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Maths
A Level

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

AT
Answered by Ahmed T. Maths tutor
6174 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 u1/3 is much simpler to differentiate. Then find du/dx = 2x. Now find dy/du = 1/3 * u-2/3 = 1/3 * (...

WW
Answered by Will W. Maths tutor
3507 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,...

GK
Answered by Girthanaah K. Maths tutor
6720 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 ...

GA
Answered by Georgios A. Maths tutor
3322 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 39x+5 > 4

FM
Answered by Frances M. Maths tutor
3754 Views

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