Write the augmented matrix for each system and give its dimension. Do not solve.

$$\begin{aligned} &4 x-2 y+3 z-4=0\\ &3 x+5 y+z-7=0\\ &5 x-y+4 z-7=0 \end{aligned}$$

Particle accelerators, such a s the Large Hadron Collider, use magnetic fields to steer charged particles a round a ring. Consider a proton ring with 36 identical bending mag nets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. What magnetic field strength is needed i n each magnet to steer protons around the ring with a speed of $2.5 \times 10^{7} \mathrm{m} / \mathrm{s}$? Assume that the field is uniform inside the magnet, zero outside.

Suppose an experimenter intends to do a regression analysis by taking a total of 2n data points, where the $x_{i}$'s are restricted to the interval [0,5]. If the xy-relationship is assumed to be linear and if the objective is to estimate the slope with the greatest possible precision, what values should be assigned to the $x_{i}$'s?

Monochromatic light at 577 nm illuminates a diffraction grating with 325 lines/mm. Determine the highest order that can be observed with this grating at the given wavelength.

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. $7(5 t+3)^{-5 / 3}+14(5 t+3)^{-2 / 3}-21(5 t+3)^{1 / 3}$

Work each problem. Let U={1, 2, 3, 4, 5} and A={1, 2, 3}. Find A'.

Find $f^{\prime}(x)$. $f(x)=3 x^{e}-2 e^{x}$

Refer to the n=5 data points $\left(x_{1}, y_{1}\right)=(0,4)$ $\left(x_{2}, y_{2}\right)=(1,5),\left(x_{3}, y_{3}\right)=(2,7),\left(x_{4}, y_{4}\right)=(3,9)$, and $\left(x_{5}, y_{5}\right)=(4,13)$. Calculate the indicated sum or product of sums. $\sum_{k=1}^{5} x_{k} y_{k}$

Seven different financing plans with their D-E mixes and costs of debt and equity capital for a new innovations project are summarized below. Use the data to determine what mix of debt and equity capital will result in the lowest WACC. $$ \begin{array} \text{ } & \text{Debt Capital} & \text{ } & \text{Equity Capital} & \text{ }\\ \hline \text{Plan} & \text{Percentage} & \text{Rate, \\%} & \text{Percentage} & \text{Rate, \\%}\\ \hline \text{1} & \text{100} & \text{14.5} & \text{-} & \text{-}\\ \text{2} & \text{70} & \text{13.0} & \text{30} & \text{7.8}\\ \text{3} & \text{65} & \text{12.0} & \text{35} & \text{7.8}\\ \text{4} & \text{50} & \text{11.5} & \text{50} & \text{7.9}\\ \text{5} & \text{35} & \text{9.9} & \text{65} & \text{9.8}\\ \text{6} & \text{20} & \text{12.4} & \text{80} & \text{12.5}\\ \text{7} & \text{-} & \text{-} & \text{100} & \text{12.5}\\ \hline \end{array} $$

A large crate of mass m is placed on the back of a truck but not tied down. As the truck accelerates forward with an acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate forward? the force of gravity.

You are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year. (Let t=12 represent 2012.)

$$\begin{matrix} \text{2012 Value} & \text{Rate}\\ \text{\$245,000} & \text{\$5600 increase per year}\\ \end{matrix}$$

Out of one hundred twenty senior citizens polled, sixty-five favored a complete overhaul of the health care system while fifty-five preferred more modest changes. When the same choice was put to eighty-five first-time voters, forty said they were in favor of major reform while forty-five opted for minor revisions.

Get a shape card from your teacher. Look at your shape and decide if your shape is a parallelogram, another form of a quadrilateral, a triangle, or some other shape. Follow your teacher's directions to create a linear model and circle graph. Then answer the questions below. a. Your class built a circle graph with your bodies. How can this model be drawn on paper? Work with your team to sketch a picture of your class circle graph showing the portion of your class that held parallelograms, other quadrilaterals, triangles, and other polygons. Be sure to label each section with the category of shape it represents and with an estimated percentage or angle measure. b. Approximately what portion of the class held triangles? Write your answer as a percent. Then estimate the measure of the central angle on the graph for that portion. A central angle is an angle with its vertex at the center of a circle. Its sides are formed by two radii, and its measure is a portion of $360^{\circ}$. c. Was there a section of the circle that had a central angle of approximately $90^{\circ}$? If so, what type of figure is represented in that section?

Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by n = 4.