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Find the general solution of: y'' + 4y' + 13y = sin(x)

First we find the auxilary equation by substituting y with m^0, y' with m^1 and y'' with m^2. We get m^2 + 4m + 13 and find the roots using the differential equation, m = (-4 +- (16-4x1x13)^0.5)/(2x1). From ...
TT
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Solve 5x^2 - 9x + 4 = 0 using the quadratic formula

The quadratic formula is (-b±sqrt(b^2-4ac))/2a where a is the coefficient of the x^2 term, b is the coefficient of the x term and c is the number. So, in this case a=5, b=-9 and c=4. Substitute this into the...
MP
Answered by Matilda P. • Maths tutor
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Solve these equations simultaneously: (1) 5x - 10z = -45 and (2) 9x = -5z + 80

There are two methods to solve this equation. 1) Rearrange equation 2 to get all the xs and zs on the left hand side (9x+5z=80). Multiply either equation to get an equal number of xs or zs in both equations,...
MP
Answered by Matilda P. • Maths tutor
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Which compound is a member of the same homologous series as 1-chloropropane? A. 1-chloropropene B. 1-chlorobutane C. 1-bromopropane D. 1,1-dichloropropane

It's B. Chlorobutane In explaining this answer, I'd test the students knowledge of what a homologous series is. And then we'd draw out the alternative answers and I'd ask the student to explain why each inco...
JP
Answered by Joe P. • Chemistry tutor
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Explain why, in theory, a perfectly contestable market results in an efficient allocation of resources

William J Baumol’s theory of contestable markets (1982) holds that there are markets served by a small number of firms, which are nevertheless characterized by competitive equilibria, and therefore, desirabl...
RM
Answered by Rebecca M. • Economics tutor
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