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wariber [46]
3 years ago
12

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Mathematics
2 answers:
gulaghasi [49]3 years ago
4 0
This equation is an example of a Limacon with inner loop. By using the symmetry tests where:

POLAR AXIS/HORIZONTAL:
replace a) θ by -θ, b) r by -r and θ by π-<span>θ

VERTICAL AXIS:
replace a) </span>θ by π-θ, b) r by -r and θ by -<span>θ

POLE:
replace a) </span>θ by π+<span>θ, b) r by -r 

If any of these rules, after replacing it in the equation, results to the original equation (making it the equivalent) then it is symmetrical to that axis. 

In this case, it is only symmetrical about the polar/horizontal axis. </span>
siniylev [52]3 years ago
4 0

Answer:

x-axis only

Step-by-step explanation:

Look at the graph

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VashaNatasha [74]

Answer:

a = \frac{4\sqrt3}3; d= 2\sqrt 2

Step-by-step explanation:

First one is half an equilateral triangle. It means the hypotenuse is twice the shorter side, so 2a. Then let's apply the Pythagorean theorem:

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At this point is simply take the square root, use the positive value since they're lengths, and rearrange the fraction to have things look nice:

a^2 = \frac{16}3\\a= {4\over \sqrt3}\\a = {4\sqrt3\over \sqrt3 \sqrt3}}\\ a = \frac{4\sqrt3}3

Second one is half a square - or if you prefer, it's an isosceles right triangle, both side lengths are 2. Then its Pythagoras again:

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Again, we just have to pick the square roots, and rearrange in a better looking way.

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Which property can be used to solve the equation?
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Division property of equality

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