SECTION A.1 Algebra Essentials A13 136. Perimeter of an Equilateral Triangle The perimeter P of an equilateral triangle is 3 times the length x of one side. 137. Volume of a Sphere The volume V of a sphere is 4 3 times π times the cube of the radius r. r 138. Surface Area of a Sphere The surface area S of a sphere is 4 times π times the square of the radius r. 139. Volume of a Cube The volume V of a cube is the cube of the length x of a side. x x x 140. Surface Area of a Cube The surface area S of a cube is 6 times the square of the length x of a side. 141. Manufacturing Cost The weekly production cost C of manufacturing x watches is given by the formula C x 4000 2 , = + where the variable C is in dollars. (a) What is the cost of producing 1000 watches? (b) What is the cost of producing 2000 watches? 142. Balancing a Checking Account At the beginning of the month, Mike had a balance of $210 in his checking account. During the next month, he deposited $80, made an ATM withdrawal for $120, made another deposit of $25, and made two electronic payments: one for $60 and the other for $32. He was also assessed a monthly service charge of $5. What was his balance at the end of the month? In Problems 143 and 144, write an inequality using an absolute value to describe each statement. 143. x is at least 6 units from 4. 144. x is more than 5 units from 2. 145. U.S. Voltage In the United States, normal household voltage is 110 volts. It is acceptable for the actual voltage x to differ from normal by at most 5 volts. A formula that describes this is x 110 5 − ≤ (a) Show that a voltage of 108 volts is acceptable. (b) Show that a voltage of 104 volts is not acceptable. 146. Foreign Voltage In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is x 220 8 − ≤ (a) Show that a voltage of 214 volts is acceptable. (b) Show that a voltage of 209 volts is not acceptable. 147. Making Precision Ball Bearings The FireBall Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within 0.01 cm of this stated radius are acceptable. If x is the radius of a ball bearing, a formula describing this situation is x 3 0.01 − ≤ (a) Is a ball bearing of radius x 2.999 = acceptable? (b) Is a ball bearing of radius x 2.89 = acceptable? 148. Body Temperature Normal human body temperature is 98.6 F. ° A temperature x that differs from normal by at least 1.5 F° is considered unhealthy. A formula that describes this is x 98.6 1.5 − ≥ (a) Show that a temperature of 97 F° is unhealthy. (b) Show that a temperature of 100 F° is not unhealthy. 149. Does 1 3 equal 0.333? If not, which is larger? By how much? 150. Does 2 3 equal 0.666? If not, which is larger? By how much? Explaining Concepts 151. Is there a positive real number “closest” to 0? 152. Number game I’m thinking of a number! It lies between 1 and 10; its square is rational and lies between 1 and 10. The number is larger than .π Correct to two decimal places (that is, truncated to two decimal places), name the number. Now think of your own number, describe it, and challenge a fellow student to name it. 153. Write a brief paragraph that illustrates the similarities and differences between “less than” ( )< and “less than or equal to” . ( )≤ 154. Give a reason why the statement 5 8 < is true.
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