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How would I write (1+4(root)7)/(5+2(root)7) in the form m + n(root)7, where m and n are integers?

We know that any value divided by itself is equal to 1, therefore we can multiply the value in the question by (5-2(root)7)/(5-2(root)7) and the value would not change. We are only changing the values format...
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Answered by Alexander D. • Maths tutor
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Solve the following pair of simultaneous equations: 2x - y = 7 and 4x + y = 23

2x - y = 74x + y = 23In this pair of simultaneous equations, we have two unknowns. We can solve them simultaneously using substitution or elimination, but I will go through the elimination method. I wish to ...
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Answered by Lauren R. • Maths tutor
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Differentiate cos(2x^3)/3x

Using quotient rule y = u/v - dy/dx = (v.du/dx - u.dv/dx)/v 2 .u = cos(2x 3 ) , a = 2x 3 . du/da = -sin(a), da/dx = 6x 2 . From chain rule, we know that du/dx = du/da . da/dx, so du/dx = -6x 2 sin(2x 3 ). We...
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Answered by Charlie W. • Maths tutor
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Differentiate x^2 ln(3x) with respect to x

This question requires the use of differentiation by product rule. First differentiate the first term, whilst keeping the second term the same, i.e. we get 2xln(3x). Secondly we keep the first term the same,...
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Answered by Ricky F. • Maths tutor
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The line y = (a^2)x and the curve y = x(b − x)^2, where 0<a<b , intersect at the origin O and at points P and Q. Find the coordinates of P and Q, where P<Q, and sketch the line and the curve on the same axes. Find the tangent at the point P.

Firstly, for the points of intersection we need to equate the two expressions for y. Since we know that they intersect at the origin, we can immediately cancel the x values and then solve the quadratic for t...
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Answered by Josh B. • Maths tutor
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