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Solve the simultaneous equations x + y = 3 and x^2 + y^2 = 5

Find an expression for y y = 3 - x sub this into the second equation x^2 + (3 - x)^2 = 5 then expand the brackets x^2 + x^2 - 6x + 9 = 5 simplify 2(x^2 - 3x + 2) = 0 factorise 2(x - 2)(x - 1) = 0 so x = 2, 1...
KW
Answered by Kate W. • Maths tutor
16629 Views

y = 2x^3 + 15x^2 + 24x + 10 Find the stationary points on this curve and determine their nature

First differentiate the function to obtain dy/dx = 6x^2 + 30x + 24 Then set this equal to 0 and solve to find the x values of the stationary points 6x^2 + 30x + 24 = 0 6(x^2 + 5x + 4) = 0 6(x +1)(x+4) = 0 th...
KW
Answered by Kate W. • Maths tutor
10600 Views

How do I know when to use the ‘imparfait’ (imperfect) and ‘passé composé’ tenses?

Be assured that this question makes all French learners stop and think sometimes! So I will do my best to explain it in a way that helps me remember when to use which tense. Both of these tenses are used to ...
SF
Answered by Sarah F. • French tutor
3604 Views

Which of these periods was the more successful for the treatment of disease and infection, Ancient Greece or the Medieval World? You must include both periods in your answer.

To successfully answer this question the student needs to describe and evaluate both periods in depth and compare their successes - defined here as the extent to which the period contributed to the advanceme...
CA
Answered by Catrin A. • History tutor
3674 Views

Translate the following passage into Spanish. "I like to go on holiday to Spain. It is always sunny and our favourite hotel has a big swimming pool. Last summer we went to Madrid and I saw a concert. I am going to study Spanish at university."

"Me gusta ir de vacaciones a España. Siempre hace sol y nuestro hotel favorito tiene una gran piscina. El verano pasado fuimos a Madrid y vi un concierto. Voy a estudiar español en la universidad."...
RW
Answered by Robert W. • Spanish tutor
7119 Views