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The Volume of a tin of radius r cm is given by V=pi*(40r-r^2-r^3). Find the positive value of r for which dV/dr=0 and find the value of V for this r.

Firstly differentiate the function V with respect to x (dV/dx)=pi*(40-2r-3r^2). Set dV/dr =0 and solve to find r. Divide both sides by pi and divide both side by -1 so that the r^2 term is positive (I person...
CK
Answered by Chorley K. • Maths tutor
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how do i sketch the graph of y=ln(|x|) ?

To sketch any modulus function, we begin with the sketch of the function itself, y=ln(x). Notice that the question asks for the graph of y=ln(|x|) and not y=|ln(x)|, this is an important distinction.recall t...
DO
Answered by Dáire O. • Maths tutor
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How do I differentiate: (3x + 7)^2?

We can see that (3x + 7) 2 is a 'composite function'. We can rewrite this as g(f(x)), where f(x) = 3x + 7 and g(x) = x 2 . As you will have learnt, you will need to use the chain rule for this type of differ...
LK
Answered by Lloyd K. • Maths tutor
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Prove that n is a prime number greater than 5 then n^4 has final digit 1

Last digit of n determines last digit of n^4. All even numbers divide by 2, so are not prime. Any number ending in 5 is a multiple of 5 so is not prime. Primes > 5 end in 1, 3, 7 or 9. If n ends in 1, 1^4...
AP
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how to turn a fraction in the form of (x + a)/(x + b)^2 into partial fractions?

Many students at first will incorrectly separate the fraction into two fractions in the form of A/(x + b) + B/(x + b). If we then multiplied the two back together we will find that it does not equate to the ...
IC
Answered by Isla C. • Maths tutor
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