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Prove that the multiple of an even number and an odd number is always even.

2n is even, so (2n+1) is odd ; Multiplying even by odd gives: 2n(2n + 1) ; which is a multiple of 2, thus even * odd = even.
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Answered by Oliver T. • Maths tutor
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A person leaves their flat at 8:00am and travels to work at an average speed of 32 mph. They arrive at work at 9:15am. Calculate the distance they travel to work.

SUVAT equations give s = vt ; v = 32mph ; t = 1h 15mins = 1.25h ; s = 32 * 1.25 = 40 miles
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Answered by Oliver T. • Maths tutor
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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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