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Brut [27]
2 years ago
9

R = sec(θ) − 2cos(θ), where -π/2 < θ < π/2

Mathematics
1 answer:
Alex2 years ago
4 0

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

__

  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)

  \boxed{y=\dfrac{x\sqrt{1-x^2}}{1-x}}

__

The attached graph shows the equivalence of the polar and rectangular forms.

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9 and 12 have a common factor of 3 so 9/12 = 3/4
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3 years ago
Circle O has a circumference of approximately 2507 ft.
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Answer:

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Hope it helps

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1.
Paraphin [41]

Answer:

a. – 4 or –3

b. –4 or –2

c. 4 or –3

d. 7 or 4

Step-by-step explanation:

To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.

Now, we shall give the answers to the question.

a. x² + 7x + 12 = 0

x² + 3x + 4x + 12 = 0

Factorise

x(x + 3) + 4(x + 3) = 0

(x + 4)(x + 3) = 0

x + 4 = 0 or x + 3 = 0

x = 0 – 4 or x = 0 – 3

x = – 4 or –3

Therefore, the roots of the equation are – 4 or –3

b. t² + 6t + 8 = 0

t² + 2t + 4t + 8 = 0

Factorise

t(t + 2) + 4(t + 2) = 0

(t + 4)(t + 2) = 0

t + 4 = 0 or t + 2 = 0

t = 0 – 4 or t = 0 – 2

t = –4 or –2

Therefore, the roots of the equation are –4 or –2

c. 2n² – 2n – 24 = 0

Divide through by 2

n² – n – 12 = 0

n² + 3n – 4n – 12 = 0

Factorise

n(n + 3) – 4(n + 3) = 0

(n – 4)(n + 3) = 0

n – 4 = 0 or n + 3 = 0

n = 0 + 4 or n = 0 – 3

n = 4 or n = –3

Therefore, the roots of the equation are 4 or –3

d. y² – 11y + 28 = 0

y² – 4y – 7y + 28 = 0

Factorise

y(y – 4) – 7(y – 4) = 0

(y – 7)(y – 4) = 0

y – 7 = 0 or y – 4 = 0

y = 0 + 7 or y = 0 + 4

y = 7 or 4

Therefore, the roots of the equation are 7 or 4.

4 0
3 years ago
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