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kirza4 [7]
1 year ago
15

Identify the type of polar graph for the equation: r = 3-5cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex lima

con eRose Curve fCircle gLemniscate

Mathematics
1 answer:
svp [43]1 year ago
5 0

Given the equation:

r=3-5\cos \theta

Let's identify the type of polar graph for the equation.

To identify the type of polar graph, use the formula below to get the Cartesian form:

(x^2_{}+y^2)=r(\cos \theta,\sin \theta)

Thus, we have:

(x^2+y^2)=3\sqrt[]{x^2+y^2}-5x

We have the graph of the equation below:

We can see the graph forms a Limacon with an inner loop.

Therefore, the type of polar graph for the given equation is a limacon with inner loop.

ANSWER:

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Hunter-Best [27]

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence (a_{i}) (range) and their respective indexes (i) (domain):

i         a_{i}

1         6

2        11

3        16

4        21

5        26

b) The algebraic expression for the general term of the sequence is a(i) = 6 + 5\cdot (i - 1).

c) The 25th term in the sequence is 126.

Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence (a_{i}) (range) and their respective indexes (i) (domain):

i         a_{i}

1         6

2        11

3        16

4        21

5        26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

a(i) = a_{1} + r\cdot (i - 1) (1)

Where:

a_{1} - First element of the sequence.

r - Arithmetic difference.

i - Index.

If we know that a_{1} = 6 and r = 5, then the algebraic expression for the general term of the sequence is:

a(i) = 6 + 5\cdot (i - 1)

c) If we know that a(i) = 6 + 5\cdot (i - 1) and i = 25, then the 25th term in the sequence is:

a(25) = 6 + 5\cdot (25 - 1)

a(25) = 126

The 25th term in the sequence is 126.

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I hope this helps.

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Answer:

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Step-by-step explanation:

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