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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 –...
JM
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...
KK
Answered by Kendra K. • Maths tutor
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The normal price of the pair of shoes is £28. In a sale the price is reduced by 35%. What is the new price of the shoes?

If you take £28, what is 10% of 28? 2.8 So what is 30% of 28? You would do 2.8 x 3... which is? 8.4 And what is 5% of 28? You would half 2.8...so 1.4 Now add together 30% of 28 and 5% of 28... this gives 9.8...
SD
Answered by Seyta D. • Maths tutor
4493 Views

Integrate x*ln(x)

Let u = ln(x) and dv/dx = x Thus du/dx = 1/x and v = x 2 /2 Using the formula: Integral of u dv/dx = u v - Integral of v*du/dx This becomes: Integral of x*ln(x) = (x 2 ln(x))/2 - Integral of x/2 Completing t...
AG
Answered by Anindita G. • Maths tutor
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Differentiate the function f(x) = 2x^3 + (cos(x))^2 + e^x

When differentiating a function that is the sum of three different parts we can differentiate each part separately: a) 2x 3 is easy to differentiate. We remember the rule d/dx[ax b ] = abx b-1 . So 2x 3 --&g...
SP
Answered by Seth P. • Maths tutor
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