Factor out the common factor. 6y-30

Solve the system by the method of elimination. Then state whether the system is consistent or inconsistent.

$$\left\{\begin{array}{r} {2 x-3 y=4} \\ {-2 x-y=4} \end{array}\right.$$

A pump is to be selected for a waterfall in a garden. The water collects in a pond at the bottom, and the elevation difference between the free surface of the pond and the location where the water is discharged is 3 m. The flow rate of water is to be at least 8 L/s. Select an appropriate motor– pump unit for this job and identify three manufacturers with product model numbers and prices. Make a selection and explain why you selected that particular product. Also estimate the cost of annual power consumption of this unit assuming continuous operation.

An 8-m-long, uninsulated square duct of cross section $0.2 \mathrm{m} \times 0.2 \mathrm{m}$ and relative roughness $10^{-3}$ passes through the attic space of a house. Hot air enters the duct at 1 atm and $80^{\circ} \mathrm{C}$ at a volume flow rate of $0.15 \mathrm{m}^{3} / \mathrm{s}.$ The duct surface is nearly isothermal at $60^{\circ} \mathrm{C}.$ Determine the rate of heat loss from the duct to the attic space and the pressure difference between the inlet and outlet sections of the duct. Evaluate air properties at a bulk mean temperature of $80^{\circ} \mathrm{C}.$ Is this a good assumption?

Use the given zero of f to find all the zeros of f. $f(x)=x^{4}-2 x^{3}+37 x^{2}-72 x+36$, 6i

Let $J=\int_{0}^{1} d z \int_{0}^{z} d y \int_{0}^{y} f(x, y, z) d x$. Express J as an iterated integral where the integrations are to be performed in the following order: first z, then y, then x.

For what value of the constant c is the function f continuous on $(-\infty,+\infty)$?

$$\begin{align*} f(x)&=\left\{\begin{matrix}cx^2+4x &\text{ if } x\lt 5\\ x^3-cx &\text{ if }x\geq 5\end{matrix}\right. \end{align*}$$

c=

Find the zeros of the polynomials. $P(z)=z^{2}-2 z+i$

Calculate and simplify the wedge product of the given forms $\phi \text { and } \psi$. Write the $d x_{i} s$ in the answers in increasing subscript order.

$$\begin{aligned}&\phi=d x_{1}+2 d x_{2}+3 d x_{3}+4 d x_{4}+5 d x_{5}\\&\psi=d x_{1} \wedge d x_{2} \wedge d x_{3} \wedge d x_{4}+2 d x_{2} \wedge d x_{3} \wedge d x_{4} \wedge d x_{5}\end{aligned}$$

During a flood, the water level in a river first rose faster and faster, then rose more and more slowly until it reached its highest point, then went back down to its preflood level. Consider water depth as a function of time. Is the time when the water first began to rise more slowly a critical point or an inflection point?

Let $\Phi$ be the following differential 1-form: $\Phi=e^{2 y} \sin (3 z) d x+2 x e^{2 y} \sin (3 z) d y+3 x e^{2 y} \cos (3 z) d z$. Directly calculate $d \Phi$. Why are you not surprised at the result ?

A yam has just been taken out of the oven and is cooling off before being eaten. The temperature, T, of the yam (measured in degrees Fahrenheit) is a function of how long it has been out of the oven, t (measured in minutes). Thus, we have T=f(t). What are the units for f'(t)?

Find a plane vector field F(x , y) that satisfies the following conditions: (i) The field lines of Far e the curves xy = C. (ii) $|\mathbf{F}(x, y)|=1 \text { if }(x, y) \neq(0,0)$. (iii) $\mathbf{F}(1,1)=(\mathbf{i}-\mathbf{j}) / \sqrt{2}$. (iv) F is continuous except at (0, 0).

Media Vocabulary: sound effects, editing, pacing. In the L.A. Theatre Works audio performance, how is the mood established?