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Write cosx - 3sinx in the form Rcos(x + a)

Rcos(x + a) = Rcosxcosa - Rsinxsina
By comparing cosx - 3sinx to the new expression, we can see that:
Rsina = 3 and Rcosa = 1
If we square both and add them, we can see R = √(1²

Answered by Odin G. • Maths tutor

9249 Views

Samuel had 3 piles of coins, I, II and III. Altogether there was 72p. Pile II had twice as much as pile I. Pile III had three times as much as pile II. How much money was in Pile III?

First let coins in pile I equal x. Then we the question tells us II has twice pile A so we can now write this as 2x. Finally, we can write pile III as 6x - reason is that III has three times pile II...

Answered by Syed R. • Maths tutor

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A) Differentiate ln(x) b) integrate ln(x)

A) y=ln(x) E^y = x E^y(dy/dx ) = 1 E^ln(x)(dy/dx) = 1 X(dy/dx) = 1 Dy/dx = 1/xb) y = 1 * ln(x) V = ln(x) U= x dv/dx =1/x Du/dx = 1xln(x) - (integral) x * (1/x)xln(x) - (integ...

Answered by Stanley R. • Maths tutor

3241 Views

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) The surface area of a 3 dimensional shape is the sum total of the area of each side of the shape. This cuboid is 3x4x2, and so it has 2 sides with area 3x4 = 12, 2 sides with area 4x2 = 8, and 2 sides ...

Answered by Luke J. • Maths tutor

7194 Views

Factorise fully the following expression: 2a^(2)b + 6ab^(2)

Factorise fully the following expression: 2a²b + 6ab²
First, find the common terms by treating, 2a²b and 6ab²as separate objects.
We see common term...

Answered by Michael W. • Maths tutor

6202 Views