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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) = (y₂-y₁)/(x₂-x₁) = (10-4)/(1-(-2)) = 6/3 = 2

(b) General equation of a straight line: y = mx + c (c = y-intercept)

For our st...

Answered by Samuel B. • Maths tutor

13022 Views

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 ax² + bx + c = 0 which we can factorize. If we subtract 6 from each side, we end up ...

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

Answered by Chris S. • Further Mathematics tutor

30499 Views

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 w...

Answered by Gold O. • Maths tutor

17705 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)= 6x²+15x+2x+5 6x²+17x+5 Set formula of area equal to known area value. 6x²+17x+5= 8 6x²+17x-3 ...

Answered by Conrad D. • Maths tutor

5715 Views