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A straight line passes through the points (-2, 4) and (1, 10). What is (a) the gradient of the line, (b) the y-intercept of the line and (c) the equation of the line?

(a) Gradient (m) = (y 2 -y 1 )/(x 2 -x 1 ) = (10-4)/(1-(-2)) = 6/3 = 2 (b) General equation of a straight line: y = mx + c (c = y-intercept) For our straight line: y = 2x + c Test points: 4 = 2(-2) + c ---&g...
SB
Answered by Samuel B. • Maths tutor
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Factorise the equation x^2 +5x = 6

On first glance, this looks like it is going to be a quadratic equation, so let’s try and put it in the form ax 2 + bx + c = 0 which we can factorize. If we subtract 6 from each side, we end up with x 2 +5x ...
MJ
Answered by Matthew J. • Maths tutor
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Express cos5x in terms of increasing powers of cosx

De Moivre's theorem: (cos5x + isin5x) = (cosx + isinx) 5 To get cos5x we will need to expand (cosx + isinx) 5 and then take the real parts. Binomial expansion: (cosx + isinx) 5 = (5C0)(cosx) 5 + (5C1)(cosx) ...
CS
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Integrate cos(2x)

The intergral for cosx is sinx, but '2x' must be considered. When differentiating a sinx/cosx function, the '2x' would be differentiated separately and placed in the front (multipling). So when intergating y...
GO
Answered by Gold O. • Maths tutor
18926 Views

The area of a rectangle is 8cm^2. The rectangle is (3x+1) by (2x+5). Find the value of x

Area of a rectangle is width times height (3x+1)(2x+5)= 6x 2 +15x+2x+5 6x 2 +17x+5 Set formula of area equal to known area value. 6x 2 +17x+5= 8 6x 2 +17x-3 = 0 (6x-1)(x+3)=0 (or use quadratic formula) x=-3 ...
CD
Answered by Conrad D. • Maths tutor
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