The paraboloid z = 3 − x − x2 − 2y2 intersects the plane x = 1 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (1, 3, −17). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.

the required parametric equation is:

x = 1

y = t + 3

z = -12t - 17

Step-by-step explanation:

From the given information:

We are to express x,y, and z in terms of t.

The purpose of this question is to find the parametric equations in terms of t.

Given that the tangent line related to the parabola is the point (1,3, -17)

Provided that the paraboloid z = 3 - x - x² - 2y² intersect the plane x = 1 in a paraboloid; then:

z = 3 - 1 - (1)² - 2y²

z = 1 - 2y²

Suppose y = t, then the parametrization is given by:

(x (t), y(t), z(t) ) = (1, t, 1 - 2t²)

(x' (t), y'(t), z'(t) ) = (0,1, -4t)

At the point (x,y,z) = (1,3, -17)

For t (=y) = 3

Hence, (x'(3),y'(3),z'(3)) = (0,1, -12)

Therefore, the equation of the tangent line can be expressed as:

x - 1 = 0, y -3 = t, z + 17 = -12t

x = 1, y = t + 3 , z = -12t - 17

Thus, the required parametric equation is:

x = 1

y = t + 3

z = -12t - 17

need points to ask question

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

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to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.