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Differentiate: f(x)=2(sin(2x))^2 with respect to x, and evaluate as a single trigonometric function.

f(x) = 2sin 2 (2x)Therefore, using the chain rule: f'(x)=2 x 2cos(2x) x 2sin(2x)(The 2 at the front arises from the constant 2, at the start of f(x), the 2cos(2x) comes from differentiating sin 2 (2x), then ...
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Answered by Sam H. • Maths tutor
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If photons of wavelength 0.1nm are incident on a 2m x 2m Solar Panel at a rate of 2.51x10^15s^-1, calculate the intensity, I, of the photons on the Solar Panel.

If wavelength = 0.1nm, we know (as E=hc/λ ), the energy provided by each photon, E= 1.99x10 15 J .Therefore, if they hit the panel at a rate of 2.51x10 15 s -1 , we know Power = Energy x Rate, =4.99WIntensit...
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Answered by Sam H. • Physics tutor
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Describe what happens when an action potential reaches an axon terminal.

When an action potential reaches an axon terminal, the depolarisation from causes voltage-gated calcium ion channels in the plasma membrane of the synaptic knob to open. As there is a much higher concentrati...
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Answered by Sian J. • Biology tutor
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solve 3sinh^2(2x) + 11sinh(2x) = 4 for x, giving your answer(s) in terms of the natural log.

3sinh^2(2x) + 11sinh(2x) - 4 = 0 --> (3sinh(2x) - 1)(sinh(2x) + 4) = 0 --> sinh(2x) = 1/3, sinh(2x) = -4(e^(2x) - e^(-2x))/2 = 1/3 --> e^(4x) -(2/3)e^(2x) - 1 = 0 --> e^(2x) = 1/3 + 2sqrt(5)/3 th...
WM
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Compare how an author of a text you have studied presents ideas about romantic commitment

For Gatsby, his love for Daisy remains present throughout the five years apart, as he treats his romantic affection towards her as reminiscent of a religious commitment. In pursuing Daisy, Gatsby committed h...
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