Each of Sunil's beagle puppies weighs less than 11.3 oz at birth.
1 answer:
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Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = (
) =
( or 60° )
The equation of the directrix is x = -3
<h3>What is Parabola?</h3>A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.
<h3>According to the given information: </h3>Given the general equation of a parabola expressed as
(y-y0)² = 4a(x-x0) ... 1
Equation of the directrix will be expressed as x = x0 - a
From the equation given;
y² = 12x ... 2
Comparing 1 and 2;
x - x0 = x
-x0 = x - x
-x0 = 0
x0 = 0
Similarly;
y-y0 = y
-y0 = y - y
-y0 = 0
y0 = 0
Also;
4a = 12
a = 12/4
a = 3
Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;
x = x0 - a
x = 0 - 3
x = -3
Hence,
the equation of the directrix is x = -3
To know more about Parabola visit:
#SPJ4
