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A curve is described by f(x) = x^2 + 2x. A second curve is described by g(x) = x^2 -5x + 7. Find the point (s) where both curves intersect.

To find the points where two curves meet a difference function needs to be calculated. This function is formed by subtracting one function from the other: d(x) = f(x) - g(x). It also works the other way arou...
Answered by • Maths tutor
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What keys can I modulate to when harmonizing a Bach chorale?

There are 5 keys which a Bach chorale could modulate to*. Two of these are the dominant and the subdominant (based on the 5th and 4th degree of the home key respectively). If the home key is major then the c...
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Answered by Aaron K. • Music tutor
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A curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx and d2y/dx2. Verify C has a stationary point at x = 2. Determine the nature of this stationary point, giving a reason for the answer.

y = 3x 4 - 8x 3 - 3Bringing the power down on each term and subtracting one from the power (as to differentiate, nx m —> nmx m-1 ), we get for each derivative:dy/dx = 12x 3 - 24x 2 d 2 y/dx 2 = 36x 2 - 48...
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Answered by Connor W. • Maths tutor
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In an interview, a local politician has claimed "Sportunterricht ist überbewertet und zu teuer. Wir sollten ihn streichen." You are trying to change his mind. Write a short statement!

The following answer is exemplary and covers only some of the themes that a good answer might include: Sport ist mit das wichtigste das jemand für seine Gesundheit tun kann. Es ist nicht nur wichtig für die ...
Answered by • German tutor
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Find the x values for stationary points in the curve y=3sin(2x) for 0<x<180

Firstly we differentiate the equation y=3sin(2x) w.r.t. x.By using the chain rule, we find the dy/dx=6cos(2x)Since a stationary point in the curve is a point where the gradient is 0, we can find them by find...
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