9514 1404 393
Answer:
see attached
Step-by-step explanation:
I like to use a spreadsheet for repetitive calculations. The distances are computed from the distance formula:
d = √((x2 -x1)^2 +(y2 -y1)^2)
The results are shown in the second attachment. The drawing in the first attachment has the lengths rounded to the nearest tenth.
Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
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r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
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The attached graph shows the equivalence of the polar and rectangular forms.
The option are missing in the question. The options are :
A. P = 2, a = 1
B.
C.
D. P = 2, a = 3
Solution :
The given function is
So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.
When the four option being substituted in the function, we get
A). It is a constant function since
B). Here, the value of a is a fraction which is less than 1, so it is a decay function.
C). It is a constant function since the value of a is 1.
D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.
Therefore, option (D). represents an exponential function.