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You would have to rewrite 25 as 5^2 hence 25^x = (5^2)^x = 5^(2*x).

Then 5^(2x) = 5^(4x+1) and therefore 2x = 4x + 1 hence 2x = -1 hence x = -1 / 2. 

Write down the formulas involving cos2x and select the one which involves only cosine, this is because cosine (or derivations of it) is the only trigonometric function in this question. Substitute the cho...

dy/dx = 6x² + 4x + 9

dy = (6x² + 4x + 9) dx 

integrating gives:

y= (6x³/3) + (4x²/2) + 9x + c

y= 2x³ + 2x² + 9...

The general form of a quadratic equation is, ax² +bx + c = 0. If we divide all terms by a we get, x² +(b/a)x + c/a = 0. then by completing the square we get (x+(b/2a))² + ...

Just because a function is continuous at a point, that doesn't mean it has a derivative at that point. If a function is differentiable on an interval, then it is continuous on that interval, but the rever...