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2 answers:
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Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
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r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
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The attached graph shows the equivalence of the polar and rectangular forms.
Answer:
49
Step-by-step explanation:
Given:
Width = 0.4
Let's take the z value of 95% which is = 1.96
Let's assume population proportion p1 and p2 = 0.5
For margin of error E, the relation between the width and margin of error is 2E.
i.e 2E = 0.4
E = 0.2
To find the sample size, n, let's use the formula :
= 48.02
≈ 49