Ms. Picasso is also considering having the students in the art club make and sell candles to raise money for supplies. The function

$$P(x) = -20x^2 + 320x – 780$$

models the profit the club would make by selling the candles for x dollars each. Give the reasonable domain and range of P(x), assuming that the club does not want to lose money by selling the candles. Explain how you determined the reasonable domain and range

When you are dividing two decimals, how can you check whether you have divided the decimals correctly?

Many chemical reactions are the result of the interaction of two molecules that undergo a change to produce a new product. The rate of the reaction typically depends on the concentrations of the two kinds of molecules. If a is the amount of substance A and b is the amount of substance B at time t = 0, and if x is the amount of product at time t, then the rate of formation of x may be given by the differential equation

$$\frac { d x } { d t } = k ( a - x ) ( b - x ),\ or\ \frac { 1 } { ( a - x ) ( b - x ) } \frac { d x } { d t } = k,$$

where k is a constant for the reaction. Integrate both sides of this equation to obtain a relation between x and t

if a = b

A simple pendulum is made from a 0.65-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released , how much time elapses before it attains its greatest speed?

Consider supersonic airflow approaching the nose of a two-dimensional wedge and experiencing an oblique shock. Under what conditions does an oblique shock detach from the nose of the wedge and form a bow wave? What is the numerical value of the shock angle of the detached shock at the nose?

Use the Root Test to determine the convergence or divergence of the series.

$$Σ_(n=1)^∞ (n-2 / 5n+1)^n$$

Consider a population that grows according to the logistic growth model with growth parameter r(r>1). Find

$$p_0$$

in terms of r so that the population is constant.

Find the inverse of the function.

$$f ( x ) = \frac { 2 x + 1 } { 3 }$$

Determine the Laplace transform of the given function f.

$$f ( t ) = \cos t\ u _ { \pi } ( t ).$$

A chemist wants to produce 12.00 g of barium sulfate by reacting a 0.600 M

$$\mathrm { BaCl } _ { 2 }$$

solution with excess

$$\mathrm { H } _ { 2 } \mathrm { SO } _ { 4 }$$

, as shown in the reaction below. What volume of the

$$\mathrm { BaCl } _ { 2 }$$

solution should be used?

$$\mathrm { BaCl } _ { 2 } + \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 } \rightarrow \mathrm { BaSO } _ { 4 } + 2 \mathrm { HCl }$$

(a) What Is a feedback loop? (b) Give three examples of feedback loops in Earth’s climate system.

The substance chlorine monoxide, ClO(g), is important in atmospheric processes th at lead to depletion of the ozone layer. The ClO molecule has an experim ental dipole moment of 1.24 D, and the Cl - O bond length is

$$1.60 \dot {A.}$$

Based on the electron egativities of the elements, which atom would you expect to have a partial negative charge in the CIO molecule?

Write the chemical formula for each of the following compounds: (a) Lanthanum(III) sulfide, (b) Cesium sulfate, (c) Dinitrogen trioxide, (d) Iodine pentafluoride, (e) Chromium(III) sulfate, (f) Potassium permanganate

If f is continuous on [-1, 1], show that

$$\int_0^{\pi/2}f\left(\cos x\right)dx=\int_0^{\pi/2}f\left(\sin x\right)dx=\frac{1}{2}\int_0^{\pi}f\left(\sin x\right)dx.$$