 10/7 from both sides

x < 10/7

Inequality Plot :

2.4 Inequality plot for

7.000 x - 10.000 > 0

One solution was found :

x < 10/7

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2 years ago

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Answer:

I dont know sorry!! I would help though

Step-by-step explanation:

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2 years ago