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mathematics
basic technical mathematics

Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions

Find the measures of the indicated angles use Fig. 2.12.∠4 41 = 22 150° 2, Fig. 2.12 3 5 4
Find the area of each triangle.Equilateral triangle of sides 3200 yd
Find the area of each figure.Parallelogram in Fig. 2.61 3.7 m 2.5 m Fig. 2.61 2.7 m
Calculate the indicated areas. All data are accurate to at least two significant digits.Soundings taken across a river channel give the following depths with the corresponding distances from one shoreFind the area of the cross section of the channel using Simpson’s rule. Distance (ft) 0 50 100
Find the perimeter of each triangle.Fig. 2.41(c) 239 cm (c) 415 cm 322 cm
Find the area of each figure.Parallelogram in Fig. 2.62 27.3 in. 12.6 in. Fig. 2.62 14.2 in.
Find the volume or area of each solid figure for the given values.Lateral area of right prism: equilateral triangle base of side 1.092 m,h = 1.025 m
Find the indicated sides of the right triangle shown in Fig. 2.132.a = 0.782, c = 0.885, b = ? a C b Fig. 2.132
Find the area of the circle with the given circumferencec = 40.1 cm
Calculate the indicated areas. All data are accurate to at least two significant digits.The widths of a bell crank are measured at 2.0-in. intervals, as shown in Fig. 2.111. Find the area of the bell crank if the two connector holes are each 2.50 in. in diameter. O 16.2 in. 18.6 in. 19.0 in. 17.8
Find the perimeter of each triangle.Fig. 2.41(d) 0.535 in. (d) 0.862 in. 0.684 in.
Find the measures of the indicated angles use Fig. 2.12.∠5 21 = 22 150⁰ Fig. 2.12 3 5 4
Find the volume or area of each solid figure for the given values.Lateral area of right circular cylinder: diameter = 250 ft, h = 347 ft diameter = 250 ft, h = 347 ft
Refer to Fig. 2.86, where AB is a diameter, TB is a tangent line at B, and ∠ABC = 65°. Determine the indicated angles.∠CBT Fig. 2.86 A 0 B с T
Find the area of the circle with the given circumferencec = 147 m
Find the area of each figure.Trapezoid in Fig. 2.63 0.362 ft 0.730 ft 0.298 ft 0.612 ft Fig. 2.63 0.440 ft
Calculate the area of the circle by the indicated method.The lengths of parallel chords of a circle that are 0.250 in. apart are given in the following table. The diameter of the circle is 2.000 in. The distance shown is the distance from one end of a diameter.Using the formula A = πr2 , the area
Find the perimeter or area of the indicated figure.Perimeter: equilateral triangle of side 8.5 mm
Find the measures of the angles in Fig. 2.13.∠1 A C- 1 5 62° 6 AB || CD 3 Fig. 2.13 B D
Find the volume or area of each solid figure for the given values.Volume of hemisphere: diameter = 0.65 yd
Find the perimeter of each triangle.An equilateral triangle of sides 21.5 cm
Find the perimeter or area of the indicated figure.Perimeter: rhombus of side 15.2 in.
Find the volume or area of each solid figure for the given values.Volume of regular pyramid: square base of side 22.4 m, s = 14.2 m
Refer to the circle with center at O in Fig. 2.85. Identify the following.(a) Two Perpendicular lines(b) An isosceles triangle A B E Fig. 2.85 0 C D
Determine ∠A in the indicated figures.Fig. 2.40 (c) B 4 66° A (c) 4 C
Identify the indicated angles and sides in Fig. 2.10.The straight angleFigure 2.10 A- E B D -C
Calculate the indicated areas. All data are accurate to at least two significant digits.The widths of a kidney-shaped swimming pool were measured at 2.0-m intervals, as shown in Fig. 2.107. Calculate the surface area of the pool, using the trapezoidal rule.Fig. 2.107 0.0 m 6.4 m 2.0 m 7.4 m 7.0
Use Fig. 2.131. Determine the indicated angles.∠CGEFig. 2.131. ABICD C A 148⁰ E I H G F D B
Find the volume or area of each solid figure for the given values.Total surface area of right circular cylinder: r = 689 mm, h = 233 mm r = 689 mm, h = 233 mm
Determine ∠A in the indicated figures.Fig. 2.40 (d) A 3 C 110° (d) 3 B
Refer to the circle with center at O in Fig. 2.85. Identify the following.(a) A segment(b) A sector with an acute central angle A B E Fig. 2.85 0 C D
Use Fig. 2.131. Determine the indicated angles.∠EGFFig. 2.131. ABICD C A 148⁰ E I H G F D B
Identify the indicated angles and sides in Fig. 2.10.The obtuse angleFigure 2.10 A- E B D -C
Find the surface area of a tennis ball whose circumference is 21.0 cm.
Calculate the indicated areas. All data are accurate to at least two significant digits.Calculate the surface area of the swimming pool in Fig. 2.107, using Simpson’s rule.Fig. 2.107 0.0 m 6.4 m 2.0 m 7.4 m 7.0 m 6.1 m 5.2 m 5.0 m 5.1 m 0.0 m
Find the volume or area of each solid figure for the given values.Area of sphere: r = 0.067 in.
Find the perimeter of each figure.Rectangle: l = 142 cm, w = 126 cm
Identify the indicated angles and sides in Fig. 2.10.If ∠CBD = 65°, find its complement.Figure 2.10 A- E B D -C
Find the perimeter of each figure.Parallelogram in Fig. 2.61 3.7 m 2.5 m Fig. 2.61 2.7 m
In Fig. 2.148, find ∠1. A 64° 0 C Fig.2.148 2 B
Calculate the indicated areas. All data are accurate to at least two significant digits.The widths of a cross section of an airplane wing are measured at 1.00-ft intervals, as shown in Fig. 2.108. Calculate the area of the cross section, using Simpson’s rule.Fig. 2.108 0.52 ft- 0.00 ft 0.75
Find the volume of a right circular cone of radius 2.08 m and height 1.78 m.
Find the volume or area of each solid figure for the given values.Volume of sphere: r = 1.037 yd
Identify the indicated angles and sides in Fig. 2.10.If ∠CBD = 65°, find its supplement.Figure 2.10 A- E B D -C
Find the circumference of the circle with the given radius or diameter.r = 275 ft
Find the perimeter of each figure.Parallelogram in Fig. 2.62 27.3 in. 12.6 in. Fig. 2.62 14.2 in.
Calculate the indicated areas. All data are accurate to at least two significant digits.Calculate the area of the cross section of the airplane wing inFig. 2.108, using the trapezoidal rule.Fig. 2.108 0.52 ft- 0.00 ft 0.75 ft- 1.00 ft
Use Fig. 2.131. Determine the indicated angles.∠EGIFig. 2.131. ABICD C A 148⁰ E I H G F D B
Find the area of each triangle.Fig. 2.41(b)Figure 2.41(b) 9.62 mm 6 22 (b) 16.0 mm
In Fig. 2.148, find ∠2. A 64° 0 C Fig.2.148 2 B
Find the volume or area of each solid figure for the given values.Volume of right circular cone: r = 25.1 m, h = 5.66 m
Find the indicated sides of the right triangle shown in Fig. 2.132.a = 12, b = 35, c = ? a C b Fig. 2.132
Find the circumference of the circle with the given radius or diameter.r = 0.563 m
Find the area of each triangle.Fig. 2.41(c)Figure 2.41(c) 239 cm 415 cm 322 cm
Find the perimeter of each figure.Trapezoid in Fig. 2.63 0.362 ft 0.730 ft 0.298 ft 0.612 ft Fig. 2.63 0.440 ft
Calculate the indicated areas. All data are accurate to at least two significant digits.Using aerial photography, the widths of an area burned by a forest fire were measured at 0.5-mi intervals, as shown in the following table:Determine the area burned by the fire by using the trapezoidal rule.
Find the indicated sides of the right triangle shown in Fig. 2.132.a = 14, b = 48, c = ? a C b Fig. 2.132
Identify the indicated angles and sides in Fig. 2.10.The sides adjacent to ∠DBCFigure 2.10 A- E B D -C
Find the volume or area of each solid figure for the given values.Lateral area of right circular cone: r = 78.0 cm, s = 83.8 cm
In Fig. 2.149, find the perimeter of the figure shown. It is a square with a semicircle removed. 2.25 cm Fig. 2.149
Find the area of each triangle.Fig. 2.41(d)Figure 2.41(d) 0.535 in. (d) 0.862 in. 0.684 in.
Identify the indicated angles and sides in Fig. 2.10.The acute angle adjacent to ∠DBC.Figure 2.10 A- E B D -C
Find the circumference of the circle with the given radius or diameter.d = 23.1 mm
Find the perimeter of each figure.Trapezoid in Fig. 2.64 272 cm 392 cm 201 cm 672 cm Fig. 2.64 223 cm
Find the indicated sides of the right triangle shown in Fig. 2.132.a = 400, b = 580, c = ? a C b Fig. 2.132
Calculate the indicated areas. All data are accurate to at least two significant digits.Find the area burned by the forest fire of Exercise 11, using Simpson’s rule.Data from Exercises 11Using aerial photography, the widths of an area burned by a forest fire were measured at 0.5-mi intervals, as
Find the volume or area of each solid figure for the given values.Lateral area of regular pyramid: p = 345 ft, s = 272 ft
In Fig. 2.149, find the area of the figure shown. 2.25 cm Fig. 2.149
Find the circumference of the circle with the given radius or diameter.d = 8.2 in.
Answer the given questions related to the indicated examples of this section.In Example 1, if widths of the face of the same cam were given at 1.00-cm intervals (five more widths would be included), from the methods of this section, what is probably the most accurate way of finding the area?
Answer the given questions about the indicated examples of this section.In Example 2, what is the measure of ∠ABE in Fig. 2.2(a)?Data from Example 2In Fig. 2.2(a), lines AC and DE are perpendicular (which is shown as AC ⊥ DE) because they meet in a right angle (again, shown as⊾) at B.
In Fig. 2.146, determine ∠1.Fig. 2.146 C- A- 52° 2 AB || CD -D B
Answer the given questions about the indicated examples of this section.In Example 1, if the length is doubled and the thickness is tripled, by what factor is the volume changed?Data from Example 1What volume of concrete is needed for a driveway 25.0 m long, 2.75 m wide, and 0.100 m thick?The
Answer the given questions about the indicated examples of this section.In Example 1, if ∠AOB = 72° in Fig. 2.78, then what is the measure of ∠OAB?Data from Example 1In Fig. 2.78, O is the center of the circle, and AB is tangent at B. If ∠OAB = 25°, find ∠AOB.Because the center is O, OB
Determine each of the following as being either true or false. If it is false, explain why.In Fig. 2.6, ∠AOC is the complement of ∠COB. C A Vertical angles 0 Fig. 2.6 B D
Find the volume or area of each solid figure for the given values.Volume of regular pyramid: square base of side 0.76 in., h = 1.30 in.
Answer the given questions about the indicated examples of this section.In Example 2, if ∠1 = 70° and ∠5 = 45° in Fig. 2.25, what is the measure of ∠2?Data from Example 2Fig. 2.25, because ∠1, ∠2, and ∠3 constitute a straight angle, ∠1 + ∠2 + ∠3 = 180°Also, by noting alternate
Find the area of each figure.Square: s = 6.4 mm
Make the given changes in the indicated examples of this section and then solve the given problems.In Example 1, interchange the lengths of b1 and b2 in Fig. 2.53(e). What type of quadrilateral is the resulting figure?Data from Example 1A parallelogram is shown in Fig. 2.53(a). Opposite sides a are
Find the area of the circle with the given radius or diameter.r = 0.0952 yd
Answer the given questions about the indicated examples of this section.In the first line of Example 2, if “diameter” is changed to “radius,” what are the results?Data from Example 2A circular oil spill has a diameter of 2.4 km. It is to be enclosed within special flexible tubing. What is
Perform the indicated calculations.A computer’s memory is 5.25 ×1013 bytes, and that of a model 30 years older is 6.4 ×104 bytes. What is the ratio of the newer computer’s memory to the older computer’s memory?
Answer the given questions about the indicated examples of this section.In Example 5, change 16.2 in. to 61.2 in. What is the answer?Data from Example 5Find the areas of the triangles in Fig. 2.31(a) and Fig. 2.31(b).Even though the triangles are of different shapes, the base b of each is 16.2 in.,
Answer the given questions related to the indicated examples of this section.In Example 4, if you use only the data from the south end of (in km) 0, 3.00, 6.00, 9.00, 12.0, and 15.0, would you choose the trapezoidal rule or Simpson’s rule to calculate the area? Explain. Do not calculate the area
In Fig. 2.146, determine ∠2.Fig. 2.146 C- A- 52° 2 AB || CD -D B
Answer the given questions about the indicated examples of this section.In Example 2, if the value of the slant height s = 17.5 cm is given instead of the height, what is the height?Data from Example 2How many square centimeters of sheet metal are required to make a protective cone shaped cover if
Answer the given questions about the indicated examples of this section.In Example 3(b), if ∠POR = 35° in Fig. 2.4, what is the measure of ∠QOR?Data from Example 3(b)In Fig. 2.4, we see that ∠POQ is a right angle, or ∠POQ = 90°. Because ∠POR + ∠ROQ = ∠POQ = 90°, ∠POR is the
Make the given changes in the indicated examples of this section and then solve the given problems.In Example 2, change the equilateral triangle of side 21 in. to a square of side 21 in. and then find the length of molding.Data from Example 2 An architect designs a room with a rectangular
Make the given changes in the indicated examples of this section and then solve the given problems.In Example 3, change the dimension of 45 ft to 55 ft in each figure and then find the area.Data from Example 3A city park is designed with lawn areas in the shape of a right triangle, a parallelogram,
Answer the given questions related to Fig. 2.105.Which should be more accurate for finding the area, the trapezoidal rule or Simpson’s rule? Explain.Fig. 2.105 1 I I I I I I I I
Answer the given questions about the indicated examples of this section.In Example 3, if the machine part is the unshaded part (rather than the shaded part) of Fig. 2.80, what are the results?Data from Example 3A machine part is a square of side 3.25 in. with a quarter-circle removed (see Fig.
In Example 2, if the radius is halved and the height is doubled, what is the volume?Data from Example 2Answer the given questions about the indicated examples of this section.How many square centimeters of sheet metal are required to make a protective cone shaped cover if the radius is 11.9 cm and
Answer the given questions about the indicated examples of this section.In Example 7, change 2.65 m to 6.25 m. What is the answer?Data from Example 7A pole is perpendicular to the level ground around it. A guy wire is attached 3.20 m up the pole and at a point on the ground, 2.65 m from the pole.
Determine each of the following as being either true or false. If it is false, explain why.A triangle of sides 9, 12, and 15 is a right triangle.
In Example 4, how many different pairs of adjacent angles are there in Fig. 2.6?Data from Example 4In Fig. 2.6, lines AB and CD intersect at point O. Here, ∠AOC and ∠BOD are vertical angles, and they are equal. Also, ∠BOC and ∠AOD are vertical angles and are equal.
Answer the given questions about the indicated examples of this section.In Example 9, interchange 4.0 ft and 3.0 ft. What is the answer?Data from Example 9On level ground, a silo casts a shadow 24 ft long. At the same time, a nearby vertical pole 4.0 ft high casts a shadow 3.0 ft long. How tall is
In Example 5, if the segments of 6.50 ft and 7.75 ft are interchanged,(a) What is the answer,(b) Is the beam along which x is measured more nearly vertical or more nearly horizontal?Data from Example 5In Fig. 2.9, part of the beam structure within a building is shown. The vertical beams are
A tree is 8.0 ft high and casts a shadow 10.0 ft long. At the same time, a telephone pole casts a shadow 25.0 ft long. How tall is the pole?
In Example 4, change 2.0 mm to 3.0 mm, and then solve.Data from Example 4The length of a rectangular computer chip is 2.0 mm longer than its width. Find the dimensions of the chip if its perimeter is 26.4 mm.Because the dimensions, the length and the width, are required, let w = the width of the
Answer the given questions related to Fig. 2.105.If the trapezoidal rule is used to find the area, will the result probably be too high, about right, or too little? Explain.Fig. 2.105 1 I I I I I I I I

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