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A spherical balloon of radius r cm has volume Vcm^3 , where V =4/3 * pi * r^3. The balloon is inflated at a constant rate of 10 cm^3 s^-1 . Find the rate of increase of r when r = 8.

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 differentiating V = 4/3...
MA
Answered by Max A. • Maths tutor
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Find the roots of y=x^{2}+2x+2

y=x 2 +2x-3 Can solve using quadratic equation. Using the square method to obtain for the square term and x term (x+1)(x+1) = x 2 +2x+1 Therefore (x+1)(x+1)-4=y To find roots equate to zero: (x+1)(x+1)-4=0 T...
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Answered by Harry S. • Maths tutor
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Simplify i^{4}?

Simplify i 4 ? We know that i = -1 1/2 Therefore i 2 =-1 As i 4 =i 2 xi 2 Then i 4 =-1x-1=1
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Find the intercept between the two equations below?

y = 2x+5 y=x+1 First equate: 2x+5=x+1 Rearrage for x: 2x-x=1-5 Which gives: x=-4
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Answered by Harry S. • Maths tutor
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Describe how ventilation of the lungs occurs.

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 move ...
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Answered by Emily S. • Biology tutor
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