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.
2x^2 + x + 3=0 has only complex roots.
The determinant is 1-4*2*3 = -23
-23 (or any determinant) is the part under the square root sign, If that determinant is negative, knowing you cannot take the square root of a negative number, we know the answers must be complex.
Ughhh I’m not totally sure I’m sorry I tried looking it up for you
Answer:
B. 39.59
Step-by-step explanation:
So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as 
. So let's plug in known values:
Multiply both sides by x
divide both sides by sin(43)
Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682
simplify the fraction
