Points W and X are chosen on the side AB of triangle ABC and points Y...
Points W and X are chosen on the side AB of triangle ABC and points Y and Z are chosen on side AC. Suppose that cr(A,W,X,B)=cr(A,Y,Z,C) and that WY is parallel to XZ. Prove that XZ is parallel to BC. Hint: let T be the point where the parallel to XZ through B meets line AC. Note that neither a nor Y can lie on segment TC and use excercise 3C.2 to show that T is C.
cr=cross ratio
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Points W and X are chosen on the side AB of triangle ABC and
points Y...
520. Given triangle ABC, let F be the point where segment BC meets the bisector of angle BAC, Draw the line through B that is parallel to segment AF, and let E be the point where this parallel me...
520. Given triangle ABC, let F be the point where segment BC meets the bisector of angle BAC, Draw the line through B that is parallel to segment AF, and let E be the point where this parallel meets the extension of segment CA. (a) Find the four congruent angles in your diagram. (b) How are the lengths EA, AC, BF, and FC related? (c) The Angle-Bisector Theorem: How are the lengths AB, AC, BF, and FC related?
520. Given...
1. Consider the isosceles triangle ABC, with AB = AC, and BAC = 20. Choose points...
1. Consider the isosceles triangle ABC, with AB = AC, and BAC = 20. Choose points E, D on the sides AB, AC, respectively, so that ZCBD = 60', and BCE = 50'. We will find LEDB. (i) Bring the parallel DF to BC, with F on AB. Connect points and F. and let K be the intersection of BD and CF. Show that DFBC is an isosceles trapezium. Mark all its angles. (ii) What type of triangles are BKC...
Suppose that ABC is an equilateral triangle with all sides of length 1 unit. We extend side AB by 1 unit beyond B to get...
Suppose that ABC is an equilateral triangle with all sides of length 1 unit. We extend side AB by 1 unit beyond B to get P, we extend BC by 1 unit beyond C to get Q and AC beyond A to get R. Compute the length of the sides in triangle PQR.
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C"...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
Q1. A weight of W is supported by three cables AD, BD and DE as shown below. Cables AD and BD are attached to a ver...
Q1. A weight of W is supported by three cables AD, BD and DE as shown below. Cables AD and BD are attached to a vertical wall. Points A, B and C are on the y-z plane while Points C, D and E lie on the x-y plane. Line D-E and Line A-C-B are parallel to x-axis and z-axis, respectively. Given AC-CB and AB-AD-BD, W-10 kN and F -5 kN, determine the tension force in cables AD and BD. (7...
aw au B. Find the points in which the line x = 1 + 2t, y...
aw au B. Find the points in which the line x = 1 + 2t, y = -1 – t, z = 3t, meets the three coordinate planes. C. Evaluate and at the given point. w = In (x2 + y2+ z2), x = ue") y = ue'sinu, z = uecosu, (u, v) = (-2,0) A. Find the volume of the solid. II. z = 4 - 4(x2 + y2) z = (x2 + y2)2 - 1
Consider these three moment generating functions, for X, Y and Z: (5 points each) m (t)=W-3...
Consider these three moment generating functions, for X, Y and Z: (5 points each) m (t)=W-3 m, (t)=e + m,(t)=eW-7 a. What is the mean of X? b. What is the mean of Y? c. What is the mean of Z? d. What is the variance of X? e. What is the variance of Y? f. What is the variance of Z? Consider independent random variables X and Y with the following pmfs: y=1 (0.5 x=1 S(x)= {0.5 x =...
Problems 1. Thirty-two data points The computer output fro ab Vu dat y and X are...
Problems 1. Thirty-two data points The computer output fro ab Vu dat y and X are employed to estimate the parameters in the linear relation Putput from the regression analysis is (4 points) DEPENDENT VARIABLE: Y OBSERVATIONS: 32 R-SQUARE F-RATIO 7.0852 P-VALUE ON F 0.0124 0.1911 STANDARD PARAMETER ESTIMATE ERROR VARIABLE INTERCEPT T-RATIOP-VALUE 2.18 0.0373 -2.66 0.0124 a 76.25 box-124.20 34.98 46.66 The equation of the sample regression line is: y = lb.25 - 124.20 b. The p-value for b...
Given the State Table Below ?" ?" X-1 AB C 0 0 0O01 0OI011 01 00...
Given the State Table Below ?" ?" X-1 AB C 0 0 0O01 0OI011 01 00 0IOI01 1 01 01OIO0 01 A. Draw a state Diagram. B. Create the "design truth table" for the "next state" and the "output" C. Make a Karnaugh for each "next state" and the "output" When making the Karnaugh maps, "xA" should be along the top and "BC" along the side (The two missing states should be considered "DONT CARES") D. Write the "Next State"...
4. [20 points) Draw a timing diagram with causality arrows for b, w, x, y, and...
4. [20 points) Draw a timing diagram with causality arrows for b, w, x, y, and z for the following circuit and associated delays. Assume that a, b, and c have all been 1 for a long time. At t=1, b transitions from 1 →0. Gate Delay (units) Delay (units) Dom Gate NOT 2-input NAND 2-input AND 2-input XOR t || 1 2 | 3 4 | 5 | 6 7 8 9 10 | | 8 N
520. Given triangle ABC, let F be the point where segment BC meets the bisector of angle BAC, Draw the line through B that is parallel to segment AF, and let E be the point where this parallel meets the extension of segment CA. (a) Find the four congruent angles in your diagram. (b) How are the lengths EA, AC, BF, and FC related? (c) The Angle-Bisector Theorem: How are the lengths AB, AC, BF, and FC related?
520. Given...
1. Consider the isosceles triangle ABC, with AB = AC, and BAC = 20. Choose points E, D on the sides AB, AC, respectively, so that ZCBD = 60', and BCE = 50'. We will find LEDB. (i) Bring the parallel DF to BC, with F on AB. Connect points and F. and let K be the intersection of BD and CF. Show that DFBC is an isosceles trapezium. Mark all its angles. (ii) What type of triangles are BKC...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
Q1. A weight of W is supported by three cables AD, BD and DE as shown below. Cables AD and BD are attached to a vertical wall. Points A, B and C are on the y-z plane while Points C, D and E lie on the x-y plane. Line D-E and Line A-C-B are parallel to x-axis and z-axis, respectively. Given AC-CB and AB-AD-BD, W-10 kN and F -5 kN, determine the tension force in cables AD and BD. (7...
aw au B. Find the points in which the line x = 1 + 2t, y = -1 – t, z = 3t, meets the three coordinate planes. C. Evaluate and at the given point. w = In (x2 + y2+ z2), x = ue") y = ue'sinu, z = uecosu, (u, v) = (-2,0) A. Find the volume of the solid. II. z = 4 - 4(x2 + y2) z = (x2 + y2)2 - 1
Consider these three moment generating functions, for X, Y and Z: (5 points each) m (t)=W-3 m, (t)=e + m,(t)=eW-7 a. What is the mean of X? b. What is the mean of Y? c. What is the mean of Z? d. What is the variance of X? e. What is the variance of Y? f. What is the variance of Z? Consider independent random variables X and Y with the following pmfs: y=1 (0.5 x=1 S(x)= {0.5 x =...
Problems 1. Thirty-two data points The computer output fro ab Vu dat y and X are employed to estimate the parameters in the linear relation Putput from the regression analysis is (4 points) DEPENDENT VARIABLE: Y OBSERVATIONS: 32 R-SQUARE F-RATIO 7.0852 P-VALUE ON F 0.0124 0.1911 STANDARD PARAMETER ESTIMATE ERROR VARIABLE INTERCEPT T-RATIOP-VALUE 2.18 0.0373 -2.66 0.0124 a 76.25 box-124.20 34.98 46.66 The equation of the sample regression line is: y = lb.25 - 124.20 b. The p-value for b...
Given the State Table Below ?" ?" X-1 AB C 0 0 0O01 0OI011 01 00 0IOI01 1 01 01OIO0 01 A. Draw a state Diagram. B. Create the "design truth table" for the "next state" and the "output" C. Make a Karnaugh for each "next state" and the "output" When making the Karnaugh maps, "xA" should be along the top and "BC" along the side (The two missing states should be considered "DONT CARES") D. Write the "Next State"...
4. [20 points) Draw a timing diagram with causality arrows for b, w, x, y, and z for the following circuit and associated delays. Assume that a, b, and c have all been 1 for a long time. At t=1, b transitions from 1 →0. Gate Delay (units) Delay (units) Dom Gate NOT 2-input NAND 2-input AND 2-input XOR t || 1 2 | 3 4 | 5 | 6 7 8 9 10 | | 8 N
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