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(The full answer produced answer is annotated working out, but since this text box won't let me submit pictures, I'll do my best to transcribe)First, we gather the two fractions by using a common denomina...

If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac<0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^...

This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us...

S: 900 700D: 2 m/sT: 960s
Need to find speed in seconds so convert 16 mins to seconds.
To find average, we must find time for the first part. Using...

Product Rule: dy/dx (uv) = u'v + uv'
Let u = 6x+7 and v = e^x. Using simple disintegartion, u' is 6 and v' is e^x.
Therefore, answer is: 6e^x + (6x +7)e^x