Match the term below with its correct definition. cerebral cortex A. system that regulates the body's vital functions B. the outer layer of the brain C. basic building blocks of heredity D. chemicals that transmit messages in the nervous systems E. system that transmits messages between the central nervous system and all other parts of the body F. system of glands that secrete hormones into the bloodstream G. the junction between an axon terminal and a dendrite H. a scan that observes the brain at work I. resembling an intricate or complex net J. the forebrain with two hemispheres

Calculate the following approximations to $\int _ { 0 } ^ { 6 } x ^ { 2 } d x.$ (a) LEFT(2) (b) RIGHT(2) (c) TRAP(2) (d) MID(2)

If a matrix A is $5 \times 3$ and the product AB is $5 \times 7$, what is the size of B?

While being X-rayed, a person absorbs $3.2 \times 10^{-3} \mathrm{J}$ of energy. Determine the number of 40,000-eV X-ray photons absorbed during the exam.

Use the random numbers to solve the following problem. Tankers arrive at an oil port with the distribution of interarrival times shown in Table 12. The port has two terminals, A and B. Terminal B is newer and therefore more efficient than terminal A. The time it takes to unload a tanker depends on the tanker’s size. A supertanker takes 4 days to unload at terminal A and 3 days at terminal B. A midsize tanker takes 3 days at terminal A and 2 days at terminal B. The small tankers take 2 days at terminal A and 1 day at terminal B. Arriving tankers form a single waiting line in the port area until a terminal becomes available for service. Service is given on an FCFS basis. The type of tankers and the frequency with which they visit this port is given by the distribution in Table 13. Develop a simulation model for this port. Compute such statistics as the average number of tankers in port, the average number of days in port for a tanker, and the percentage of idle time for each of the terminals. TABLE 12:

$$\begin{matrix} \text{Interarrival Times (days)} & \text{Probability}\\ \text{1} & \text{.20}\\ \text{2} & \text{.25}\\ \text{3} & \text{.35}\\ \text{4} & \text{.15}\\ \text{5} & \text{.05}\\ \end{matrix}$$

TABLE 13:

$$\begin{matrix} \text{Type of Tanker} & \text{Probability}\\ \text{Supertanker} & \text{.40}\\ \text{Midsize tanker} & \text{.35}\\ \text{Small tanker} & \text{.25}\\ \end{matrix}$$

Determine the value of k so that x+3 is a factor of x^3+4x^2-2kx+3 .

Let $y_1$ and $y_2$ be two solutions of $A ( x ) y ^ { \prime \prime } + B ( x ) y ^ { \prime } +C(x)y$ on an open interval $I$ where $A$, $B$, and $C$ are continuous and $A(x)$ is never zero. (a) Let $W=W \left( y _ { 1 } , y _ { 2 } \right)$. Show that

$$A ( x ) \frac { d W } { d x } = \left( y _ { 1 } \right) \left( A y _ { 2 } ^ { \prime \prime } \right) - \left( y _ { 2 } \right) \left( A y _ { 1 } ^ { \prime \prime } \right).$$

Then substitute for $A y _ { 2 } ^ { \prime \prime }$ and $A y _ { 1 } ^ { \prime \prime }$ from the original differential equation to show that

$$A ( x ) \frac { d W } { d x } = - B ( x ) W ( x )$$

(b) Solve this first-order equation to deduce Abel’s formula

$$W ( x ) = K \exp \left( - \int \frac { B ( x ) } { A ( x ) } d x \right)$$

where $K$ is a constant. (c) Why does Abel’s formula imply that the Wronskian $W \left( y _ { 1 } , y _ { 2 } \right)$ is either zero everywhere or nonzero everywhere?

Write the solution set of the given homogeneous system in parametric vector form.

$$\begin{array}{r}{x_{1}+3 x_{2}+x_{3}=0} \\ {-4 x_{1}-9 x_{2}+2 x_{3}=0} \\ {-3 x_{2}-6 x_{3}=0}\end{array}$$

.

Graph the quadrilateral ABCD with vertices A(-4, 1), B(-3, 3), C(0, 1) and D(-2, 0) and its image after the translation. (x, y)→(x + 4, y - 2)

A motor scooter rounds a curve on the highway at a constant speed of 20.0 m/s. The original direction of the scooter was due east; after rounding the curve the scooter is going

$$36 ^ { \circ }$$

north of east. The radius of curvature of the road at the location of the curve is 150 m. What is the average acceleration of the scooter as it rounds the curve?

Lucy, Eduardo, Carmen, and Frank live on the same street. Eduardo's house is halfway between Lucy's house and Frank's house. Lucy's house is halfway between Carmen's house and Frank's house If the distance between Eduardo's house and Lucy's house is 150 ft, what is the distance in feet between Carmen's house and Eduardo's house?

Solve the equation. Approximate the solutions to the nearest hundredth.

$$t ^ { 2 } = t + 4$$

Two identical television signals are sent between two cities that are 400.0 km apart. One signal is sent through the air, and the oilier signal is sent trough a fiber optic network. The signals are sent at the same time, but the one traveling through air arrives $7.7 \times 10 ^ { - 4 }$ s before the one traveling through the glass fiber. What is the index of refraction of the glass fiber?

Evaluate using Integration by Parts as a first step.

$$\int \frac { \sin ^ { - 1 } x } { x ^ { 2 } } d x$$