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Equation 1: r = -5 * cos theta

Equation 2: r = 1 – ( 4 * sin theta  )

Step-by-step explanation:

Graph 1:

This graph is a circle along negative x- axis.

General equation for graph:

R = a cos theta          ∴ a =  diameter of circle

From given graph, it is included that:

a = -5  

a/2 = -2.5 (center of circle)

Equation 1: r = -5 cos theta

Graph 2:

This graph is an inner-loop limacon.

The inner-loop limacon is in the downward direction along the negative y-axis

The general equation for the graph will be :

r = a – b sin theta  

a will represent x – intercept, from graph it is included that:

a = { +1, -1  }

For inner-loop on y-axis, b - a = 3     ………….1  

For outer-loop on y-axis, a + b = 5    …………2

Adding both 1 and 2 to find values of a and b

b – a = 3

a + b = 5

2b     = 8     ⇒      b = 4

Putting value of b in 2

a + 4 = 5       ⇒       a = 1

substituting values of a and b in general equation:

Equation 2: r = 1 – 4 sin theta

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify