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Math

What is the cosine rule and when can it be used?

Cosine Rule is used:  When the length of all 3 sides of a triangle is given. OR When 2 sides and an included angle is given. (C is an included angle of lin...

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Show that the derivative of ln(x) = 1/x

Derivative of ln (x) =  1/xGiven (d(ex)/dx=exeln(x)=x using implicit differentiation:y = ln (x)eln(x)=x ey = eln(x)=x,y=ln (x) Differen...

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Solve the equation log(1-x) - log(x) = 1 where log() is the logarithmic function, base 10.

log (1 - x) - log (x) = 1 In this question, quotient rule is used. log (m/n) = log (m) - log (n) Let 1 - x = m, x = n: log (m) - log (n) =...

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Write 36 as a product of prime factors. Give your answer in index form.

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number...

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Express 56 as the product of the its prime factors.

In order to find the prime factors, whose product equals 56, we need to break down 56 into its basic components. Always begin with dividing the number by a prim...

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How do I differentiate sin^2(x)?

In order to understand the differentiation of this function, it is advised to use the Chain Rule. Why Chain Rule? Because Chain Rule allows you to break down th...

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How to solve simultaneous equations with two unknowns?

The two main methods that you can solve simultaneous equations with two unknowns are:● Algebraically   ○ Substitution Method   ○ Elimination...

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a)Work out the total surface area of this cuboid (3cm x 4cm x 2cm). b) The cuboid has density 7g/cm^3, what is the mass of the cuboid?

 a) As shown in the diagram above, unlike a cube which has all equal sides, a cuboid can have varying lengths for the height, width and length.In order to...

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A,B,C and D are points on a circle. ABCD is a square of side 7 cm. Work out the total area of the shaded regions. Give your answer correct to the nearest whole number.

BD= diameter of the circle As shown in the diagram and the question, the square is inscribed inside the circle and we are supposed to find the area of th...

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How to convert a recurring decimal into fraction

Firstly, we need to define what a recurring decimal and a fraction are. A fraction is an expression in which a number is being divided by another number. T...

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