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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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State Newton's 1st Law:

An object will remain at rest or constant velocity if all the forces acting upon it are equal (net force=0N).
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Answered by Sam H. • Physics 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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How many Protons, Neutrons and Electrons are there in an atom of Silicon, Si?

Using a copy of the periodic table, look up the Mass and Atomic numbers of Silicon. Mass number = 28; Atomic number = 14. The Atomic number is equivalent to the number of Protons in an atom, so there are 14 ...
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Answered by Eloise S. • Chemistry tutor
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Given a right-angled triangle with an angle of 35 degrees and an Opposite side of 12cm, calculate the length of the hypotenuse to 3 significant figures.

First, determine which of SOH-CAH-TOA you need to use. As this question involves the Hypotenuse and the Opposite side, use Sine. As such, write out the equation as: sin(35) = 12/x. (Let x represent the Hypot...
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Answered by Eloise S. • Maths tutor
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