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A is a function of P . It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P . When P = 24 , A = 36 and when P = 18 , A = 9. Express A in terms of P .

Let A = aP + bP2 , where a and b are constants. Sub. P = 24 , A = 36 , 24a + 576b = 36 2a + 48b = 3 ………… (1) Sub. P = 18 , A = 9 , 18a + 324b = 9 2a + 36b = 1 ………… (2) Solving (1) and (2) a=-5/2 b=1/6 ∴A=-5/...
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Answered by Chun Yin L. • Maths tutor
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Show that n^2 -n - 90 = 0

This is the full question: There are n sweets in a bag. 6 sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet out of the bag at random. She eats the sweet and then takes another at ran...
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Answered by Dylan N. • Maths tutor
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Solve the simultaneous equation: 6x+y = 27 3x-2y = 6

To work out simultaneous equations, the aim is to remove one letter from the equations, i.e. Remove the y's so you have only x's and numbers (or vice versa). One way to do this is to get the coefficient in f...
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Answered by Emily B. • Maths tutor
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Solve the simultaneous equations: 4x + y = 25, x - 3y = 16

We need to have either the same number of x's or the same number of y's in each equation so that we can add or subtract them to be left with just x or just y. We can do this by multiplying the second equatio...
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Answered by Lydia H. • Maths tutor
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What is the derivative of ln(x)?

First let y=ln(x). Recall that the exponential function, e x , is defined as the inverse of the logarithmic function, ln(x). To make x the subject of the formula, use the inverse function exp. This gives tha...
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Answered by Benjamin G. • Maths tutor
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