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nikdorinn [45]
3 years ago
6

in the xy-plane, the line x + y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0
When a line and a curve are tangent to each other, they are joined together by 1 point (x,y). So, you equate both equations either in terms of x or y. For this problem, let's equate in terms of y.

y = k - x
y = x² + 3x + 1

k - x = x² + 3x + 1
k = x² + 3x + x + 1
k = x² + 4x + 1

This would be the value of k. Since we are not given the common point, it can only be expressed in terms of x or y.
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