As these two angles are vertically opposite angles, they are equal:
14x+7=8x+15
14x-8x=15-7
6x=8
x=8/6
x=4/3 or 1.34
The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
<h3>What is a Parabola ?</h3>
A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
The equation of the parabola is
(x-2)² = (y+2)
Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
To know more about Parabola
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Answer:
θ = 60° or θ = 120°, which in radians is equivalent to θ = π/3 rad or θ = 2π/3 rad.
Explanation:
The given equation is sin θ = (√3)/2
Solving that equation is finding the value of the angle, θ, whose sine is (√3)/2.
The function that returns the value of the angle whose sine is (√3)/2 is the inverse function of the sine and it has a special name: arc sine or arcsin.
Hence, θ = arcsin (√3)/2.
You can use your knowledge of the notable angles to solve for that equation.
1) The function sine is positive in first and second quadrants.
2) The angles in the first quadrant go from 0° to 90°.
3) The sine of 60° (√3)/2, Hence the first value of θ is 60°
4) The angles in the second quatrant go from 90° to 120°. 60° is the reference angle in the second quadrant, and the angle searched is
- 180° - reference angle = 180° - 60° = 120°. So, 120° is the other solution of the equation.
5) You can convert both angles to radians using the equivalence
- π radians = 180° ⇒ 1 = π rad / 180°
- 60° = 60° × π rad / 180° = π/ 3 rad
- 120° = 120° × π rad / 180° = 2π/3 rad
6) You can verify that sin 60° = (√3)/2 = sin 120° .
4x - 8y = 8
8y = 4x - 8
y = 1/2 x - 1
slope: 1/2
y-intercept:(0, -1)
Line perpendicular- negative reciprocal slope
y-(-1) = -2 (x-0) Hahaha I don't know what is the point slope form though hahaha not sure with this.
It's the first choice. If you multiply the first equation by 3, your y term is a +12, and if you multiply the second equation by 4, your y term is a -12. When you add them the y terms cancel each other out.
