Find the general solution of the system of differential equations.

$$\begin{align*} y_1'&=2y_1\\ y_2'&=3y_1+2y_2+3y_3\\ y_3'&=-3y_1-y_3 \end{align*}$$

Determine whether the binomial is a factor of the polynomial.

$$g ( x ) = 3 x ^ { 3 } - 28 x ^ { 2 } + 29 x + 140 ; x + 7$$

The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is one-twentieth of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is

$$1025 \mathrm { kg } / \mathrm { m } ^ { 3 }$$

Use mathematical induction to prove that each statement is true for every positive integer n.

$$\sum _ { i = 1 } ^ { n } 7 \cdot 8 ^ { i } = 8 \left( 8 ^ { n } - 1 \right)$$

Determine whether each number is a prime number or a composite number. 161

Base your answer on the text below. A narrow 160-kilometer-long series of barrier islands stretches from New York City to the eastern tip of Long Island at Montauk Point. These sand islands protect the South Shore from the full force of storms. However, the barrier islands also prevent uninterrupted access to the Atlantic Ocean. The Shinnecock Inlet connects Shinnecock Bay and other sheltered waterways with the ocean. The inlet was formed by the Great Hurricane that stuck Long Island in 1938. This storm permanently broke through a barrier island at Hampton Bays. Since then, dredging has been necessary to keep the Shinnecock Inlet open. Maintenance of the inlet has interrupted the flow of sand along the south shore of Long Island. Efforts to preserve local beaches with jetties and groins have pushed erosion problems farther west resulting in narrower beaches along Long Island's south shore. What process threatens to fill in Shinnecock Inlet? (1) weathering (2) erosion (3) deposition (4) recrystallization

Multiply. (15r/18r²+9r-27)(3r-3/r²)

Determine whether the given pairs of lines are parallel, coincident, or intersecting.

$$\$$

$$L:\ \ \ \ 2x - 3y = -8 ,\\ M: \ \ \ 6x - 9y = -2$$

Determine whether the survey clearly projects the winner. Explain your response. According to a survey of a random sample of students voting for student council president, 57% planned to vote for James and 43% plan to vote for Thea. The survey’s margin of error is

$$\pm 6 \%$$

Graph the linear equation: x = -3.

The bond dissocia tion energies for the species NO, CF-, and CF+ are ordered as Cf+> NO> CF- . Use MO theory to explain this ordering.

Jasmine's race time was 34.287 minutes. Round her race time to the nearest tenth of a minute.

find any points of intersection of the graphs of the equations algebraically and then verify using a graphing utility.

$$x^2-4y^2-20x-64y-172=0$$

,

$$16x^2+4y^2-320x+64y+1600=0$$

A certain particle has a weight of 22 N at a point where g = 9.8 m/s². What are its (a) weight and (b) mass at a point where g = 4.9 m/s²? What are its (c) weight and (d) mass if it is moved to a point in space where g = 0?