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8th Edition

Charles P. McKeague + 1 other

Publisher: Cengage Learning

ISBN: 9781305652224

Chapter 1.1, Problem 71PS

Textbook Problem

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Geometry: Characteristics of a Cube The object shown in Figure 27 is a cube (all edges are equal in length). Use this diagram for Problems 69 through 72.

Figure 27

If the length of each edge of the cube is unknown, we can represent it with the variable *x*. Then we can write formulas for the lengths of any of the diagonals. Finish each of the following statements:

a. If the length of each edge of a cube is *x,* then the length of the diagonal of any face of the cube will be _______.

b. If the length of each edge of a cube is *x,* then the length of any diagonal that passes through the center of the cube will be________.

**a.**

To determine

To fill in the blanks of the given statement.

**Given:**

The statement “If the length of each edge of a cube is x, then the length of the diagonal of any face of the cube will be

**Calculation:**

Construct the right triangle CDH as shown below.

The triangle CDH is

**b.**

To determine

To fill in the blanks of the given statement.

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Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Indicate which of the angles below are acute...Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Problems 17 through 22 refer to Figure 19....Ch. 1.1 - Figure 20 shows a walkway with a handrail. Angle ...Ch. 1.1 - Figure 20 shows a walkway with a handrail. Angle ...Ch. 1.1 - Figure 20 shows a walkway with a handrail. Angle ...Ch. 1.1 - Figure 20 shows a walkway with a handrail. Angle ...Ch. 1.1 - Rotating Light A searchlight rotates through one...Ch. 1.1 - Rotation of Earth It takes the earth 24 hours to...Ch. 1.1 - Geometry An isosceles triangle is a triangle in...Ch. 1.1 - Geometry An equilateral triangle is a triangle in...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Problems 31 through 36 refer to right triangle ABC...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Solve for x in each of the following right...Ch. 1.1 - Problems 43 and 44 refer to Figure 21. Figure 21...Ch. 1.1 - Problems 43 and 44 refer to Figure 21. Figure 21...Ch. 1.1 - Problems 45 and 46 refer to Figure 22, which shows...Ch. 1.1 - Problems 45 and 46 refer to Figure 22, which shows...Ch. 1.1 - Pythagorean Theorem The roof of a house is to...Ch. 1.1 - Surveying A surveyor is attempting to find the...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Find the remaining sides of a 306090 triangle if...Ch. 1.1 - Escalator An escalator in a department store is to...Ch. 1.1 - Escalator What is the length of the escalator in...Ch. 1.1 - Problems 57 and 58 refer to the two-person tent...Ch. 1.1 - Problems 57 and 58 refer to the two-person tent...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Find the remaining sides of a 454590 triangle if...Ch. 1.1 - Distance a Bullet Travels A bullet is tired into...Ch. 1.1 - Time a Bullet Travels If the bullet in Problem 65...Ch. 1.1 - Problems 67 and 68 refer to Figure 26. Figure 26...Ch. 1.1 - Problems 67 and 68 refer to Figure 26. 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Give the reciprocal of each number. yrCh. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use the reciprocal identities for the following...Ch. 1.4 - Use a ratio identity to find tan given the...Ch. 1.4 - Use a ratio identity to find tan given the...Ch. 1.4 - Use a ratio identity to find tan given the...Ch. 1.4 - Use a ratio identity to find tan given the...Ch. 1.4 - For Problems 23 through 26, recall that sin2 means...Ch. 1.4 - For Problems 23 through 26, recall that sin2 means...Ch. 1.4 - For Problems 23 through 26, recall that sin2 means...Ch. 1.4 - For Problems 23 through 26, recall that sin2 means...Ch. 1.4 - For Problems 27 through 30, let sin=12/13, and...Ch. 1.4 - For Problems 27 through 30, let sin=12/13, and...Ch. 1.4 - For Problems 27 through 30, let sin=12/13, and...Ch. 1.4 - 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Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Find the remaining trigonometric ratios of based...Ch. 1.4 - Using your calculator and rounding your answers to...Ch. 1.4 - Using your calculator and rounding your answers to...Ch. 1.4 - Using your calculator and rounding your answers to...Ch. 1.4 - Using your calculator and rounding your answers to...Ch. 1.4 - Recall from algebra that the slope of the line...Ch. 1.4 - Recall from algebra that the slope of the line...Ch. 1.4 - Suppose the angle formed by the line y = 3x and...Ch. 1.4 - Find tan if is the angle formed by the line y =...Ch. 1.4 - Find sec if cos=1/3. a. 22 b. 223 c. 3 d. 324Ch. 1.4 - Use a ratio identity to find tan if cos=23 and...Ch. 1.4 - 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Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Write each of the following in terms of sin and...Ch. 1.5 - Add or subtract as indicated, then simplify if...Ch. 1.5 - Add or subtract as indicated, then simplify if...Ch. 1.5 - Add or subtract as indicated, then simplify if...Ch. 1.5 - Add or subtract as indicated, then simplify if...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Add and subtract as indicated. Then simplify your...Ch. 1.5 - Multiply. (ab)2 (cossin)2Ch. 1.5 - Multiply. (a+1)(a1) (sec+1)(sec1)Ch. 1.5 - Multiply. (a2)(a3) (sin2)(sin3)Ch. 1.5 - Multiply. (a1)(a+6) (cos1)(cos+6)Ch. 1.5 - Multiply. (sin+4)(sin+3)Ch. 1.5 - Multiply. (cos+2)(cos5)Ch. 1.5 - Multiply. (2cos+3)(4cos5)Ch. 1.5 - Multiply. (3sin+4)(5cos+2)Ch. 1.5 - Multiply. (1sin)(1+sin)Ch. 1.5 - Multiply. (1cos)(1+cos)Ch. 1.5 - Multiply. (1tan)(1+tan)Ch. 1.5 - Multiply. (1csc)(1+csc)Ch. 1.5 - Multiply. (sincos)2Ch. 1.5 - Multiply. (cos+sin)2Ch. 1.5 - Multiply. (sin4)2Ch. 1.5 - Multiply. (cos+3)2Ch. 1.5 - Simplify the expression x2+4 as much as possible...Ch. 1.5 - Simplify the expression x2+1 as much as possible...Ch. 1.5 - Simplify the expression 9x2 as much as possible...Ch. 1.5 - Simplify the expression 16x2 as much as possible...Ch. 1.5 - Simplify the expression x236 as much as possible...Ch. 1.5 - Simplify the expression x264 as much as possible...Ch. 1.5 - Simplify the expression 644x2 as much as possible...Ch. 1.5 - Simplify the expression 4x2+16 as much as possible...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Show that each of the following statements is an...Ch. 1.5 - Express tan in terms of sin only. a. sinsin21 b....Ch. 1.5 - Simplify cotcsc. a. cos b. sin c. sec d. tanCh. 1.5 - Simplify x2+16 as much as possible after...Ch. 1.5 - Which of the following is a valid step in proving...Ch. 1 - Find the complement and the supplement of 70.Ch. 1 - Solve for x in the right triangle shown in Figure...Ch. 1 - Referring to Figure 2, find (in order) h, r, y,...Ch. 1 - Figure 3 shows two right triangles drawn at 90 to...Ch. 1 - Through how many degrees does the hour hand of a...Ch. 1 - Find the remaining sides of a 306090 triangle if...Ch. 1 - Escalator An escalator in a department store is to...Ch. 1 - Geometry Find the measure of one of the interior...Ch. 1 - Find the distance between the points (4, â€“2) and...Ch. 1 - Find x so that the distance between (â€“2, 3) and...Ch. 1 - Verify that (12,32) lies on the graph of the unit...Ch. 1 - Find all angles that are coterminal with 150.Ch. 1 - Human Cannonball A human cannonball is shot from a...Ch. 1 - Find sin , cos , and tan for each of the...Ch. 1 - Find sin , cos , and tan for each of the...Ch. 1 - Indicate the two quadrants could terminate in if...Ch. 1 - In which quadrant will lie if csc0 and cos0?Ch. 1 - Find all six trigonometric functions for if the...Ch. 1 - Why is sin 1 for any angle in standard position?Ch. 1 - Find the remaining trigonometric functions of if...Ch. 1 - Find sin and cos if the terminal side of lies...Ch. 1 - If sin=47, find csc.Ch. 1 - If sin=13, find sin3.Ch. 1 - If sec=3 with in QIV, find cos, sin, and tan .Ch. 1 - Expand and simplify (cossin)2.Ch. 1 - Subtract 1sinsin.Ch. 1 - Simplify the expression 4x2 as much as possible...Ch. 1 - Show that each of the following statements is an...Ch. 1 - Show that each of the following statements is an...Ch. 1 - Show that each of the following statements is an...Ch. 1 - The diagram shown in Figure 1 was used by the...Ch. 1 - The second proof, credited to former president...Ch. 1 - For the third proof, consider the two squares...Ch. 1 - Although Pythagoras preceded William Shakespeare...

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