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Given that y= x^(-3/2) + (1/2)x^4 + 2, Find: (a) the integral of y (b) the second differential of y

This is a typical question for a Core 1 paper. (a) integral of y = (-2)x^(-1/2) + 0.1x^5 + 2x +C Method: Increase the power of x by +1, divide the term through by the new power. (b) dy/dx = (-3/2)x^(-5/2)...

Answered by • Maths tutor

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Explain how antibiotic resistance can be developed by bacterial populations.

Within the initial population of bacteria, some will have an allele that provides them with resistance to a specific antibiotic which is due to mutations, random spontaneous changes in the base sequence o...

Answered by • Biology tutor

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When conjugating a verb into the past simple, when do you use the -te or -de extension?

The best way to remember when to use -te(n) or -de(n), is with the mnemonic 't kofschip or 't fokschaap. Take the infinitive of the verb you wish to conjugate, and remove the -en at the ...

Answered by Ellen S. • Dutch tutor

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Why does a small puddle of water evaporate at room temperature, even though the temperature is way below the boiling point of water?

To understand why the water evaporates, we need to know what we mean when we say something has a certain temperature. Temperature is proportional to the average kinetic energy of the microscopic molecules...

Answered by Ellen S. • Physics tutor

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According to Newton's third law, every action has an equal and opposite reaction. Why then does a box move when I push it? Shouldn't the two opposing forces cancel out to a zero net force?

The key to this question is realising that the action and corresponding reaction refer to forces that act on different objects. When I push the box, I exert a force on the box. As a result of thi...

Answered by Ellen S. • Physics tutor

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