Search our library of homework questions

Top answers

All subjects

All levels

Distinguish between a codified and an uncodified constitution.

A codified constitution is a single, written document that underpins the nature and structure of governance within a state. Codifed constitutions will usually outline the powers of different branches of g...

Answered by Joe H. • Government and Politics tutor

8879 Views

A trillion is 10^12. Which of the following is bigger: the three trillionth root of 3 or the two trillionth root of 2? You may assume that if 0 < x < y, then 0 < x^n < y^n for integer values of n greater than or equal to 1.

For this sort of question, the easiest approach is to make an educated guess at the correct answer, and prove that this must be correct by contradiction. As taking the root of something has a large effect...

Answered by Benjamin C. • MAT tutor

1735 Views

Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.

In order to find the equation of the tangent to a curve at a point (x₁, y₁), we use the equation y - y₁ = m(x - x₁), where m is the gradient of the curve at (x<...

Answered by Benjamin C. • Further Mathematics tutor

2940 Views

log8(5) = b. Express log4(10) in terms of b

log₈5=b

using the base change rule

log₈5=log₄5/log₄8

log₄8 can be solved:...

Answered by Beatrice M. • Maths tutor

10600 Views

Let f(x) = x * sin(2x). Find the area beneath the graph of y = f(x), bounded by the x-axis, the y-axis and the line x = π/2.

After short consideration, we see that we must integrate f(x) with respect to x, between 0 and π/2, using integration by parts. Taking the formula for integration by parts, we set u = x and dv/dx = sin(2x...

Answered by Benjamin C. • Maths tutor

5157 Views