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(8/125)^(-2/3)

Denominator of the power expression indicates the degree of the root in this case its the cubic root. Numeriator denotes the degree of power in this case squared. The negative sign means to inverse the base ...
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Answered by Andrew D. • Maths tutor
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When I integrate by parts how do I know which part of the equation is u and v'?

To determine which function is your u value in the by parts equation, you can use the acronym LATE to find the order of precedence for this value. LATE stands for: Logarithmic functions Arithmetric functions...
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Answered by Ben A. • Maths tutor
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Solve (3x +1)/x + (2x-1)/3 = -3, giving x to two decimal places.

(3x+1)/x +(2x-1)/3 = (2x 2 + 8x + 3)/3x by cross multiplying. So equation becomes 2x 2 + 8x + 3 = -9x by multiplying both sides by 3x. Adding 9x to both sides gives 2x 2 + 17x + 3 = 0. Using a calculator, an...
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Answered by Jorge A. • Maths tutor
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A car is moving on an inclined road with friction acting upon it. When it is moving up the road at a speed v the engine is working at power 3P and when it is moving down the road at v the engine is working at a power P. Find the value of P.

Incline is at θ where sin θ = 1/20 and mass of the car is 800kg and v is 12.5 m/s Up the road: Power = Fv F = R + (800g)/20 Power = (R + 40g)*25/2 = 3P …. P = (R + 40g)*25/6 Down the road: Power = Fv F = R –...
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Answered by Jonathan M. • Maths tutor
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Given two functions f and g where f(x)=3x-5 and g(x)=x-2. Find: a) the inverse f^-1(x), b) given g^-1(x)=x+2, find (g^-1 o f)(x), c) given also that (f^-1 o g)(x)=(x+3)/3, solve (f^-1 o g)(x)=(g^-1 o f)(x)

a) For an inverse function- "inputs become outputs" so swap the positions of the input-variable (i.e "x") with the output variable (i.e f(x)) and then rearange. Once rearanged so that f(x...
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Answered by Kendra K. • Maths tutor
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