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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Use the given figure, translation vectors v and w, and reflection lines l and m to construct the indicated glide reflections. Show the triangle in the positions both before and after the glide
Use the given figure and rotation point P to construct the indicated rotations. Show the trapezoid in the positions both before and after the rotation.Construct a 270° rotation of parallelogram ABCD
Use the given figure and rotation point P to construct the indicated rotations. Show the trapezoid in the positions both before and after the rotation.Construct a 180° rotation of parallelogram ABCD
Use the given figure and rotation point P to construct the indicated rotations. Show the trapezoid in the positions both before and after the rotation.Construct a 90° rotation of parallelogram ABCD
Use translation vectors v and w to construct the indicated translations. Show the rectangle in the positions both before and after the translation.Construct the translation of rectangle ABCD using
Use translation vectors v and w to construct the indicated translations. Show the rectangle in the positions both before and after the translation.Construct the translation of rectangle ABCD using
Use the given triangle and reflection lines to construct the indicated reflections. Show the triangle in the positions both before and after the reflection.Construct the reflection of triangle ABC
Use the given triangle and reflection lines to construct the indicated reflections. Show the triangle in the positions both before and after the reflection.Construct the reflection of triangle ABC
Dale has a water trough whose ends are trapezoids and whose sides are rectangles, as illustrated. He is afraid that the base it is sitting on will not support the weight of the trough when it is
Determine the volume of the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. E 7 in. -14 in.
Determine the volume of the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 9 cm 4 ст-
Determine the volume of the figure. 5 ft 17 ft 5 ft 6 ft
Determine the volume of the figure. 12 m 9 m 8 m -15 m·
Determine(a) The volume. (b) The surface area of the figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 5 yd
Determine(a) The volume. (b) The surface area of the figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 12 mm 16 mm
Determine(a) The volume. (b) The surface area of the figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 9 ft 13 ft
Determine(a) The volume. (b) The surface area of the figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 5 cm 11 cm 3 cm
Determine the total cost of covering a rectangular 14-ft by 16-ft kitchen floor with hardwood flooring. The cost of the flooring selected is $9.75 per square foot.
Determine the shaded area. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 12 yd б yd 12 yd
Determine the shaded area. When appropriate, use the π key on your calculator and round youranswer to the nearest hundredth. 10 m
Determine (a) The area.(b) The circumference of the circle.Use the π key on a calculator and round your answer to the nearest hundredth. 7 ft
Determine (a) The area (b) The perimeter of the figure. 3 km 4 km
Determine (a) The area (b) The perimeter of the figure. |7 in. 9 in. 12 in.
Determine (a) The area (b) The perimeter of the figure. 5 m 5 m 3 m 6 m 3 m
Determine (a) The area (b) The perimeter of the figure. 9 mi 11 mi
Determine the sum of the measures of the interior angles of an octagon.
In the following figure, l1 and l2 are parallel lines. Determine m∡1 through m∡6. 43° 117° >4 6, 5, 3.
Use the similar triangles ABC and A'B'C shown to determine the following.m∡ABC 6 in. B' 3.4 in. (88° 300 A' Уа A -4 in. → - 8 in.
Use the similar triangles ABC and A'B'C shown to determine the following.m∡BAC 6 in. B' 3.4 in. (88° 300 A' Уа A -4 in. → - 8 in.
Use the similar triangles ABC and A'B'C shown to determine the following.The length of A̅’B̅’ 6 in. B' 3.4 in. (88° 300 A' Уа A -4 in. → - 8 in.
Use the similar triangles ABC and A'B'C shown to determine the following.The length of B̅C̅ 6 in. B' 3.4 in. (88° 300 A' Уа A -4 in. → - 8 in.
m∡B = 100.58. Determine the measure of the supplement of ∡B.
m∡A = 27.68. Determine the measure of the complement of ∡A.
Use the figure shown to determine the following. B D Н. °CF N°CG
Use the figure shown to determine the following. B D Н. НІ EG
Use the figure shown to determine the following. B D Н. BH U `HB НВ
Use the figure shown to determine the following. B̅F̅ ∪ F̅C̅ ∪ B̅C̅ B D Н.
Use the figure shown to determine the following. ∡CBF ∩ ∡BCF B D Н.
Use the figure shown to determine the following. B D Н. BF U BC
State the theorem concerning the sum of the measures of the angles of a triangle in(a) Euclidean geometry.(b) Hyperbolic geometry.(c) Elliptical geometry
List at least five natural forms that appear chaotic that we can study using fractals.
List the three types of curvature of space and the types of geometry that correspond to them.
What do we mean when we say that no one axiomatic system of geometry is “best”?
In forming the Koch snowflake in Figure 8.104, the perimeter becomes greater at each step in the process. If each side of the original triangle is 1 unit, a general formula for the perimeter, L, of
(a) Develop a fractal by beginning with a square and replacing each sidewith a. Repeat this process twice. (b) If you continue this process, will the fractal’s perimeter be finite or infinite?
Use this fractal-like figure as a guide in constructing fractal-like figures with the letter given. Show three steps, as is done here.W мУ M м М
Use this fractal-like figure as a guide in constructing fractal-like figures with the letter given. Show three steps, as is done here.H мУ M м М
Use this fractal-like figure as a guide in constructing fractal-like figures with the letter given. Show three steps, as is done here.E мУ M м М
Use this fractal-like figure as a guide in constructing fractal-like figures with the letter given. Show three steps, as is done here.I мУ M м М
Fill in the blanks with an appropriate word, phrase, or symbol(s).The study of chaotic processes is known as __________ theory.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The shortest and least-curved arc between two points on a curved surface is a(n) __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A model for hyperbolic geometry is a(n) __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A model for elliptical geometry is a(n) __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A model for Euclidean geometry is a(n) __________.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The fifth axiom of hyperbolic geometry states that given a line and a point not on the line, __________ or more lines can be drawn
Fill in the blanks with an appropriate word, phrase, or symbol(s).The fifth axiom of elliptical geometry states that given a line and a point not on the line, __________ line can be drawn through the
Fill in the blanks with an appropriate word, phrase, or symbol(s).The fifth axiom of Euclidean geometry states that given a line and a point not on the line, one and only one line can be drawn
Take a strip of paper, make one whole twist and another half twist, and then tape the ends together. Test by a method of your choice to determine whether this has the same properties as a Möbius
(a) Take a strip of paper, give it one full twist, and connect the ends. Is the result a Möbius strip with only one side? Explain. No, it has an inside and an outside.(b) Determine the number of
Make a Möbius strip. Cut it one-third of the way from the edge, as in Experiment. You should get two loops, one going through the other. Determine whether either (or both) of these loops is itself a
How many separate strips are obtained in Experiment 4?Experiment 4:Make a Möbius strip. Make a small slit at a point about one-third of the width of the strip. Cut along the strip, keeping the
How many separate strips are obtained in Experiment 3?Experiment 3:Make a Möbius strip. Use scissors to make a small slit in the middle of the strip. Starting at the slit, cut along the strip,
Use the result of Experiment 2 to find the number of surfaces on a Möbius strip.Experiment 2:Make a Möbius strip. Place the tip of a felt-tip pen on the surface of the strip (Fig. 8.87). Pull the
Use the result of Experiment 1 to find the number of edges on a Möbius strip.Experiment 1:Make a Möbius strip using a strip of paper and tape as illustrated in Fig. 8.85. Place the point of a
Name at least three objects not mentioned in this section that have(a) Genus 0. (b) Genus 1. (c) Genus 2. (d) Genus 3 or more.
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.” SODA
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Give the genus of the object. If the object has a genus larger than 5, write “larger than 5.”
Determine if the point is inside or outside the curve.Point D B
Determine if the point is inside or outside the curve.Point C B
Determine if the point is inside or outside the curve.Point B B
Determine if the point is inside or outside the curve.Point A B
Determine whether point Bin Fig. 8.95(d) is inside or out-side the Jordan curve.Figure 89.5(d)
Determine whether point A in Fig. 8.95(d) is inside or outside the Jordan curve.Figure 89.5(d)
Maps show certain areas of the United States, Canada, and Mexico. Shade in the states (or provinces) using a maximum of four colors so that no two states (or provinces) with a common border have the
Maps show certain areas of the United States, Canada, and Mexico. Shade in the states (or provinces) using a maximum of four colors so that no two states (or provinces) with a common border have the
Maps show certain areas of the United States, Canada, and Mexico. Shade in the states (or provinces) using a maximum of four colors so that no two states (or provinces) with a common border have the
Maps show certain areas of the United States, Canada, and Mexico. Shade in the states (or provinces) using a maximum of four colors so that no two states (or provinces) with a common border have the
Color the map by using a maximum of four colors so that no two regions with a common border have the same color. 12/3 4 10
Color the map by using a maximum of four colors so that no two regions with a common border have the same color. 3 4 5 6. 8.
Color the map by using a maximum of four colors so that no two regions with a common border have the same color. 3 6. 7. (5 6,
Color the map by using a maximum of four colors so that no two regions with a common border have the same color. 2 3 4
Fill in the blanks with an appropriate word, phrase, or symbol(s).The number of holes that go through an object determines the _________ of the object.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A topological object that can be thought of as a circle twisted out of shape is a(n) ___________ curve.
Fill in the blanks with an appropriate word, phrase, or symbol(s).If you color a map of the United States, the maximum number of colors needed so that no two states that share a common border have
Fill in the blanks with an appropriate word, phrase, or symbol(s).A topological object that resembles a bottle but has only one side is a(n) __________ bottle.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A one-sided, one-edged surface is a(n) ___________ strip.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Because it deals with bending and stretching of geometric figures, topology is sometimes referred to as _________ sheet geometry.
Change all the measurements in the cookie recipe on page 431 to metric units. Do not forget pan size, temperature, and size of cookies.Magic Cookie Bars1/2 C graham cracker crumbs12 oz nuts8 oz
A basement is to be 50 ft long, 30 ft wide, and 8 ft high. How much dirt will have to be removed when this basement is built? Answer in cubic meters.When necessary round your answers to the nearest
Convert each temperature as indicated. When appropriate, give your answer to the nearest tenth of a degree.15°C = _________ °F.

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