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
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Answer:
1)
The point estimate for the proportion of college graduates among women who work at home is 0.327
2)
The 80% confidence interval is given by (0.315; 0.339)
Step-by-step explanation:
For this case we have the following info given:
represent the women who worked at home who were college graduates
the sample size selected
Part 1
In order to find the proportion of college graduates among women who work at home and we can use the following formula:
The point estimate for the proportion of college graduates among women who work at home is 0.327
Part 2
Construct an 80% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to three decimal places. An 80% confidence interval for the proportion of women who work at home Is < p <
The confidence interval for the true proportion would be given by this formula
For the 80% confidence interval the value for the significance is and
, the critical value would be given by:
And replacing we goot:
The 80% confidence interval is given by (0.315; 0.339)