Answer:
All the real number greater than or equal to 2
60x - 150 = 30
60x - 150 + 150 = 30 + 150
60x = 180
60x/60 = 180/60
x = 3
tan²(<em>θ</em>) - sin²(<em>θ</em>) = sin²(<em>θ</em>)/cos²(<em>θ</em>) - sin²(<em>θ</em>)
-- because tan(<em>θ</em>) = sin(<em>θ</em>)/cos(<em>θ</em>) by definition of tangent --
… = sin²(<em>θ</em>) (1/cos²(<em>θ</em>) - 1)
-- we pull out the common factor of sin²(<em>θ</em>) from both terms --
… = sin²(<em>θ</em>) (1/cos²(<em>θ</em>) - cos²(<em>θ</em>)/cos²(<em>θ</em>))
-- because <em>x</em>/<em>x</em> = 1 (so long as <em>x</em> ≠ 0) --
… = sin²(<em>θ</em>) ((1 - cos²(<em>θ</em>))/cos²(<em>θ</em>))
-- we simply combine the fractions, which we can do because of the common denominator of cos²(<em>θ</em>) --
… = sin²(<em>θ</em>) (sin²(<em>θ</em>)/cos²(<em>θ</em>))
-- due to the Pythagorean identity, sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1 --
… = sin²(<em>θ</em>) tan²(<em>θ</em>)
-- again, by definition of tan(<em>θ</em>) --
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
Answer:
y=7
y=5
y=4
y=6
y=2
Step-by-step explanation:
