Homework Answers
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(1 point) Find the length of the curver r(t) = i +3t'j + tºk, 0<t</96 L
(1 point) Find the length of the curver r(t) = i +3t'j + tºk, 0<t</96 L
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1&#...
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1' parallel to through P in the usual way: drop a perpendicular PQ to / and construct /" perpendicular to PQ. Let I" be any line through P distinct from l'. To see that /" intersects I, pick a point A on PQ between...
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms o...
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms of (r,0) What are the coordinates of the same point in cartesians coordinates (x.y)? Give an equivalent version of the point in polar coordinates with r <o. What is the slope of of the tangent line to the circler 2...
Using Python please Problem 3 (15 pts): Using the Secant Method, for A>0, (10 pts) Write a program which finds A/m for any positive value m. Note, you need to choose a function f(r) for the Secant...
Using Python please
Problem 3 (15 pts): Using the Secant Method, for A>0, (10 pts) Write a program which finds A/m for any positive value m. Note, you need to choose a function f(r) for the Secant Method whose root is A1 'm. (5 pts) How does your choice of m effect how many iterations your program takes to converge for a given tolerance choice? Plots will help me to understand your thinking here In [11]: #present your program for...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25....
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
given values are correct. find others (l point (al) Starting with a 1.7,b-2.8, do 4 lterations of the secant method to estimate wheref(x) -G2 +sin(2 x)-5)s equal to 0. f(a) 1 1.7 2.8 -2.3655 2.208...
given values are correct. find others
(l point (al) Starting with a 1.7,b-2.8, do 4 lterations of the secant method to estimate wheref(x) -G2 +sin(2 x)-5)s equal to 0. f(a) 1 1.7 2.8 -2.3655 2.2087 = 212.8 2.26885 0.8371 i3 2.2688 2.4148 -0.8371 0.1617 24 2.40 011 4 2.4148 -0.1617 b) Repeat using the false position method. f(c) 17223052037 2.8 -2.3655 2.2087 2 2.2688 -0.8371 2.2087 3 2.4148 2.8 -0.1617 2.2087 i = 4.1 2.4411 2.8 0.0266 2.2087
(l point...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T,...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r,...
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
(1 point) -4 Let L be the line spanned by 0 in R Find a basis...
(1 point) -4 Let L be the line spanned by 0 in R Find a basis of the orthogonal complement L1。L Answer:
(c) Let L be the line given by the parametric vector equation r=ro + tv, where...
(c) Let L be the line given by the parametric vector equation r=ro + tv, where ro = i +2j + 3k and v = -i+j - k, and let P be the plane given by the vector equation (r-ru).n=0, where rı = 3j + 3k and n=i+ 3j+k. Find the point where L and P intersect.
(1 point) Find the length of the curver r(t) = i +3t'j + tºk, 0<t</96 L
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1' parallel to through P in the usual way: drop a perpendicular PQ to / and construct /" perpendicular to PQ. Let I" be any line through P distinct from l'. To see that /" intersects I, pick a point A on PQ between...
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms of (r,0) What are the coordinates of the same point in cartesians coordinates (x.y)? Give an equivalent version of the point in polar coordinates with r <o. What is the slope of of the tangent line to the circler 2...
Using Python please
Problem 3 (15 pts): Using the Secant Method, for A>0, (10 pts) Write a program which finds A/m for any positive value m. Note, you need to choose a function f(r) for the Secant Method whose root is A1 'm. (5 pts) How does your choice of m effect how many iterations your program takes to converge for a given tolerance choice? Plots will help me to understand your thinking here In [11]: #present your program for...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
given values are correct. find others
(l point (al) Starting with a 1.7,b-2.8, do 4 lterations of the secant method to estimate wheref(x) -G2 +sin(2 x)-5)s equal to 0. f(a) 1 1.7 2.8 -2.3655 2.2087 = 212.8 2.26885 0.8371 i3 2.2688 2.4148 -0.8371 0.1617 24 2.40 011 4 2.4148 -0.1617 b) Repeat using the false position method. f(c) 17223052037 2.8 -2.3655 2.2087 2 2.2688 -0.8371 2.2087 3 2.4148 2.8 -0.1617 2.2087 i = 4.1 2.4411 2.8 0.0266 2.2087
(l point...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
(1 point) -4 Let L be the line spanned by 0 in R Find a basis of the orthogonal complement L1。L Answer:
(c) Let L be the line given by the parametric vector equation r=ro + tv, where ro = i +2j + 3k and v = -i+j - k, and let P be the plane given by the vector equation (r-ru).n=0, where rı = 3j + 3k and n=i+ 3j+k. Find the point where L and P intersect.
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