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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

Initially, one might think to use area = 1/2 x base x height, however drawing the triangle immediately shows that this is not possible here. We then think to use the formula for area using two adjacent si...