Answer:
y = 1/6 x^2 + 8/3 x + 49/6
Step-by-step explanation:
This is a parabola which opens upwards.
The distance of a point (x, y) from the focus is
√[(x - -8)^2 + (y - -1)^2] and
the distance of the point from the line y = -4
= y - -4
These distances are equal for a parabola so:
√[(x - -8)^2 + (y - -1)^2] = y + 4
Squaring both sides:
(x + 8)^2 + (y + 1)^2 = (y + 4)^2
x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16
x^2 + 16x + 64 + 1 - 16 = 8y - 2y
6y = x^2 + 16x + 49
y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.
An applicable equation of a vertical parabola in vertex form is:
y-k = a(x-h)^2
Let x=2, y=4, h=-1 and k=-1, where (h,k) is the vertex. Then,
4-(-1) = a(2-[-1])^2, which becomes 5 = a(9). Therefore, a = 5/9, and the
equation of the parabola is
y+1 = (5/9)(x+1)
0.1 mile per min
Step-by-step explanation:
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The Y intercept is (0,275) and the X intercept is (125,0). the intercepts should be the point of when the line hits the axis'
Answer:
- sin(X) = 4/5
- cos(X) = 3/5
- tan(X) = 4/3
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to help you remember the relations between sides and trig functions in a right triangle.
Sin(X) = Opposite/Hypotenuse = 24/30 = 4/5
Cos(X) = Adjacent/Hypotenuse = 18/30 = 3/5
Tan(X) = Opposite/Adjacent = 24/18 = 4/3
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You may be expected to leave the trig ratios in the original unreduced form.
