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
Semenov [28]
3 years ago
5

Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

(x-h)^2+(y-k)^2=r^2

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

You might be interested in
How to solve this problem
Shkiper50 [21]
You have to ask the question with the right type of something.
6 0
3 years ago
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a h
Kipish [7]

Answer:

The home would be worth $249000 during the year of 2012.

Step-by-step explanation:

The price of the home in t years after 2004 can be modeled by the following equation:

P(t) = P(0)(1+r)^{t}

In which P(0) is the price of the house in 2004 and r is the growth rate.

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.

This means that r = 0.047

$172000 in 2004

This means that P(0) = 172000

What year would the home be worth $ 249000 ?

t years after 2004.

t is found when P(t) = 249000. So

P(t) = P(0)(1+r)^{t}

249000 = 172000(1.047)^{t}

(1.047)^{t} = \frac{249000}{172000}

\log{(1.047)^{t}} = \log{\frac{249000}{172000}}

t\log(1.047) = \log{\frac{249000}{172000}}

t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}

t = 8.05

2004 + 8.05 = 2012

The home would be worth $249000 during the year of 2012.

8 0
3 years ago
A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers
sashaice [31]

The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = \frac{36}{40} * 100%%  

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

Therefore, the confidence interval is (0.685, 0.735).

Learn more about confidence interval here:

brainly.com/question/24131141

#SPJ4

3 0
2 years ago
If P=2b +2s, what is P if b= 3inches and s =5 inches ?
iren2701 [21]

Answer:

16

Step-by-step explanation:

If P=2b +2s then you plug in the variables

5 0
3 years ago
What are the zeros of this graph?
Nikitich [7]

B. x=10 and x=60. these are the points where she doesn't loses or gain money.

Hope this helped! Mark as Brainliest Please! :))

4 0
3 years ago
Other questions:
  • Please use the image below in order to find out the answer to the following question:
    15·1 answer
  • Find the sum: -48 + -12 =
    7·1 answer
  • Triangle ABC has side a= 12, b=16, and c=c find the measure of angle a to the nearest whole number
    12·1 answer
  • In 3434 pound of a spice mix, there is 5656 cup of cinnamon. How much cinnamon does the spice mix contain per pound? 5858 cup ​
    15·1 answer
  • If xy = 144, x + y = 30, and x &gt; y, what is the value of x – y ?
    12·1 answer
  • Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking w
    15·1 answer
  • How is 56 divided by 8 = 7
    10·2 answers
  • You have a budgeted $3200 per month for your total expenses. The cost of rent per month is $1050 and the cost of food is $300. T
    9·1 answer
  • Determine whether the given value is a statistic or a parameter. In a study of all 1580 seniors at a college comma it is found t
    11·1 answer
  • The sum of two numbers is 7. The larger number is 16 more than 2 times the smaller number. What are the numbers?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!