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NNADVOKAT [17]
3 years ago
9

What is the name of the shape graphed by the function r = 2 - costheta

Mathematics
1 answer:
Afina-wow [57]3 years ago
8 0

Answer:

limaçon (no inner loop)

Step-by-step explanation:

The equation of a limaçon is written generically as ...

r = b + a·cos(θ)

For b=2 and a=1, this would put the flat side on the left. Rotating it 180° can be accomplished by adding or subtracting π from θ. Then the equation can be ...

r = 2 + cos(θ-π) . . . . or ...

r = 2 - cos(θ)

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3 years ago
Which of the following is an extraneous solution of (45-3x)^1/2=x-9?
Iteru [2.4K]

Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6

Hence, we can conclude that x=3 is an extraneous solution of the equation ..

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4 years ago
Please help me figure out the answers !
OverLord2011 [107]

Answer:

Step-by-step explanation:

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