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Fully factorise and simplify (x^2 +7x + 10) / (x^2 - 25)

Simplify the numerator (top) by finding the pair of numbers which multiply together to give the C term of the quadratic, and add to give the B term. This gives 2 and 5 so the equation becomes (x+2)(x+5) /...

Answered by Nikolai P. • Maths tutor

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We are given y=(x^2)+3x-5. Find the derivative of y in terms of x.

From the question we have, y=x²+3x-5
The rule of differentiation, is that you take the power on the x and bring it to the front, leaving the power-1 behind. In other words if you have x

Answered by Maya B. • Maths tutor

5522 Views

A house is bought for £150,000 at the start of 2005. For 3 years it loses 10% of its original value per year. After this time it loses 10% per year. What was its value at the end of 2011/start of 2012?

Original value = 150,000 10% original value =15,000 After 3 years year is 2008, house value = 150,000 - 3*(15,000) = 105,000Until start of 2012 from start of 2008, so 4 years of compound intrest. New v...

Answered by Henry F. • Maths tutor

2559 Views

If a student wishes to have a ratio of 2:7 red pens to yellow pens in their pencil case: a) if they have 50 pens total what is the maximum amount they can carry with them b) if they have 18 red and 31 yellow what is the maximum amount they can carry

a) 50 pens total. 2 + 7 = 9. Number of pens is done in 9s. 50/9 = 5r5, so multiple of 5. Then 25 + 75 pens. 10 red and 35 yellow, 45 pens
b) 18 red / 2 = [9]r0 31 yellow ...

Answered by Henry F. • Maths tutor

2382 Views

Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt Integrate both sides: ln[2/(1+2x)] = -8e^(-2t) + c input x = 1/2, t = 0: ln(2/2) = -8*(1) + c ln 1 = 0, so c = 8ln[2/1+2x] = 8[1-e^(-2t)]

Answered by Henry F. • Maths tutor

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