To find the equation of a tangent line, we will need the slope m and a point (xo, yo). Then, we will use any method to find an equation of a line (i.e. point-slope form, y-intercept form). Here, we will have to find the slope and then the point (-e3,f(-e3)).
Finding the...

I use a 5-step process when working with word problems: (1) read and understand the problem; (2) translate the words into mathematical equations and expressions; (3) check and make sure that I understand what I am solving for; (4) solve the problem; and (5) check to see if the answer makes sense...

Step 1: Replace "f(x)" with "y": y=x/5 - 6
Step 2: Switch the "x" and "y": x = y/5 - 6
Step 3: Solve for y:
x = y/5 - 6
5x = y - 30 (multiply the equation...

Put the ellipse into standard form. An ellipse with center (h,k), semi-major axis a, and semi-minor axis b has an equation of the form:
(x - h)²/a² + (y - k)²/b² = 1
If the major axis runs horizontally, and
(x - h)²/b² + (y - k)²/a² = 1
If the major axis runs...