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We are being asked to find the rate of change of radius, dr/dt. We will need to use the chain rule to do this: dV/dt = dV/dr * dr/dt.

We are given that dV/dt is 10cm^3 per second, and differentiati...

y=x²+2x-3

Can solve using quadratic equation. Using the square method to obtain for the square term and x term (x+1)(x+1) = x²+2x+1

Therefore (x+1)(x+1)-4=y

To f...

Simplify i⁴?

We know that i = -1^1/2

Therefore i²=-1

As i⁴=i²xi² 

Then i⁴=-1x-1=1

y = 2x+5

y=x+1

First equate:       2x+5=x+1

Rearrage for x:    2x-x=1-5

Which gives:       x=-4

Ventilation is the process of moving air in and out of the lungs. This is brought about by pressure changes in the thoracic cavity. During inspiration, the diaphragm contracts causing it to flatten and mo...