D 3. Write the coordinates of the points of intersection of the line y = 2x...
QUESTION 2 - 1 POINT Find the intersection points of the parabola y = -0? - 2 and the line-x+y= 4. Give your answer as two ordered pairs separated by a comma. For example, if you found that the solutions were (1,2) and (3, 4) you would enter (1,2), (3,4).
Find a vector parallel to the line of intersection of the two planes 2x - y + z = 1, 3x + y + z = 2.
If y = x^2 - 2x - 8 has two intersection points A and B with the x-axis, and its vertex is P. Find the area of ΔPAB.
Please Use MATLAB to solve: Thank you
Please use MATLAB to solve: Thank you
thhat volume d 19. Consider the parabola: 2(-2)+3, and the point P(3, 4) P(3,4) (a) Write a polynomial expres- sion for the distance d from point P to an arbitrary point y 2 on the parabola. 0 2 46 8 10 12 (b) Make a plot of d versus y for 0Sys4. (c) Determine the coordinates of Q if d 3 (there are two points) (d)...
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks
3. Consider the two planes, P and P2, where Pi is given by the...
5. (15 points) Find the line of intersection of the two planes. Show your work. 3x - 2y +1 2x+y - 3x = 3.
Find a plane containing the point (2,3,−1) and the line of intersection of the planes 2x+y-2z=22 and x+2y+3z=-14 The equation of the plane is
3. Find the points of intersection of the pairs of curves a. y = x² +3; y = 3x +1 b. 2x² +2 y2 = 5; xy = 1 4. Identify and sketch the curve represented by the given equation. x? - + y2 = 1 a. 4 (y+1) 4 b. (x - 1)? + 4 c. x² - y2 =-1
1 point) Suppose that the line l is represented by r(t)- (12+ 2t, 23 +6t, 8 + 2t) and the plane P is represented by 2x + 4y + 52-23. 1. Find the intersection of the line & and the plane P. Write your answer as a point (a, b, c) where a, b, and c are numbers. Answer 2. Find the cosine of the angle 0 between the line l and the normal vector of the plane P Answer:...
3. (10 total points) A particle travels along the intersection of (2) 1z=x+y (a) (2 points) Write the path of particle as a vector might find cos2(t)+ sin? (t) = 1 useful. function r(t) =< x(t),y(t), z(t) > of t. Hint: you (b) (4 points) Find the equation of the tangent plane of z = x+y at (1,3). (c) (4 points) Find the tangent line of the particle path at the point (1,0,1).
3. (10 total points) A particle travels...