Which of the following is correct, if x = 4?
n\leq3x^{2}
\leq3(4)^{2}
\leq48
or
n\leq3x^{2} =3(4)^{2} =48
In other words, in what situations is it necessary to switch from inequality to equality, and it is always required to have only one comparison symbol per line?
You just go back to the definition of abs[(f(x)]
abs[f(x)] = f(x) \forall f(x) \geq 0
abs[f(x)] = -f(x) \forall f(x) < 0
And differentiate separately.
In other words, 'splitting the domains', as someone above said.
I would like some advice on choosing an engineering specialisation. I have a love of mathematics so preferably I would like an engineering degree/profession with as much math as possible.
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It is relatively simple if you assume no air resistance/friction etc. But it will depend on how much space you have and how quickly you want to reach your target speed.
\frac{1}{2}m (\Delta v)^{2} = mg \Delta h (kinetic energy gained = gravitational potential energy lost)
\Delta h =...
Firstly mass and energy are equivalent; they are the same thing.
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By Newton's first law once the car is moving at 55mph you will not need to add any more energy as you will not be accelerating it any more.
K=\frac{1}{2}mv^{2}
\Delta{K} = \frac{1}{2}m(\Delta{v})^{2} as \frac{dm}{dt} is constant
\approx\frac{1}{2}(\frac{1000}{2.2})(55*1.6)^{2}
\approx\1.76 *...
let a = mcis(kpi) where m => 0, k is integer
and b = ncis(hpi) where n => 0, h integer
(clearly a,b are real)
|a||b|= mn
|ab|=|mcis(kpi)*ncis(hpi)| = |mncis[pi(k+h)]| = mn
as required