Provide an appropriate response.Consider the curves corresponding to polar equations of the form  where  Explain how the graph changes as a changes. Identify any values of a for which the basic shape of the curve changes.

What will be an ideal response?


For 0 < a < 1, the curve is an oval. As a ? 1-, the oval develops a dimple. When  the graph resembles a parabola with a dimple at the vertex. When  the curve has two parts that resemble the branches of a hyperbola, although the left-hand "branch" has a loop and, as a increases, the right-hand "branch" develops a bulge.

Mathematics

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Find the exact area under the curve between the indicated values of x.y = ; between x = 1 and x = 3

A.
B.
C. 3
D.

Mathematics

Identify the group of terms as like or unlike.14z, -13z

A. Unlike B. Like

Mathematics

Convert the units using unit fractions.84 qt =  gal

A. 168 B. 336 C. 21 D. 42

Mathematics

Find the percent using a proportion. Round your answer to the nearest tenth if necessary.$539.18 is what percent of $66.33?

A. 8129% B. 12.3% C. 812.9% D. 1.2%

Mathematics