The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 2, −12). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

When , we get the parabola

We can parameterize this parabola by

Then the tangent vector to this parabola is

We get the point (3, 2, -12) when , for which the tangent vector is

Then the line tangent to the parabola at passing through the point (3, 2, -12) has vector equation

which in parametric form is

for .

answer: i'm not sure

step-by-step explanation:

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.