Symmetry can be determined visually in a graph. If both graphs are mirror-image of each other, then both of the equations are symmetric. But, you can also determine it analytically through testing the symmetry. These are the rules:
If
f(r, θ) = f(r,-θ), symmetric to the polar axis or the x-axis
f(r, θ) = f(-r,θ), symmetric to the y-axis
f(r, θ) = f(-r,-θ), symmetric to the pole or the origin
Test for symmetry about the x-axis
f(r,θ): r=4 cos3θ
f(r,-θ): r = 4 cos3(-θ) ⇒ r = 4 cos3θ
∴The graph is symmetric about the x-axis.
Test for symmetry about the y-axis
f(r,θ): r=4 cos3θ
f(-r,θ): -r = 4 cos3θ
∴The graph is not symmetric about the y-axis.
Test for symmetry about the origin
f(r,θ): r=4 cos3θ
f(-r,-θ): -r = 4 cos3(-θ) ⇒ r = -4 cos3θ
∴The graph is not symmetric about the origin.
Since the unit rate of Tito is greater than that of Jonah, hence T<u>ito is running at a faster rate</u>
<h3>Unit rates</h3>
The ratio of distance covered by an object to tme taken is unit rate.
Calculate the unit rate for both Jonah and Tito
For Jonah
Unit rate = 5laps/9minutes
Unit rate = 0.56 laps per minute
For Tito
Unit rate = 7laps/11.2minutes
Unit rate = 0.625laps per minute
Since the unit rate of Tito is greater than that of Jonah, hence T<u>ito is running at a faster rate</u>
Learn more on rate here: brainly.com/question/24304697
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The rest of the question is the attached figure.
Solution:
As shown in the figure
ΔABC is an isosceles right triangle at B
AB = BC and AC is the hypotenuse ⇒ AC = 260 ft
using Pythagorean theorem
∴ AC² = AB² + BC² = AB² + AB² = 2 AB²
∴ AB² = AC²/2 = 0.5 AC²
∴ AB = √(0.5 AC²) = √(0.5 * 260²) = 130√2 ft →(1)
Also as shown in the figure
ΔADB is a right triangle at D
from (1) AB = 130√2 ft
given BD = 105 ft
we should know that ⇒
∴ θ = sin⁻¹ 0.571 ≈ 34.82° = 35° ( to the nearest degree )
So, the value of θ = 35°