A costume designer bought 1.4 kg of sequince. She used 250 grams to make a crown and 400 grams to make a cape. How many grams of
2 answers:
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The slope of the tangent line to the curve at (8, 2) is given by the derivative at that point. By the chain rule,
Differentiate the given parametric equations with respect to :
Then
We have and
when
, so the slope at the given point is
.
The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation
Alternatively, we can eliminate the parameter and express explicitly in terms of
:
Then the slope of the tangent line is
At , the slope is again
, so the normal has slope +4, and so on.