6.2 Use the synoptic code to present the weather data in diagram 2 (4)      

  QUESTION 8   The pie chart shows the relative amounts of some gases in air. Right-click on the button to open the data booklet in a new tab.     8.1 Name of the gas that makes up most of the air. (1)   8.2 What is the approximate percentage of oxygen in air? (1)   Rain water is naturally slightly acidic because carbon dioxide dissolves in it. The word equation for the reaction that occurs is: carbon dioxide + water

Find the absolute maximum of the function \(f(x,y,z)=x^2-2y^2+z^2\) on the ellipsoid \(\frac{x^2}{4}+\frac{y^2}{9}+\frac{z^2}{25}=1\)

Compute the following integral \(\iint_{D} e^{-x^2-y^2}dA\), where \(D\) is the set \(D=\{ (x,y) |\quad 1\leq x^2+y^2 \leq 4, \quad x\geq 0,\quad y\geq 0 \}\)

Let \(E\) be a solid with volume equal to \(2.\) Let \(S\) be it’s boundary. Compute: \(\iint_{S} {\bf F}\cdot {\bf n} dS\) where \({\bf F}=y{\bf i}+x{\bf j}+3z{\bf k}\) and \({\bf n}\) is oriented outwards.

Compute the directional derivative of \(f(x,y)=x^2+y^2\) at the point \(p=(2,1)\) in the direction of the vector \({\bf v}= \langle 1,1 \rangle\)

Calculate \(\frac{\partial(x,y)}{\partial(u,v)}\) if \(u=2x+y\) and \(v=x+\ln(2y)\).

Compute the flux of the vector field \({\bf F}=yz^2{\bf i}+x^2\cos z{\bf j}+xy{\bf k}\) over the paraboloid parametrized by \({\bf r}(u,v)=\langle u,v,1-u^2-v^2 \rangle,\quad u^2+v^2\leq 1\) with downward orientation. [HINT: Try integrating over a different surface]

Which of the following is the form of the particular solution of the differential equation \(y”-4y’+4y=e^{2t}\cos(t)\)as given by the method of undetermined coefficients?

Consider the triangle with vertices \(P=(1,0,1)\), \(Q=(3,0,0)\), and \(R=(2,-1,4)\). (i) Find a vector \(\mathbf{v}\) orthogonal to the triangle \(PQR\) (ii) Find the area of \(PQR\).