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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 of D...
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 end. What you have le...
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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 in...
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Answered by Ellen S. • Physics tutor
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A ball with radius 10cm is filled with an ideal gas at pressure 2*(10)^5Pa and temperature 300K. The volume of the gas is changed at constant pressure so that the radius of the ball is reduced with 1cm. Find the amount of gas and the new temperature

In a question like this, you will be given that the molar gas constant is R = 8.31JK -1 mol -1 . However, committing this to memory will be helpful. We should use the ideal gas law: PV = nRT but the volume o...
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Answered by Ivan G. • Physics tutor
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