Show that the equation of the tangent to $y=2 x^{2}-1$ at the point where x = a, is $4 a x-y=2 a^{2}+1$.

Use your calculator to write the following in the form $e^{k}$ where k is correct to 4 decimal places: 0.006

For each of the following data sets, make sure the data is ordered and then find: (i) the median (ii) the upper and lower quartiles (iii) the range (iv) the interquartile range. 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9

Sequence the steps in how a nerve impulse moves from one neuron to another neuron, by writing the numbers 1 to 5 in the squares to the left of the steps. ___ The neurotransmitter moves across the synapse and binds to receptors on the dendrite of a neighboring neuron. ___ An electrical impulse is sent along an axon, jumping from node to node in axons covered with myelin. ___ The neuron is at rest, with more sodium ions outside the cell and more potassium ions inside the cell. ___ The impulse reaches the synapse, where channels again open. Vesicles fuse with the plasma membrane and release a neurotransmitter by exocytosis. ___ The threshold for an action potential is reached at a dendrite, opening channels in the plasma membrane and causing a reversal in electrical charge.

The 2000 census reported that 66.4% of the households in Alaska were homeowners, and the remainder were renters. During the next decade, 37.2% of the homeowners became renters, and the rest continued to be homeowners. Similarly, 71.5% of the renters became homeowners, and the rest continued to rent. (A) Write the appropriate transition matrix. (B) According to this transition matrix, what percentage of households were homeowners in 2010? (C) If the transition matrix remains the same, what percentage of households will be homeowners in 2030?

What social and economic effects did the Black Death have on Europe?

Match the appropriate definition in the right column with each term in the left column.

$$\begin{array}{l l } \text{ } & \text{A. The condition of a system as described by its properties}\\ \text{ } & \text{B. A region of space through which mass may flow}\\ \text{ } & \text{C. Whatever is studied}\\ \text{ } & \text{D. A transformation from one state to another}\\ \text{ } & \text{E. A property whose value for an overall system is the sum of its}\\ \text{ } & \text{ values for the parts into which the system is divided}\\ \text{ } & \text{F. Everything external to the system}\\ \text{ State } & \text{G. A fixed quantity of matter}\\ & \text{H. A property whose value is independent of the size or extent }\\ & \text{of a system and may vary from place to place within the system at any moment}\\ & \text{I. Distinguishes the system from its surroundings}\\ & \text{J. A macroscopic characteristic of a system to which a numerical value can be}\\ & \text{assigned at a given time without knowledge of the previous behavior of the system}\\ \end{array}$$

You are helping design boxes for game balls that are 1 inch in diameter. Your supervisor wants the balls to be packaged in one rectangular layer of rows and columns. a. Use a table to show all the ways to package 24 balls in rows and columns. b. Plot these points on a graph. c. Do the possible box dimensions represent direct or inverse variation? Explain how you know. d. Represent the situation with an equation. Does the equation have any limitations? If so, what are they?

the product of three integers is 90. the second number is twice the first number. the third number is two more than the first number. what are the three numbers?

Use the method of partial fractions to evaluate the following integrals. $\int \frac { d x } { x ^ { 3 } - x }$

For any triangle, derive the formula $a=b \cos C+c \cos B.$

What is wrong with the following statement: “Given any two bodies, the one with the higher temperature contains more heat.”

Suppose that a $90-k g$ person walks for 1 hour each day for a year, expending 50,000 extra kilocalories of metabolic energy (in addition to his normal resting metabolic energy use). What approximately is the person’s mass at the end of the year, assuming his food consumption does not change? (a)$57 \mathrm{kg}$ (b)$61 \mathrm{kg}$ (c)$64 \mathrm{kg}$ (d)$66 \mathrm{kg}$ (e)$67 \mathrm{kg}$

A rancher wants to enclose a pen for new calves using 60 ft of fencing. Which shape uses all of the fencing and encloses the greatest area? F. a rectangle that is 12 ft by 18 feet G. a square 15 ft on each side H. a rectangle that is 20 ft by 30 feet I. a circle with an 8-ft radius