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We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5)
For the second part o...

The equation for a circle is pi x radius x radius. So,first we need to find the radius which is half the diameter, 140 divided by 2 equals 70 cm. As the question asks for the answer as a multiple of pi th...

To solve this question, we have to use substitution. We substitute the line equation,y=x+1, into the circle equation so that we get, x^2 + (x+1-1)^2=18. This reduces to 2x^2 = 18, then dividing both sides...

Using integration by parts by letting u=x and dv/dx=e^-x. this implies that du/dx=1 and v=-e^-xThe By Parts formulae is u.v - integral(v.du/dx) = -xe^-x - in...

This is a relatively complicated mechanics question requiring the student to put aside their initial assumption and work with the actual meaning of average speed. In order to do this the student must find...