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Express root(125^x)/5^(2x-1) in terms of 5^a where a is an expression in terms of x.

root(125^x) = 125^(x/2) = 5^(3x/2)
5^(3x/2) / 5^(2x-1) = 5^(3x/2 - 2x +1) = 5^(-x/2 + 1)

Answered by Sophie N. • Maths tutor

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Find the value of cot(π/3)

Pi radians is equal to 180 degrees . Radians are a unit of measurement for angles, just like degrees are, and pi is just the number of radians that makes up that angle. 180 divided by 3 is 60 so we get c...

Answered by Stefan D. • Maths tutor

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Explain the basics of projectile motion

If the projectile is released at an angle, it will have 2 components: 1. horizontal component of motion and 2. vertical component Horizontally, the projectile is assumed to travel at a constant speed (ie ...

Answered by Aadam Q. • Maths tutor

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Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.

The unsimplified form of the derivative can be obtained fairly easily with use of the quotient rule. The trick for simplification is to multiply top and bottom by (x+4)^0.5, this allows manipulation of th...

Answered by Seb R. • Maths tutor

2903 Views

Integrate 3x^4-4x^2+3/x

Firstly, integrate each term individually, starting off with the 3x^4. In order to integrate the index on the x term needs to be raised by 1, and the coefficient of the x should be divided by this new val...

Answered by Muhammad R. • Maths tutor

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