1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mnenie [13.5K]
2 years ago
9

What is the radius of a circle with the equation x^2+y^2+6x-2y+3?

Mathematics
2 answers:
atroni [7]2 years ago
8 0

Answer:

r = √13

Step-by-step explanation:

Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms:  x^2 + 6x            + y^2 -2y             = 3.  Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."  

We need to "complete the square" of x^2 + 6x.  I'll just jump in and do it:  Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x:     x^2 + 6x  + 3^2 - 3^2.  Then do the same for y^2 - 2y:  y^2 - 2y + 1^2 - 1^2.

Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2.  Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1.  Making these replacements:

(x + 3)^2 - 9 + (y - 1)^2 -1 = 3.  Move the constants -9 and -1 to the other side of the equation:  (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13

Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r:  r^2 = 13, so that the radius is r = √13.


Komok [63]2 years ago
5 0

Answer:

2.646

Step-by-step explanation:

Complete the square, put the equation in standard form, then evaluate the radius.

... x² + y² + 6x - 2y +3 = 0 . . . . given equation in general form

... x² +6x + 9 +y² -2y +1 = -3 +9 +1 . . . . add the squares of half the coefficients of the x- and y-terms; subtract 3

... (x +3)² +(y -1)² = 7 . . . . standard form equation for a circle

The term on the right, 7, is the square of the radius. so the radius is ...

... r = √7 ≈ 2.646

You might be interested in
What percent is16 out of 64? It is _ .
Simora [160]
16 out of 64 is 25% hope this helped
4 0
3 years ago
The function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is
Whitepunk [10]

Answer:

  • Master Remodeling

Step-by-step explanation:

<em>Original question is attached</em>

<h3>Option 1</h3>
  • C(x) = 25x + 50
  • C(8) = 25*8 + 50 = $250
<h3>Option 2</h3>
  • As per table, the rate of change is $30 per 2 hours.
  • So 8 hours will cost
  • $190 + $30 = $220

As we see the second option is cheaper so we should hire the Master Remodeling

5 0
3 years ago
31, 680 divided by 45 I'm so confused​
kondaur [170]

Answer:

704

Step-by-step explanation:

calculator

5 0
2 years ago
Read 2 more answers
PLEASE HELP!!<br> just look at the picture
arlik [135]

Answer:

its the  math that solve

Step-by-step explanation:

4 0
2 years ago
To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data
nexus9112 [7]

Answer:

a) \sigma = 0.167

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be 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}

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of \mu. So X - \mu = 0.5 must have Z = 3 and X - \mu = -0.5 must have Z = -3.

So

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

3 = \frac{0.5}{\sigma}

3\sigma = 0.5

\sigma = \frac{0.5}{3}

\sigma = 0.167

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that \sigma = 2.8

The standard deviation of a sample of n young man is given by the following formula

s = \frac{\sigma}{\sqrt{n}}

We want to have s = 0.167

0.167 = \frac{2.8}{\sqrt{n}}

0.167\sqrt{n} = 2.8

\sqrt{n} = \frac{2.8}{0.167}

\sqrt{n} = 16.77

\sqrt{n}^{2} = 16.77^{2}

n = 281.23

We need a sample of at least 282 young men.

6 0
3 years ago
Other questions:
  • Raymond's Department Store sells dress shirts for $14.99. The cost to produce one dress shirt is $9.99 plus a one-time fee of $9
    6·1 answer
  • All of the following expressions have the same value except:
    6·1 answer
  • Carlita has 2 1/2 pounds of turkey, the cherries are 1/4 equal to the turkey, and the chocolate drips are .35 equal to the cherr
    14·1 answer
  • What is 40% of 80?
    7·2 answers
  • Use the spinner to identify the probability to the nearest hundredth of the pointer landing on a non-shaded area. HELP PLEASE!!
    12·1 answer
  • Need some help please
    6·2 answers
  • When factoring x2 – 3xy + 2y2 by grouping the first step can be:
    13·1 answer
  • Find the distance between the points (-4, 6) and (3, -7)
    5·1 answer
  • Use the function below to find F(-2) <br> F(X)= 3^x
    5·2 answers
  • Enter the solutions from least to greatest.<br> (3x -6)(-x +3)=0
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!