Solve the system by using a graph or table.

$$\left\{ \begin{array} { l } { y = - 2 ( x - 3 ) ^ { 2 } + 9 } \\ { y = - 4 x + 3 } \end{array} \right.$$

Graph the functions f and g, where g(x) = f(x + 0.01) - f(x) / 0.01. Label the graphs and describe the relationship between them. f(x) = 2x - x²

Consider a country that imports a good from abroad. For each of following statements, state whether it is true or false. Explain your answer. a. “The greater the elasticity of demand, the greater the gains from trade.” b. “If demand is perfectly inelastic, there are no gains from trade.” c. “If demand is perfectly inelastic, consumers do not benefit from trade.”

Find the x- and y-intercepts of the graph of the equation.

$$y = \frac { 2 } { 3 } x - 4$$

Margaret's recipe for alphabet soup calls for (among other items) ¼ cup snipped parsley,

$$\dfrac{1}{8}$$

teaspoon pepper, and ½ cup sliced carrots. Margaret is expecting company and needs to multiply the amounts of the ingredients by 1 ½ times. Determine the amount of (a) snipped parsley, (b) pepper, and (c) sliced carrots she needs for the soup.

Find the value of a retirement savings account paying an APR of 5.4% (compounded monthly) after 40 years of monthly contributions (contributions made at the end of each month, including the last month) when the monthly contributions is (a) $100, (b)$50, (c) $150

Write an equation for the nth term of each arithmetic sequence.

$$a _ { 5 } = - 12 , d = - 4$$

Write the verbal sentence as an equation. Then tell whether 5 is a solution of the equation. The quotient of -40 and x is -8.

In two months a puppy's weight increased from 5 lb 15 oz to 8 lb 5 oz. Find the amount of increase.

Prove that if n is an odd integer, then -n is also odd.

Review the vocabulary words listed. Match the words with the definitions below. Megaspore, micropyle, microspore, protonema, vegetative reproduction, anther, day-neutral plant, long-day plant, ovary, petals, photoperiodism, pistil, sepals, short-day plant, stamen, dormancy, double fertilization, endosperm, germination, hypocotyl, polar nuclei, radicle. Plants that produce flowers only after exposure to short nights

Verify that each equation is an identity.

$$\cos \left( \frac { \pi } { 2 } + \theta \right) = - \sin \theta$$

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular velocity ω. Write down the Lagrangian for a bead threaded on the rod, using r as your generalized coordinate, where r, φ are the polar coordinates of the bead. (Notice that φ is not an independent variable since it is fixed by the rotation of the rod to be φ = ωt.) Solve Lagrange's equation for r(t). What happens if the bead is initially at rest at the origin? If it is released from any point

$$r_o > 0$$

, show that r(t) eventually grows exponentially. Explain your results in terms of the centrifugal force mω²r.

Simplify.

$$\frac { a - b } { a ^ { - 1 } - b ^ { - 1 } }$$