Exam 2: Equations and Inequalities

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 88% of V ₀ . Round the answer to the nearest thousandth of a second.

Solve the equation by factoring.

Find the values of x and y, where x and y are real numbers.

Write the expression in the form , where a and b are real numbers.

Find the values of x and y, where x and y are real numbers.

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.20 per ft ² , determine the width of the garden that can be enclosed for $403.20.

Find the solutions of the equation

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 92% of V ₀ . Round the answer to the nearest thousandth of a second.

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 4 feet, but the height h is yet to be determined. If 25 ft ² of glass is to be used, find the height h.

Solve the inequality.

Express the inequality as an interval.

Solve the equation.

Solve the equation by using the special quadratic equation.

The speed of the current in a stream is 2.2 mi/hr. It takes a canoeist 40 minutes longer to paddle 1.9 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

Solve the equation by factoring.

Find the values of x and y, where x and y are real numbers.

Write the expression in the form , where a and b are real numbers.

Solve the formula for L.

Solve the equation

Solve the equation.