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simplify c^4 x c^3

when multiplying indices you need to add the powers (only if the base number is the same -> need to ensure they are denoted with the same letter) 4 + 3 = 7 therefore the answer is c^7
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Answered by Alice V. • Maths tutor
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simplify (3x^2 - x - 2) / (x^2 - 1)

factorise the top fraction: 3x^2 - x - 2 = (3x + 2)(x - 1) factorise the bottom fraction: x^2 -1 = (x + 1)(x - 1) cancel out the (x - 1) and the final result is (3x + 2) / (x + 1)
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Answered by Alice V. • Maths tutor
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Two points P(–4, –1) and Q(–8, 5) are joined by a straight line. Work out the coordinates of the midpoint of the line PQ.

First, you must remember what the midpoint formula is for a line with two points. M= ((x 1​ +x 2​ )/2 ​,(y 1 ​+y 2​​ )/2) Then apply it to this question. M= ((-4+-8)/2 , (-1+5)/2) Simplify and solve. M= ((-1...
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Answered by Ellen T. • Maths tutor
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Find the area under the curve y = sin(2x) + cos(x) between 0 and pi/2

to find the area integrate the function between 0 and pi/2: indefinite integral of y = -1/2 cos(2x) + sin(x) + c ignore c and input boundary conditions: [-1/2 cos(pi) + sin(pi/2)] - [-1/2 cos(0) + sin(0)] = ...
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Answered by Harry D. • Maths tutor
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Given that y = 4x^5 - 5/(x^2) , x=/=0 , find a)dy/dx b)indefinite integral of y

rewrite as y = 4x^5 - 5x^(-2) dy/dx = 20x^4 + 10x^(-3) integral of y = 4x^6 / 6 + 5x^(-1) / 1 + c simplify: 2/3 x^6 + 5/x
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Answered by Harry D. • Maths tutor
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