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Write 16× 8^2x as a power of 2 in terms of x.

16 = 2⁴8^2x = (2³)^2x = 2^6xTherefore, 16x8^2x = 2⁴x 2^6x = 2^4+6x

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A curve has equation y = 20x −x^2 −2x^3 . The curve has a stationary point at the point M where x = −2. Find the x-coordinate of the other stationary point of the curve.

dy/dx = 20 - 2x - 6x² = -6x² - 2x + 20 which factorises to dy/dx = (10 - 6x)(2 + x). This shows that x=-2 and x=10/6=5/3 are stationary points of y = 20x −x² −2x³

Answered by Xixi Y. • Maths tutor

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How to prove that Integral S 1/(a^2+x^2) dx= 1/a arctan(x/a) + C ?

In order to answer this question, at first we need to use the method of substitution. That means, we're trying to replace x with a different variable u. Lets use the substitution of x = a tan u, then du/d...

Answered by Judyta W. • Maths tutor

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Solve the following simultaneous equations: x^2 + 2y = 9, and y = x + 3.

Label the two equations as the following: x² + 2y = 9 y = x + 3 Equation 2 can be substituted into equation 1, giving: x² + 2( x + 3 ) = 9Expanding the brackets and subtracting ...

Answered by Ximena B. • Maths tutor

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How do I solve simultaneous equations by substitution?

You can solve simultaneous equations by either substitution or elimination. Say we have the equations:(1) 8y + 6x = 24 and (2) 2y - x = 6SUBSTITUTION METHODFirst, you need to find x in terms of y (or y in...

Answered by Joshua N. • Maths tutor

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