If there is such a scalar function <em>f</em>, then



Integrate both sides of the first equation with respect to <em>x</em> :

Differentiate both sides with respect to <em>y</em> :


Integrate both sides with respect to <em>y</em> :

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :



Integrate both sides with respect to <em>z</em> :

So we end up with

Answer:
2.5 minutes per quesiton
Step-by-step explanation:
75 minutes to take 30 quesitons means you divide the time equally so
75/30
#2
Change mixed numbers to improper fractions. Then change division to multiplication by the reciprocal.
1 1/2 divided by 3/5=
(3/2) * (5/3) = 5/2 = 2 1/2
#3
(5/9) divided by (5/3)
(5/9) * (3/5) =3/9 = 1/3
3/8 + 3/5 = <u>39/40</u> and 39/40 Can't be <em>simplified</em>
Answer:

Step-by-step explanation:
The half life is the amount of time it takes a substance to decay to half of its original amount.
Since the radioactive substance has a half life of 1000 years, there will be half of it left after 1000 years.
So, the fraction that will be left after 1000 years is 