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Find the centre and radius of the circle with the equation x^2 + y^2 - 8x - 6y - 20 = 0.

The general equation of a circle takes the form (x - A)^2 + (y - B)^2 = r^2 where (A,B) is the centre of the circle with radius r. Thus, we aim to rearrange the equation in the question to match this form. S...
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Answered by Thomas D. • Maths tutor
8863 Views

Find R and a such that 7*cos(x)+3*sin(x)=Rcos(x-a)

Use the cosine trig identity, cos(a-b)=cos(a)cos(b)+sin(a)sin(b) ,to write Rcos(x-a) as R(cos(x)cos(a)+sin(x)sin(a)).Now we can equate the coefficients of the sines and cosins on either side of the equation ...
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Answered by Darius Y. • Maths tutor
7265 Views

why is the number e important?

When we work with circles, one of the most popular things to pop up is pi. We know that for any circle the circumference divided by the radius gives pi, without failure always. Pi is a number that’s been fou...
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Answered by Sam V. • Maths tutor
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What is an optical isomer?

Optical isomers are a form of stereoisomers which are chemical species with the same structural formula, but have a different arrangement of atoms in 3-dimensional space. Optical isomers are characterised by...
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Answered by Thomas D. • Chemistry tutor
2848 Views

How do you write a thoroughly coherent essay?

A logical and comprehensible structure is essential to every essay if it is to be coherent enough to hit the top bands. Highlighting the key words in the chosen/given question and thoroughly ordering your ar...
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