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Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2

4 sin(x) – 8 cos(x)= Rsin(x-a) here use double angle formula 4 sin(x) – 8 cos(x)= Rsin(x)cos(a)-Rcos(x)sin(a) Rearrange so in same format as LHS 4 sin(x) – 8 cos(x)= Rcos(a)sin(x)-Rsin(a)cos(x) Equate terms ...
SE
Answered by Simon E. • Maths tutor
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Point A (-3,5) and point B (1,-15) are to be connected to form a straight line, fing the equation of the line in the form y=mx+c?

First identify your x1, y1 and x2,y2. It is helpful to write this above the two points A and B. To find the gradient the following equation can be used (I will show equation on board),as u can see the X1, Y1...
CW
Answered by Charuka W. • Maths tutor
6394 Views

What is the difference between limited and unlimited liability?

Limited liability occurs in limited companies such as a private limited company (ltd) or a public limited company (plc) as the entities have their own legal identity which is separate from the owners. This m...
SS
49855 Views

The line L has equation y = 5 - 2x. (a) Show that the point P (3, -1) lies on L. (b) Find an equation of the line perpendicular to L that passes through P.

(a) To confirm that point P lies on L, we must substitute x = 3 into the equation and see if we get y = -1. y = 5 - 2(3) = -1, therefore P lies on the line L (b) The gradient of the perpendicular line is -1/...
KS
Answered by Kitty S. • Maths tutor
14915 Views

A gardener uses this formula to work out how much he charges to make a lawn. C = 7(14 +A)/ 3. C is the charge in £. A is the area in m2. He makes a rectangular lawn measuring 12.5 m by 17.6 m. How much does he charge?

Area of lawn = 12.5 x 17.6 = 220 m2 Substituting into the formula given the cost if found, C = 7(14 + 220)/3 = £546
KS
Answered by Kitty S. • Maths tutor
5695 Views