Chapter 9: Q. 47 (page 756)
Use Theorem 9.14 to show that the circumference of the circle defined by the polar equation is .
Short Answer
The length of the curve is.
Chapter 9: Q. 47 (page 756)
Use Theorem 9.14 to show that the circumference of the circle defined by the polar equation is .
The length of the curve is.
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Get started for freeUse Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
Measurements indicate that Earth’s orbital eccentricity is and its semimajor axis is astronomical units.
(a) Write a Cartesian equation for Earth’s orbit.
(b) Give a polar coordinate equation for Earth’s orbit, assuming that the sun is the focus of the elliptical orbit.
Sketch the graphs of the equations
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What is the relationship between these graphs? What is the eccentricity of each graph?
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.
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