Solve each system of inequalities by graphing.

$$\left. \begin{array} { l } { 6 x ^ { 2 } + 9 ( y - 2 ) ^ { 2 } \leq 36 } \\ { x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 25 } \end{array} \right.$$

Graph and compare the two functions.

$$f ( x ) = | x - 1 | + 2 ; g ( x ) = 4 | x - 1 | + 8$$

Identify the following term or individuals and explain their significance. Theodore Roosevelt

The position, P(d), of the Sun at sunset, in degrees north or south of due west, depends on the latitude and the day of the year, d. For a specific latitude, the position in terms of the day of the year can be modelled by the function

$$P ( d ) = 28 \sin \left( \frac { 360 } { 365 } d - 81 \right) ^ { \circ }$$

. a) Graph the function using a graphing calculator and adjust the WINDOW settings as required. b) What is the period of the function, and what does it represent in this situation? c) What is the equation of the axis of the function, and what does it represent in this situation? d) What is the amplitude of the function, and what does it represent in this situation? e) Determine the range of the function. f) What is the angle of sunset on February 15?

Simplify the factorial expression. $\frac{2 n !}{(n+1) !}$

Let f(x)=

$$x^8$$

-2x+3; find

$$\lim _ { w \rightarrow 2 } \frac { f ^ { \prime } ( w ) - f ^ { \prime } ( 2 ) } { w - 2 }$$

Write the quotient in scientific notation: (4 × 10^12)/(8 × 10^4)

Verify that

$$w _ { x y } = w _ { y x }.$$

w = x sin y + y sin x + xy

Mr. Doody, at age 70, is expected to live for 15 years. If he can invest at 4% per annum compounded monthly, how much does he need now to guarantee himself $300 every month for the next 15 years?

In an ideal Brayton cycle, air is compressed from 100 kPa and $25^{\circ} \mathrm{C}$ to 1 MPa, and then heated to $927^{\circ} \mathrm{C}$ before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is (a) $349^{\circ} \mathrm{C}$ (b) $426^{\circ} \mathrm{C}$ (c) $622^{\circ} \mathrm{C}$ (d) $733^{\circ} \mathrm{C}$ (e) $825^{\circ} \mathrm{C}$

Use an inverse matrix to solve the linear system. 4x + y = - 2, -6x + y = 18

Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded by the cone

$$z = \sqrt { x ^ { 2 } + y ^ { 2 } }$$

and the plane z=2.

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in.. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.5% or largest 2.5%. Find the minimum and maximum head breadths that the helmets will fit.

A company offers premium cable for $39.95 per month plus a one-time setup fee. The total cost for setup and 6 months of service is$264.70. Write the equation in slope-intercept form.