Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -5.

Here, we are required to find the point, P where the lines:

intersects the plane x + y - z = -5.

The point, P where the lines intersects the plane is given by;

he point, P where the lines intersects the plane is given by;P (0, -2, 3)

Therefore, to find this point, we have to substitute for x, y and z in the equation of the plane.

Therefore, we have;

To get the coordinates of the point P where the lines intersect the plane; we can then find x, y and z by substituting t into each of their equations.

Therefore;

Therefore, the point, P where the lines intersects the plane is given by;

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Replace x, y, and z in the plane's equation with their appropriate parametric equations, then solve for t, then evaluate x, y, and z at this t to find the point P.

So the point P is (0, -2, -3).

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

351°f

step-by-step explanation: