Search our library of Maths questions

Top answers

Maths

All levels

y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which dy/dx < 0

a) We need to differentiate this equation using the quotient rule (Given that it is a fraction with an x term on both the top and bottom of the fraction). We assign the numerator and denominator as follow...

Answered by James F. • Maths tutor

6471 Views

How do I calculate a percentage increase? For example; there are 15 fish in a fish tank, after a year they have bred and now there are 20 fish in the tank. By what % has the number of fish increased?

Original value = 15 New Value = 20 Difference = New value - original value 20 - 15 = 5
(Difference / original) x 100(5/15) x 100 = 33.3%

Answered by Seyi A. • Maths tutor

2352 Views

Circle with centre C, and points A,B,D and E on the circumference of the circle. BD is the diameter of the circle. Angle CDA is 18 deg and angle AED is 31 deg. Find angle EDA.

Circle theorem: angle in a semi-circle is a right angle.Therefore angle BAE = 90 + 31 = 121 degrees ABDE is a cyclic quadrilateral and:Circle theorem: Opposite angles in a cyclic quadrilateral sum to 180 ...

Answered by Jasmin H. • Maths tutor

4908 Views

A curve has parametric equations: x=(t-1)^3 and y= 3t - 8/(t^2). Find dy/dx in terms of t. Then find the equation of the normal at the point on the curve where t=2.

dx/dt = 3(t-1)²dy/dt = 3 + 16t^-3dy/dx=(dy/dt)(dt/dx) dy/dx = 3 + 16t^-3/ 3(t-1)²
At t=2 dy/dx= (3 + 16/8) / 3 = 5/3 Gradient of the normal = -3/5with t=2 y...

Answered by Jasmin H. • Maths tutor

3099 Views

How can functions be transformed?

A function, y = f(x), with y on the vertical axis and x on the horizontal axis, can be transformed by 3 different ways: It can be stretched (or shrunk)If y = f(ax), the function is stretc...

Answered by Jack M. • Maths tutor

2633 Views