1. Observe that
is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is
2. is an exact differential if we can find a scalar function such that
Integrating both sides of the first equation with respect to yields
Differentiating with respect to gives
and we ultimately find
(We can also use the same method here to determine the scalar function in part (1).)
Then the integral is path-independent, and its value is
It is 29 because a right angle is 90 so the equation should be 61 plus x=90 so you could just subtract and it would be 29
Refer to the figure shown below.
From midnight (high tide) to 6 AM (low tide) is 6 hours, and it is half the period.
Therefore the period is
T = 12 hours.
Half the difference between 10 ft and 6 ft is the amplitude.
The amplitude is
A = 3 ft
On a graph of x versus t, where x = height (ft) after t hours, the mathematical model is
The graph of the mathematical model agrees with the illustrated sketch, as shown.
Answer:
3 students
Step-by-step explanation:
now for RSM Olympiad are 8
math kangaroo are 7
studs that did both are 4
Total number of studs that participated are
(8-4) + 4 + (7-4)
4+ 4 + 3 = 11
those who didn't participate are
14-11 = 13