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kenny6666 [7]
3 years ago
11

Which of the following types of symmetry does the graph of the equation r=6sin 5 theta have?

Mathematics
2 answers:
Ivenika [448]3 years ago
6 0

Answer:

B

Step-by-step explanation:

Plot the graph of the equation r=6\sin 5\theta on the polar coordinate plane (see attached diagram for details).

A. There is no symmetry about the horizontal axis, because three parts of the graph are above the axis and two parts of the graph are under the axis.

B. There is  symmetry about the vertical axis, because if you reflect left (or right) part about the vertical axis it will coincide with the other part.

C. There is no symmetry about the pole (see diagram)

D. This option is false, because option B is true (there is axis of symmetry)

9966 [12]3 years ago
4 0

Answer:

The correct option is 2.

Step-by-step explanation:

1. Symmetry about the x-axis: If the point (r, θ) lies on the graph, then the point  (r, -θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,  π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

The given equation is

r=6\sin (5\theta)

Check the equation by (r, -θ ).

r=6\sin (5(-\theta))

r=-6\sin (5\theta)=-r\neq r

The given equation do not have symmetry about the x-axis or horizontal axis.

Check the equation by (-r, -θ).

-r=6\sin (5(-\theta))

-r=-6\sin (5\theta)

-r=-r

LHS=RHS

The given equation have symmetry about the y-axis or vertical axis.

Check the equation by (-r, θ).

-r=6\sin (5\theta)

-r\neq r

The given equation do not have symmetry about the origin or pole.

Therefore the correct option is 2.

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Answer:

Number of students(n1)= 4,402

Step-by-step explanation:

Giving the following information:

Number of students= 4,512

Declining rate= 2.5%

<u>To calculate the number of students next year, we need to use the following formula:</u>

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3 years ago
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ollegr [7]

Answer:

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7 0
2 years ago
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3 years ago
Read 2 more answers
The measure of angle A to the nearest tenth of a degree is: A 18.5 B 19.5 C 20.5
Andrew [12]

Answer:

B


Step-by-step explanation:

<u>This is a right triangle as shown by the right angle.</u>

  • The side opposite the right angle is the hypotenuse, which is 9.
  • The side opposite angle A is 3.

So we have the opposite of A and the hypotenuse.

The trigonometric ratio that relates opposite side to hypotenuse is SINE.

sin\theta=\frac{opposite}{hypotenuse}

Since, we need angle A, \theta is A, opposite side is 3, and hypotenuse is 9, we substitute:

sinA=\frac{3}{9}\\sinA=\frac{1}{3}

<em>To solve for the angle, we use our calculator and find the inverse sin of \frac{1}{3} :</em>

A=sin^{-1}(\frac{1}{3})\\A=19.47

<em>Rounding to nearest tenth of a degree:</em>

A=19.5

B is the right choice.

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3 years ago
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Natasha2012 [34]

Answer:

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