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Solve the simultaneous equations, x^2+y^2=41, and y=2x-3

STEP 1) First, substitute 2x-3 into the quadratic equation, replacing y, which works out as x 2 +(2x-3) 2 =41 STEP 2) Now, expand the bracket, (2x-3) 2 , firstly by writing it in an easier way, (2x-3)(2x-3),...
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Answered by Hannah N. • Maths tutor
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The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.

For the line and the curve to intersect we need the for the following system of equations to have a solution. y = 3x AND y = x 2 - a The solution of the system of equations is found by solving x^2 - 3x - a =...
HK
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A point A lies on the line y = 2x^2 - 8x + 2. A has y-coordinate (-4). Find all possible values for the x-coordinate of A.

The point A = (x', y') lies on the line y = 2x 2 - 8x +2 . And we are given that y' = -4 .Therefore we have that -4 = 2x 2 - 8x +2 , which simplifies to x 2 - 4x + 3 = 0 . Solutions for this quadratic equati...
HK
Answered by Hasnat K. • Maths tutor
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50.0 g of propene reacts with hydrochloric acid to produce 1-chloropropane. Calculate the percentage yield if only 54.0g is made.

STEPS:Write the equation CH3CHCH2 + HCl -> CH3CH2CH2Cl + H2 (where 1-chloropropane made by electrophilic addition reaction)Identify number of moles of propene used. So number of moles is m/ Mr= 50.0g / (1...
RK
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In the age of modern healthcare, every time a patient dies after a routine operation or procedure, it’s a case of medical error.

This is a partial response for you to read and get a feel for the type of response examiners are looking for. This extract is around a 4A in the BMAT mark scheme. With today's surgical technology, the possib...
HC
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