Solve each system of equations. If the system is inconsistent or has dependent equations, say so.

$$\begin{aligned} 2 x+2 y-6 z &=5 \\-3 x+y-z &=-2 \\-x-y+3 z &=4 \end{aligned}$$

One of the difficulties in solving first order equations is that there are several methods of solution, each of which can be used on a certain type of equation. It may take some time to become proficient in matching solution methods with equations. solve the given differential equation. If an initial condition is given, also find the solution that satisfies it. dydx=x+yx−y

Find each product. Look for patterns. a. $\left(\dfrac{10}{13}\times54\right)\times13$
b. $\left(\dfrac{10}{13}\times81\right)\times13$
c. $\left(\dfrac{10}{13}\times1113\right)\times13$
d. Describe a pattern.

Suppose A has position vector 3i + 2j - k, B has position vector 2i - j - 8k, and C has position vector i + j + ak. Find the unit vector u in the direction of $\overrightarrow{\mathrm{BA}}$.

The width of a particular microwave oven is exactly right to support a standing-wave mode. Measurements of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. The wavelength of the microwaves is 12 cm. How wide is the oven?

Find the vertex and the axis of symmetry of the graph of the function. $f ( x ) = 5 ( x - 2 ) ^ { 2 }$

Explain why cos $\theta=\cos \left(\theta+n \cdot 360^{\circ}\right)$ for any angle $\theta$ and any integer n.

Change the order of integration by integrating first with respect to z, then x, then y. $\int _ { - 1 } ^ { 2 } \int _ { 1 } ^ { 3 } \int _ { 0 } ^ { 4 } \left( x ^ { 2 } z + \frac { 1 } { y } \right) d x d y d z$

Convert the polar equation to rectangular form and sketch its graph. $r=4 \sin \theta$

Determine the angular momentum ${H}_{P}$ of the 6-lb particle about point P .

Indicate whether each nerve tract is ascending or descending. a. rubrospinal b. corticospinal c. spinothalamic d. fasciculus gracilis e. reticulospinal f. spinocerebellar

Let $X$ and $Y$ be i.i.d. $\text{Expo}(1)$, and $L = X − Y$ . The Laplace distribution has PDF

$$f ( x ) = \frac { 1 } { 2 } e ^ { - | x | }$$

for all real $x$. Use MGFs to show that the distribution of $L$ is Laplace.

Identify and graph each polar equation. $r=1-2 \sin \theta$

Use the numbers 19, 21, and 399 to write two multiplication facts and two division facts.