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The equation x^2+ kx + 8 = k has no real solutions for x. Show that k satisfies k^2 + 4k < 32.

If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac&lt;0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^2 +...
TD
Answered by Tutor91955 D. • Maths tutor
15952 Views

What techniques can be used to improve my scores on the abstract reasoning section of the UKCAT?

The Abstract Reasoning section of the UKCAT tests the ability to interpret patterns amongst abstract shapes with irrelevant and distracting information. The section is highly time pressured so critical evalu...
AS
Answered by Adam S. • UCAT tutor
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Explain what happens to a crystal of iodine when it is heated (5marks)

A crystal of iodine sublimes from its solid state to its gaseous state without turning into a liquid. Iodine forms a molecular covalent crystal. This means that there are strong covalent bonds within the mol...
MI
Answered by Meghna I. • Chemistry tutor
25307 Views

Sodium chloride and sodium metal can both conduct electricity under differing conditions. Give the conditions required for each to conduct electricity and explain how each conducts electricity.

Sodium chloride will conduct electricity only when it is in a liquid state or in solution, this is because the ions are free to move in this state, allowing them to carry charge and conduct electricity. Sodi...
TJ
Answered by Tanmayi J. • Chemistry tutor
39689 Views

Find the equation of the tangent to the curve y^3 - 4x^2 - 3xy + 25 = 0 at the point (2,-3).

This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us 3y...
TJ
Answered by Tanmayi J. • Maths tutor
5115 Views