If P1 has coordinates (x1, y1) and P2 has coordinates (x2, y2), then the distance between the two points is given by [(x1 - x2)2 + (y1 - y2)2]½ or [(x2 - x1)2 + (y2 - y1)2]½ Using the same two points as above, the midpoint formula is M = [(x1 + x2)/2], [(y1 + y2)/2] If we wanted to find the slope of the line on which the two points lie, it would be given by: m = (y1 - y2)/(x1 - x2) or (y2 - y1)/(x2 - x1) Some quadratic equations can be easily factored, some cannot. For those cases we use the Quadratic Formula: If ax2 + bx + c = 0 then x = [-b ± (b2 - 4ac)½]/2a Notice that the Distance, Midpoint and Slope Formulas all refer to linear equations. The quadratic formula, as the name implies, is used to find roots of an equation in which the variable x is squared.
Differentiating both sides of PV = C with respect to t gives us ...
... P'V +PV' = 0
Filling in the given numbers gives us ...
... (40 kPa/min)(900 cm³) + V'(150 kPa) = 0
Solving for V' gives ...
... V' = -(40 kPa/min)(900 cm³)/(150 kPa)
.. V' = -240 cm³/min
The volume is decreasing at the rate of 240 cm³/min.
Because infedecimals. Basically 1 -.99999.... Is a number so close to zero it is impossible to define. If this were infanct the case however and a number existed that was not 0 and not 0 it would wreck mathematics so infedecimals exist only theoretically. So .999... Is equal to 1 practically but not theoretically.
The y-intercept , occasionally referred to as (b) in linear functions :D