Chapter 1

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Find each principal root without using your calculator. $$\sqrt{49}$$

Three resistors, having resistances of \(4.98 \times 10^{5} \Omega, 2.47 \times 10^{4} \Omega,\) and \(\left.9.27 \times 10^{6} \Omega, \text { are wired in series (Fig. } 1-10\right) .\) Find the total resistance, using the formula \(R=R_{1}+R_{2}+R_{3}\)

How many liters of alcohol are contained in 455 liters of a gasohol mixture that is \(5.5 \%\) alcohol by volume?

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Find each principal root without using your calculator. $$\sqrt[3]{-27}$$

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Find each principal root without using your calculator. $$\sqrt[3]{-8}$$

Find the power in watts dissipated in a resistor if a current \(I\) of \(3.75 \times 10^{-3} \mathrm{A}\) produces a voltage drop V of \(7.24 \times 10^{-4} \mathrm{V}\) across the resistor. Use the formula \(P=V I\)

A solar collector, Fig. \(1-18,\) has an area of 8834 square inches. Convert this to square meters.

Writing: We said, "Of all the mathematical topics we cover in this text, probably the one most used in everyday life is percentage." Do you agree? Write a few paragraphs saying if you agree or not, and back your reasons up with specific examples from personal experience.

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Find each principal root without using your calculator. $$\sqrt[5]{-32}$$

The voltage across an \(8.35 \times 10^{5} \Omega\) resistor is \(2.95 \times 10^{-3} \mathrm{V} .\) Find the power dissipated in the resistor, using the formula \(P=V^{2} / R\)

The volume of a balloon, Fig. \(1-19,\) is 8360 cubic feet. Convert this to cubic inches.

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt{49.2}$$

Perform the following computations. Display your answer in scientific notation. Three capacitors, \(8.26 \times 10^{-6}\) farad \((\mathrm{F}), 1.38 \times 10^{-7} \mathrm{F},\) and \(5.93 \times 10^{-5} \mathrm{F}\) are wired in parallel. Find the equivalent capacitance using the formula \(C=C_{1}+C_{2}+C_{3}\)

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt{1.863}$$

A wire \(4.75 \times 10^{3} \mathrm{cm}\) long when loaded is seen to stretch \(9.55 \times 10^{-2} \mathrm{cm} .\) Find the strain in the wire, using the formula strain \(=\) elongation \(\div\) length.

An airplane is cruising at a specd of 785 miles per hour. Convert this speed to kilometers per hour.

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt[3]{88.3}$$

Writing: Study your calculator and its manual specifically on the different display formats (normal, scientific notation, and so forth). List the different formats available to you and explain the diferences between them. Write a few lines explaining how to switch from one format to another.

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt{772}$$

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt{3875}$$

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt[3]{7295}$$

Evaluate each expression. Retain the proper number of significant digits in your answer. Roots Evaluate each radical by calculator, retaining the proper number of digits in your answer: $$\sqrt[3]{-2.774}$$

Evaluate each expression. Retain the proper number of significant digits in your answer. Applications of Roots. The period \(T\) (time for one swing) of a simple pendulum (Fig. \(1-8\) ) \(2.55 \mathrm{ft}\) long is $$T=2 \pi \sqrt{\frac{2.55}{32.0}} \text { seconds }$$ Evaluate \(T\)

Evaluate each expression. Retain the proper number of significant digits in your answer. Applications of Roots. The magnitude \(Z\) of the impedance in a circuit having a resistance of \(3540 \Omega\) and a reactance of \(2750 \Omega\) is $$Z=\sqrt{(3540)^{2}+(2750)^{2}} \text { ohms }$$ Find \(Z\)

Evaluate each expression. Retain the proper number of significant digits in your answer. Applications of Roots. The geometric mean \(B\) between 3.75 and 9.83 is $$B=\sqrt{(3.75)(9.83)}$$ Evaluate \(B\)