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The equation 5x sqaured + px + q , where p and q are constants, has roots α and α + 4. (a) Show that p squared = 20q +400.

a+a+4 = -p/5a+2 = -p/10(a+2)sqaured = q/5 +4p sqaured/100 = q/5 +4p sqaured = 100(q/5 +4)implies p squared = 20q+400
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Answered by Ahmed T. • Maths tutor
6445 Views

Differentiate y = (x^2 + 1)^1/3

Use the chain rule to do this. First set u= x^2 + 1. We chose u to be this because u 1/3 is much simpler to differentiate. Then find du/dx = 2x. Now find dy/du = 1/3 * u -2/3 = 1/3 * (x 2 +1) -2/3 . Now by t...
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Answered by Will W. • Maths tutor
3808 Views

If f(x)=(4x^2)-(8x)+3, find the gradient of y=f(x) at the point (0.5,0)

When you see the question asking you to find the gradient at a point in the curve, the first thing you have to do is differentiate . This is because when we differentiate, we find the equation of the tangent...
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Answered by Girthanaah K. • Maths tutor
7129 Views

You deposit 500 pounds at time t=0. At t=5 years, you have 800 pounds. The amount of money you have in the bank can be modeled as V(t)=A*(1+r)^t, where r is the interest rate. Find A and the interest rate r. After how many years will you have 1200 pounds.

At t=0, you deposit 500 pounds in the bank account: V(0)=500=A. At t=5, that amount of money is now, V(5)=800=500*(1+r)^5 i.e. 1+r = 1.6^(1/5) = 1.0986 (4dp) So the interest rate r is 9.86% (3 s.f.)Let T be ...
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Answered by Georgios A. • Maths tutor
3568 Views

Solve the inequality (9x+5)/12 > (4x+1)/3

(9x+5)/12 > (4x+1)/3**** Multiply up the denominator terms 3 (9x+5) > 12 (4x+1) * As 3 is a factor of 12, divide both sides by 3 9x+5 > 4 (4x +1) * Multiply out RHS 9x +5 > 16x + 4 * Gather like ...
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Answered by Frances M. • Maths tutor
4014 Views