Eric works for salary of $3,500 per month. He has federal income withheld at the rate of 15%, Social Security tax at the rate of
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Patrick has a total of 600 meters skein of yarn.
He used 248.9 meters of yarn to make a hat.
Now, If he has used 248.9 meters of yarn, we need to find how much yarn has he left.
We need to subtract the amount of yarn used from the total length. That is, 248.9 from 600.
So, now Patrick has left 351.1 meters of yarn.
Patrick needs to make a scarf that needs 354.03 meters of yarn but after making a hat he has left with only 351.1 meters of yarn. Therefore, Patrick does not have enough yarn to make a scarf.
Let . The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or ,
, and
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
