Once refrigerated, it will retain its freshness for three to four days before becoming stale. If you want to extend its shelf life, packaged bread will stay fresh for at least three months in the freezer. If you do see mold, however, throw the bread out.

8 0

2 years ago

Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?

Lubov Fominskaja [6]

Answer:

yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

For the first parabola, the point of intersection is ...

y^2 = 4(-y-1)

y^2 +4y +4 = 0

(y+2)^2 = 0

y = -2 . . . . . . . . one solution only

x = -(-2)-1 = 1

The point of intersection is (1, -2).

For the second parabola, the equation is the same, but with x and y interchanged:

x^2 = 4(-x-1)

(x +2)^2 = 0

x = -2, y = 1 . . . . . one point of intersection only

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If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

7 0

2 years ago