Alan

If x>15/6 then the term in brackets is negative and f(x) would be complex, so if we are dealing with the Real numbers only, then the domain is -infinity to 15/6 (2.5).

Dividing by a fraction is the same as multiplying by the inverse of that fraction.  So if we want to divide by \(\frac{5\sqrt{34}}{34}\)

that is the same as multiplying by \(\frac{34}{5\sqrt{34}}\)

Hence we have \(10\times \frac{34}{5\sqrt{34}}\rightarrow \frac{2\times34}{\sqrt{34}}\rightarrow2\times \sqrt{34}\)

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If you become a scientist or engineer you will use them all the time.  If you spend your working life stacking shelves in a supermarket you'll never need them!

The average force is given by mass*acceleration.  The acceleration here is -30/25 m/s² (it is negative because it is a deceleration), so the force is -1000*30/25 = -1200 Newtons.  It is acting in the opposite direction to the direction of travel.

If he's ridden 3/4 of the way he has 1/4 of the way left to go, so just divide 472 by 4.

In a right angled triangle with sides of length a, b and c (where c is the longest) the pythagorean theorem says

                                                                         a² + b² = c²

sin(30°) = 1/2;   cos(150°) = -cos(30°) = -sqrt(3)/2;   tan(60°) = sqrt(3)

so we have  1/4 + 3/4 + 3 = 4

-8 + 7x/2 = 6  Add 8 to both sides to get:

7x/2 = 14       Multiply both sides by 2 to get:

7x = 28          Divide both sides by 7 to get:

x = 4

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It means "divide".  i.e. 1/3 means 1 divided by 3

You've gone astray by putting an explicit negative sign in for 'a'.  Simpler to do the following:

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