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3 years ago

Determine the center and radius of the following circle equation: 2? + y2 – 12x – 18y + 17 = 0

Mathematics

1 answer:

snow_tiger [21]3 years ago

6 0

Answer:

Step-by-step explanation:

hello :

x²+ y² -12x - 18y +17 = 0 means : (x²-12x+36)-36+(y²-18y+81)-81-27 =0

(x-6)²+(y-9)² =12²....standard form when the center is (-6 , 9) and radius 12

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F(x)= x-2/ x-4

hodyreva [135]

Answer:

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵ $f(x)=\frac{x-2}{x-4}$

- To find the point of discontinuity put the denominator = 0 and find

the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

equal to 0

∴ There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes

of the denominator of the function

∵ The zero of the denominator is x = 4

∴ The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

intersection points between the graph and the x-axis

∵ f(x) = 0

∴ $\frac{x-2}{x-4}=0$ ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

denominator, then the equation of the horizontal asymptote is

y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

6 0

3 years ago

Solving the Simplified Equation

Artist 52 [7]

Answer:

- 1.5

Step-by-step explanation:

put two x variables in one place and two numbers in one place

28x- 22x = 56-65

6x = -9

x=-1.5

6 0

3 years ago

Would be great if someone can help with this.

Neporo4naja [7]

Answer:

144

Step-by-step explanation:

In a regular decagon like the one shown in the picture each angle is 144 degrees and it all adds up to 1,440. If you want proof search up "angle of a decagon"

8 0

2 years ago

3) Shayna and Anjali are selling pies for a school fundraiser. Customers can buy cherry pies and

Nadya [2.5K]

Answer

Step-by-step explanation:

10-8= 2

9-2=7

5 0

3 years ago

A study of long-distance phone calls made from General Electric's corporate headquarters in Fairfield, Connecticut, revealed the

Jet001 [13]

Answer:

a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

b) 0.0668 = 6.68% of the calls last more than 4.2 minutes

c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes

e) They last at least 4.3 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 3.6, \sigma = 0.4$

(a) What fraction of the calls last between 3.6 and 4.2 minutes?

This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.

X = 4.2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 3.6

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3.6 - 3.6}{0.4}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

(b) What fraction of the calls last more than 4.2 minutes?

This is 1 subtracted by the pvalue of Z when X = 4.2. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of the calls last more than 4.2 minutes

(c) What fraction of the calls last between 4.2 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 4.2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

0.9998 - 0.9332 = 0.0666

0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

(d) What fraction of the calls last between 3 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 3

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3 - 3.6}{0.4}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.9998 - 0.0668 = 0.9330

0.9330 = 93.30% of the calls last between 3 and 5 minutes

(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?

At least X minutes

X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.

$Z = \frac{X - \mu}{\sigma}$

$1.75 = \frac{X - 3.6}{0.4}$

$X - 3.6 = 0.4*1.75$

$X = 4.3$

They last at least 4.3 minutes

7 0

3 years ago