Two planes are given parametrically by the vector equations

$$x_1(s, t) = (−3, 4,−9) + s(9,−5, 9) + t(3,−2, 3)$$

$$x_2(s, t) = (5, 0, 3) + s(−9, 2,−9) + t(−4, 7,−4).$$

(a) Give a convincing explanation for why these planes are parallel. (b) Find the distance between the planes.

If

$$K_1\ and\ K_2$$

are disjoint nonempty compact sets, show that there exist

$$k _ { i } \in K _ { i }$$

such that

$$0 < \left| k _ { 1 } - k _ { 2 } \right| = \inf \left\{ \left| x _ { 1 } - x _ { 2 } \right| : x _ { i} \in K _ { i } \right\}.$$

Does every function have an inverse which is a function? Does every relation have an inverse which is a relation?

In 2016, J J Dishes changed its method of valuing inventory from the FIFO method to the LIFO method. At December 31, 2015, J J’s inventories were $96 million (FIFO). J J’s records were insufficient to determine what inventories would have totaled if determined on a LIFO cost basis. Briefly describe the steps J J should take to report the change.

write the complex number in trigonometric form. -5 - 12i

Carolina y Omar estan en el mercado del pueblo buscando algunos regalos para llevar a casa. Completa las conversaciones con las expresiones del cuadro. última oferta / adorno de cerámica / gran surtido / mantel bordado / se los dejo / un precio especial / rebajar el precio / está en venta / cuánto vale / pintura

-Yo quiero un (1) BLANK para mi mamá. -Mire, tenemos un (2) BLANK de artesanías. -(3) ¿BLANK este adorno rojo? -Si compra dos, le voy a dar ( 4) BLANK (5) BLANK en veinte mil pesos. -¿Cuánto vale ese (6) BLANK con encaje? -Lo siento, no (7) BLANK. -¿Me puede (8) BLANK de este pantalón de cuero? -Bueno, se lo regalo por treinta mil pesos, pero es mi (9) BLANK.

Use the following heights (in.) The data are matched so that each column consists of heights from the same family.

$$\begin{array} { | c | c | c | c | c | c|c|c|c|} \hline \text { Father } & { 68.0 } & { 68.0 } & { 65.5 } & { 66.0 } &67.5&70.0&68.0&71.0\\ \hline \text { Mother } & { 64.0 } & { 60.0 } & { 63.0 } & { 59.0 } &62.0&69.0&65.5&66.0\\ \hline \text { son } & { 71.0 } & { 64.0 } & { 71.0 } & { 68.0 } &70.0&71.0&71.7&71.0\\ \hline \end{array}$$

Are the original unrounded heights discrete data or continuous data?

¿Cuál de los siguiente oficios se gana la vida haciendo investigaciones? Es (alpinista / detective).

Write the partial fraction decomposition of each rational expression.

$$\frac { 5 x ^ { 2 } - 9 x + 19 } { ( x - 4 ) \left( x ^ { 2 } + 5 \right) }$$

Expand

$$\left( x _ { 1 } + 2 x _ { 2 } + 3 x _ { 3 } \right) ^ { 4 }$$

.

When an oxide of potassium is decomposed, 19.55 g of K and 4.00 g of O are obtained. What is the empirical formula for the compound? .

Which solute has the greatest effect on the boiling point of 1.00 kg of water: 50.0 g of strontium chloride $\left(\mathrm{Sr} \mathrm{Cl}_{2}\right)$ or 150.0 g of glucose $\left(\mathrm{C}_{\mathrm{6}} \mathrm{H}_{12} \mathrm{O}_{6}\right)$? Justify your answer.

Contestants in the Run-and-Bike-a-thon run for a specified length of time, then bike for a specified length of time. Jason ran at an average speed of 5.2 mi/h and biked at an average speed of 20.6 mi/h, going a total of 14.2 miles. Seth ran at an average speed of 10.4 mi/h and biked at an average speed of 18.4 mi/h, going a total of 17 miles. For how long do contestants run and for how long do they bike? _

A viscous oil flows down a wide plate with a uniform depth of 8 mm and an average velocity of 50 mm/s. The plate is on a $3^{\circ}$ hill and the specific gravity of the oil is 0.85. Determine the average shear stress between the oil and the plate.