What is the center and radius of the circle? * x^2+ y^2+ 4y + 4 = 36
1 answer:
Answer:
(0, - 2 ), r = 6
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Rearrange the given equation collecting the terms in y together, that is
x² + y² + 4y + 4 = 36 ( subtract 4 from both sides )
x² + y² + 4y = 32
Use the method of completing the square on the y- terms
add ( half the coefficient of the y- term)² to both sides
x² + y² + 2(2)y + 4 = 32 + 4
x² + (y + 2)² = 36 ← in standard form
with (h, k ) = (0, - 2 ) and r² = 36, thus
centre = (0, - 2 ) and r = = 6
You might be interested in
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which z is the z-score that has a p-value of .
The margin of error is of:
90% confidence level, hence, z is the value of Z that has a p-value of
, so
.
Item a:
The estimate is .
The sample size is <u>n for which M = 0.03</u>, hence:
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence
Rounding up, a sample of 752 should be taken.
A similar problem is given at brainly.com/question/25694087