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Simplify the following expression: ( (x^5) / (x^2) ) ^ 4

For this question it is key to remember the indices laws. The ones you need to recall for this question are: x a / x b = x a - b , and (x a ) b = x a * b . Using these laws, we can simplify the expression in...
SJ
Answered by Shafaan J. • Maths tutor
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Express x^2 + 10x – 3 in the form (x + p)^2 + q

= We start by halfing the 10 and putting x + 5 in a bracket = (x + 5)^2 = Opening these brackets give us x^2 + 10x + 25 = To make the 25 the same as - 3 we have to minus 28 = Therefore the answer is = (x + 5...
HP
Answered by Haasan P. • Maths tutor
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find the gradient of the line y=2x^2-12x+16 at the coordinates (5,6)

dy/dx = 4x - 12 x-coordinate= 5 so sub in 20-12 = 8
Answered by • Maths tutor
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Find dy/dx, given that y=(3x+1)/(2x+1)

Since the equation for y is given in the format y=u/v, the use of the quotient rule is the easiest way to find the differential of this equation. The quotient rule states, (vu'-uv')/v^2 is equal to the diffe...
Answered by • Maths tutor
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Imagine a sector of a circle called AOB. With center O and radius rcm. The angle AOB is R in radians. The area of the sector is 11cm². Given the perimeter of the sector is 4 time the length of the arc AB. Find r.

11 = 1/2 r 2 RAB = x = rRr + r + x = 4x2r = 3rRR = 2/3r²R = 22r² = 33r = √33
AS
Answered by Alice S. • Maths tutor
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