Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 + y2 = 16 and the surface z = xy

A vector function r(t) is represented as:

The vector function r(t) that represents the intersection of the two surfaces is  

Given

Express 16 as in

Multiply by 1

In trigonometry

So, we substitute for 1

Remove bracket

Apply law of indices

By comparison:

and

Take positive square roots

and

Recall that:

So, we have:

Substitute the values of x, y and z.

Hence, the vector function r(t) is:

Read more about vector functions at:

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step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,