Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y)=3x+3y

For the entire rectangle, find the area of each part and then find the area of the whole.

$$\begin{matrix} \text{ } & \text{11} & \text{8}\\ \text{7} & \text{ } & \text{ }\\ \text{3} & \text{ } & \text{ }\\ \end{matrix}$$

Find an equation for the contour of $f(x, y)=2x^2y+6x+25$ that goes through the point $(4, −2)$.

A $0.016773-\mathrm{m}^{3}$ tank contains 1 kg of refrigerant-134a at $110^\circ C.$ Determine the pressure of the refrigerant, using (a) the ideal-gas equation, (b) the generalized compressibility chart, and (c) the refrigerant tables.

Indicate whether the statement is true or false. If $f(x)=x^{2}$ then f'(1) is positive.

Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y)=2x-y

Reduce the equation to one of the standard forms, classify the surface, and sketch it. x2 + 2y - 2z2 = 0

Use traces to sketch and identify the surface. y=z^2-x^2

Find the point of intersection of the plane and the line. Plane x+y-z=3; line $\frac{x+2}{2}=\frac{y-3}{1}=\frac{z}{2}$

Use traces to sketch and identify the surface. x=y^2+4z^2

The average weight, W, in pounds, of an adult is a function, W=f(c), of the average number of Calories per day, c, consumed. Interpret the statements f(1800)=155 and f'(2000)=0 in terms of diet and weight.

Describe in words the level surfaces of $f(x, y, z)=$ $\sin (x+y+z)$

What is a thermal energy reservoir? Give some examples.

Use $\mathbf{u}=\langle 1,1,-6\rangle, \mathbf{v}=\langle 3,0,8\rangle$, and $\mathbf{w}=\langle- 3,-1,2\rangle$ to find each quantity. $3 \mathbf{v}-2 \mathbf{w}$