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Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H2+R2)1/2 V = (1/3)πR2(H2+R2)1/2

dV/dt = -k

dH/dt = dH/dV × dv/dt

dV/dH = (1/3)πR2H(H...

CE
Answered by Callum E. Maths tutor
3712 Views

Integrate the following function: f(x) = ln(x)

∫ln(x)dx = xln(x) - ∫x/x dx = xln(x) - x + C

CE
Answered by Callum E. Maths tutor
3516 Views

Why is the differential of a constant zero?

Any constant (say k) can be rewritten as kx0 since x0=1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest...

JC
Answered by Jawad C. Maths tutor
3756 Views

Why is it that an action potential only travels in one direction?

(draw/picture of nerve cell with its ion channels and after learning about the action potential trace and how it's derived) After each action potential, see on the trace there's a refractory period where ...

JL
Answered by Jasmine L. Biology tutor
15277 Views

How do you find the maximum/minimum value of an equation?

When finding the maximum or minimum of an equation, make sure you rearrange an equation to make y the subject of the equation i.e. y=_________. You can then differentiate with respect to x and then set th...

JC
Answered by Jawad C. Maths tutor
6787 Views

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