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differentiate y = 4x^3(12e^-4x) with respect to x

y = 4x 3 e -4x u = 4x 3 v = e -4x du/dx = 12x 2 dv/dx = -4e -4x using the product rule; vdu +udv vdu + udv = 12x 2 e -4x - 16x 3 e -4x
LM
Answered by Lewis M. • Maths tutor
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What is the 'Nth-term rule' in linear (arithmetic) sequences and how is it used?

In any sequence, the position of a term (1st, 2nd, 3rd etc.) is represented by the letter ‘n’. In linear sequences only, the ‘nth-term rule’ gives the value of any term in that sequence at position ‘n’. It i...
EI
Answered by Edmund I. • Maths tutor
47818 Views

My common feedback is that I need to write my essays in a more confident tone and build a more convincing argument. How can I do this?

Here as an example of how to make a sentence sound more confident: “I think this quote from Shakespeare’s ‘Hamlet’ is important because it shows us what virginity meant in Renaissance England. This suggests ...
RT
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Expand and simplify 3(m + 4) – 2(4m + 1)

The first thing that we are going to do to tackle this problem is to expand the bracket on the left-hand side (3(m+4)). To do this you have to multiply each of the terms inside the bracket with the 3 that is...
RR
Answered by Rahee R. • Maths tutor
4842 Views

The energy transferred from the water in the kettle to its surroundings in 2 hours is 46 200 J. The mass of water in the kettle is 0.50 kg. The specific heat capacity of water is 4200 J/kg °C. What is its temperature after 2 hours?

The water loses 4200 J/kg °C * 0.5 kg = 2100 J/°C As it's lost 46,200 J in total (regardless of the time it took for this to happen), it must have reduced in temperature by 46,200 J / 2100 J/°C = 22°C. Assum...
DB
Answered by Dewi B. • Physics tutor
27292 Views