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Prove 2^(n+2) + 3^(2n+1) is a multiple of 7 for all positive integers of n by mathematical induction.

Let P(n) be the proposition that 2 n+2 + 3 2n+1 is a multiple of 7 for all positive integers of n. Let n=12 3 + 3 3 = 8 + 27 = 35 = 7(5)This is divisible by 7. Assume n=k2 k+2 + 3 2k+1 = 7m The above equatio...
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Answered by Eashan P. • Maths tutor
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How is an Action Potential transmitted across a synapse?

-An action potential arrives at the presynaptic membrane-Ca 2+ ion channels open-Ca 2+ ions diffues into presynaptic knob-Acetylcholine/ neurotransmitter in vesicles-Vesicles move towards presynaptic membran...
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Answered by Darcie W. • Biology tutor
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A) Draw field lines around a positive point particle. B) How does a faraday cage prevent the people within it recieving a electric shock ?

A) symmetrical straight lines coming out of the particle, with arrows pointing away from the particle. A useful tool in answering these questions is to imagine what would happen if you placed a second positi...
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Answered by Thomas H. • Physics tutor
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What determined allegiance during the British Civil Wars?

It is clear that religious affiliation and religious fears were the principle factors determining allegiance in the British Civil Wars for the people who actively chose to fight, however it is important to r...
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Answered by Phoebe M. • History tutor
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Write x^2+6x+14 in the form of (x+a)^2+b where a and b are constants to be determined.

Completing the square is a method that can be used to solve the quadratic equation x^2+6x+14 in the form of (x+a)^2+b. The way we find a and b is as follows:For constant a , is found by halving the coefficie...
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Answered by Chara D. • Maths tutor
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