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Express √75 in the form of n√3 , where n is an integer. Using this information, solve the following equation: x√48 = √75 + 3√3 (4 marks)

√75 = 5√3, therefore x√48 = √75 + 3√3 x√48 = 5√3 + 3√3 x(√16 x √3) = 5√3 + 3√3 4x√3 = 5√3 + 3√3 4x√3 = (5 + 3)√3 4x√3 = 8√3 x√3 = 2√3 x = 2
AT
Answered by Alex T. • Maths tutor
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Differentiate and factorise y = x^2(3x + 1)

Product rule: dy/dx = uv' + u'v dy/dx = 2x(3x + 1) + x^2(3) dy/dx = 2x(3x + 1) +3x^2 dy/dx = 6x^2 + 2x + 3x^2 dy/dx = 9x^2 + 2x dy/dx = x(9x + 2)
EJ
Answered by Ella J. • Maths tutor
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How do you prove two straight lines intersect?

There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r 1 = 3 i + 4 j - 5 k + t ( i - 2 j + 2 k ) => r 1 = (3 + t) i + (4 – 2t)...
NM
Answered by Nicholas M. • Maths tutor
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Solve the simultaneous equations: 6x +2y = 2 and 12x - 3y = 18

6x + 2y = 2 and 12x -3y =18 Start by multiplying the first equation by two in order to balance both equations to have equal numbers of x 12x + 4y = 4 and 12x - 3y = 18 Rearrange both equations so that the x ...
JH
Answered by Jack H. • Maths tutor
3897 Views

Given that y = x^4 tan(2x), find dy/dx

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4 du...
DB
Answered by Douglas B. • Maths tutor
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