Polar form of (x+6)^2 +y^2=36
1 answer:
Answer:
r = -12cos(θ)
Step-by-step explanation:
The usual translation can be used:
- x = r·cos(θ)
- y = r·sin(θ)
Putting these relationships into the formula, we have ...
(r·cos(θ) +6)² +(r·sin(θ))² = 36
r²·cos(θ)² +12r·cos(θ) +36 +r²·sin(θ)² = 36
r² +12r·cos(θ) = 0 . . . . subtract 36, use the trig identity cos²+sin²=1
r(r +12cos(θ)) = 0
This has two solutions for r:
r = 0 . . . . . . . . a point at the origin
r = -12cos(θ) . . . the circle of interest
You might be interested in
Answer:
We are 95% confident that the true proportion of adults overweight is between 0.644 and 0.672
Step-by-step explanation:
We can begin founding the estimated proportion of people overweight:
We need to find a critical value for the confidence level using the normal standard distribution. We know that 95% is the confidence level, then the significance level would be given by and
. And the critical value would be given by:
The confidence interval for the true population proportion of interest is given by the following formula:
Replacing the data provided we got:
We are 95% confident that the true proportion of adults overweight is between 0.644 and 0.672