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Solve the following equations. Leave answers in simplest terms a)e^(3x-9)=8. b) ln(2y+5)=2+ln(4-y)

a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Another ...
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Answered by Ben W. • Maths tutor
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a) show that (cosx)^2=8(sinx)^2-6sinx can be written as (3sinx-1)^2=2 b)Solve (cosx)^2=8(sinx)^2-6sinx

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement, w...
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Answered by Ben W. • Maths tutor
24959 Views

Solve the following simultaneous equations. x^2+y^2=25. y-3x=13

The key to solving simultaneous equations is trying to reduce them into one equation. You can see that one of these equations is quadratic, so you should be thinking there will be 2 answers for x and y. You ...
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Answered by Ben W. • Maths tutor
6054 Views

Solve these two simultaneous equations.

eq.1 4x+3y=7eq.2 3x+7y=16 You want to eliminate one of the variables (either x or y) reducing the problem to just one equation with one variable which can be solved. This can be done by multiplying each equa...
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Answered by Tobias H. • Maths tutor
4789 Views

Integrate xsin(2x) by dx between the limits 0 and pi/2.

First it is important to identify that this is an integration by parts question as it can't be solved by substitution. Let I = integral for ease of notation.Write out integration by parts formula I(u)dv= uv ...
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Answered by Benedict A. • Maths tutor
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