Find the equation

Consider the curves in the first quadrant that have equations

http://webwork.math.uwyo.edu/webwork...fafcd12701.png

where http://webwork.math.uwyo.edu/webwork...0fcdd79cd1.png is a positive constant.
Different values of http://webwork.math.uwyo.edu/webwork...0fcdd79cd1.png give different curves. The curves form a family, http://webwork.math.uwyo.edu/webwork...9026c8b941.png.
Let http://webwork.math.uwyo.edu/webwork...fc7b1b7101.png Let http://webwork.math.uwyo.edu/webwork...c23ba91971.png be the member of the family http://webwork.math.uwyo.edu/webwork...9026c8b941.png that goes through P.
A. Let http://webwork.math.uwyo.edu/webwork...30fafef401.png be the equation of http://webwork.math.uwyo.edu/webwork...c23ba91971.png. Find http://webwork.math.uwyo.edu/webwork...910e13a9c1.png.

Well? You are told that the equation is of the form y= Aexp(4x) and that its graph goes through (2, 2). y= 2= A exp(4(2))= A exp(8). what is A?

ln(2)/8???

Quote:

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Originally Posted by amiv4

ln(2)/8???

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so,

Find the slope at http://webwork.math.uwyo.edu/webwork...8d5ec3a3b1.png of the tangent to http://webwork.math.uwyo.edu/webwork...c23ba91971.png.
slope =

C. A curve http://webwork.math.uwyo.edu/webwork...33f7cadea1.png is perpendicular to http://webwork.math.uwyo.edu/webwork...c23ba91971.png at http://webwork.math.uwyo.edu/webwork...8d5ec3a3b1.png. What is the slope of the tangent to http://webwork.math.uwyo.edu/webwork...33f7cadea1.png at the point http://webwork.math.uwyo.edu/webwork...8d5ec3a3b1.png? slope =

D. Give a formula http://webwork.math.uwyo.edu/webwork...0b998af321.png for the slope at http://webwork.math.uwyo.edu/webwork...daed0b5771.png of the member of http://webwork.math.uwyo.edu/webwork...9026c8b941.png that goes through http://webwork.math.uwyo.edu/webwork...daed0b5771.png. The formula should not involve http://webwork.math.uwyo.edu/webwork...0fcdd79cd1.png or http://webwork.math.uwyo.edu/webwork...dd0b8b8e91.png.
http://webwork.math.uwyo.edu/webwork...425ac2d071.png

E. A curve which at each of its points is perpendicular to the member of the family http://webwork.math.uwyo.edu/webwork...9026c8b941.png that goes through that point is called an orthogonal trajectory to http://webwork.math.uwyo.edu/webwork...9026c8b941.png. Each orthogonal trajectory to http://webwork.math.uwyo.edu/webwork...9026c8b941.png satisfies the differential equation

http://webwork.math.uwyo.edu/webwork...531eb4ed41.png

where http://webwork.math.uwyo.edu/webwork...0b998af321.png is the answer to part D.
Find a function http://webwork.math.uwyo.edu/webwork...771c8eada1.png such that http://webwork.math.uwyo.edu/webwork...ba9b20ac81.png is the equation of the orthogonal trajectory to http://webwork.math.uwyo.edu/webwork...9026c8b941.png that passes through the point http://webwork.math.uwyo.edu/webwork...8d5ec3a3b1.png.
http://webwork.math.uwyo.edu/webwork...fc8412fef1.png