1 mpm or 0.0166666666 repeating mph
<u>3</u> x 4 = <u>12</u><u>
</u>5 x 4 = <u />20
Since 5 times 4 is 20, then you must also multiply 3 by 4 because what you do to one part of the fraction you must do to the other.<u>
</u>
:<span> </span><span>You need to know the derivative of the sqrt function. Remember that sqrt(x) = x^(1/2), and that (d x^a)/(dx) = a x^(a-1). So (d sqrt(x))/(dx) = (d x^(1/2))/(dx) = (1/2) x^((1/2)-1) = (1/2) x^(-1/2) = 1/(2 x^(1/2)) = 1/(2 sqrt(x)).
There is a subtle shift in meaning in the use of t. If you say "after t seconds", t is a dimensionless quantity, such as 169. Also in the formula V = 4 sqrt(t) cm3, t is apparently dimensionless. But if you say "t = 169 seconds", t has dimension time, measured in the unit of seconds, and also expressing speed of change of V as (dV)/(dt) presupposes that t has dimension time. But you can't mix formulas in which t is dimensionless with formulas in which t is dimensioned.
Below I treat t as being dimensionless. So where t is supposed to stand for time I write "t seconds" instead of just "t".
Then (dV)/(d(t seconds)) = (d 4 sqrt(t))/(dt) cm3/s = 4 (d sqrt(t))/(dt) cm3/s = 4 / (2 sqrt(t)) cm3/s = 2 / (sqrt(t)) cm3/s.
Plugging in t = 169 gives 2/13 cm3/s.</span>
A unit fraction means that the fraction has 1 in the numerator. To make 3/8 a unit fraction, you have to make it 1/8 by dividing by 3.
So now you have 3 x 3 x 1/8. You can multiply the 3 and 3.
You are left with 9 x 1/8.
