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Use Simpson’s Rule with five ordinates to find an approximate value for the integral e^(x^2)dx between the values of 0 and 1

Find the value of dx by dividing the difference between the integral boundaries by the number of ordinates minus 1. Therefore dx=(1-0)/4=1/4. Then define your ordinates, by 5 values between 0 and 1, where th...
JF
Answered by Joshua F. • Maths tutor
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Express 4sinx + 3cosx in the form Rcos(x-a)

From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make this ...
DT
Answered by Dorothy T. • Maths tutor
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Solve |3x+1| = 1

Firstly square both sides. This way, we now know that both sides have to be positive (3x+1)^2 = 1 (3x+1)(3x+1) = 1 Expand the quadratic... 9x^2 + 12x + 4 = 1 9x^2 + 12x + 3 = 0 Now complete the square. First...
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Answered by Dorothy T. • Maths tutor
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AS Maths ->Expresss x^2 + 3x + 2 in the form (x+p)^2 + q... where p and q are rational number

So we are meant to rearrange the given equation in a way that it looks like: (x+p)^2 + q This should look familiar. It is obtained by completing the square. Which will be the method I will describe below: Fi...
JI
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What is the conditional and how do we conjugate it?

The conditional is a useful tense, used to express things that could/would/should happen. They are commonly followed by an 'if', for example: I would go to the supermarket if I had some money - J'irais au su...
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Answered by Victoria P. • French tutor
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