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zhuklara [117]
3 years ago
6

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ. PLEASE HELP ME SOLVE RN I NEED TH

IS, ALSO INCLUDE THE PROVING PART.
Mathematics
1 answer:
Fofino [41]3 years ago
4 0
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.

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Answer:

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5 0
3 years ago
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A living room measures 24 feet by 15 feet. An adjacent square dining room measures 13 feet on each side. If carpet costs $6.98 p
blsea [12.9K]

Answer:

total cost of putting carpet in both rooms is $3692.42

Step-by-step explanation:

given data

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living room width = 15 feet

dining room is square so length and width will be same

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dining room width = 13 feet

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what is the total cost of putting carpet in both rooms

solution

first we find the total area of both room that is

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area of living room = 24 × 15

area of living room = 360 feet²      ...........................2

and

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area of dining room = 13 × 13

area of dining room = 169 feet²    ...............................3

so total area = add equation 1 and 2

total area = 360 feet² + 169 feet²  

total area = 529 feet²  

and

total cost of putting carpet in both rooms are = total area × carpet costs    .................4

put here value

total cost of putting carpet in both rooms  = 529  ×  $6.98

total cost of putting carpet in both rooms  =$3692.42

6 0
3 years ago
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ivanzaharov [21]

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A'B' is 1/2 times the AB as the scale factor is 1/2.

<u>Find the length of AB using distance formula.</u>

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<u>And find A'B':</u>

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