Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.
Step-by-step explanation:
Answer:
2cm of Rainfall
Step-by-step explanation:
When the no. of mosquitoes is the highest the slope of graph will be zero
so if we differentiate this function and equate to zero we can find the rainfall amount that gives maximum number of mosquitoes in centimetres.
m(x)= -x²+4x
differentiate
d(x)/d(m(x))= -2x+4
equate to zero
-2x+4=0
2x=4
x=2
answer: 2 cm of rain
Answer:
The circulation of the field f(x) over curve C is Zero
Step-by-step explanation:
The function 
and curve C is ellipse of equation
Theory: Stokes Theorem is given by:
Where, Curl f(x) = ![\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5C%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82x%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82y%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82z%7D%20%5C%5CF1%26F2%26F3%5Cend%7Barray%7D%5Cright%5D)
Also, f(x) = (F1,F2,F3)
Using Stokes Theorem,
Surface is given by g(x) = 
Therefore, tex]\hat{N} = grad(g(x))[/tex]
Now,
Curl f(x) =
Curl f(x) = ![\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5C%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82x%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82y%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82z%7D%20%5C%5Cx%5E%7B2%7D%264x%26z%5E%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Curl f(x) = (0,0,4)
Putting all values in Stokes Theorem,
I=0
Thus, The circulation of the field f(x) over curve C is Zero
The answer is D
Have you ever heard of rise over run rise/run
Y/x. Well in this case the run is One with a rise of four
