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3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 pass...
For the following specifications of lines find the equation of the line in (a) General form (b) Point-gradient form (c) Gradient intercept form i. Passing through (2.2) with gradient 3 ii. Passing through (-3,7) parallel to the line 3x-4y+1=0 Passing through (1.1) perpendicular to the line 7x+3y-5=0 For each of the above lines find both the x intercept and the y intercept
4. Co ider dĀ, where R is the parallelogram enclosed by the lines x-3y=0, x-3y=4, 2x-y=2, Å 2x - y and 2x-y=7. Fill in the boxes: Let u=x-3y, and v= 2x - y. Then in terms of u and v, we can set up the PX - 3 ingen i 19 = 3/d2=SHH dvdu. (You do not actually evaluate the integral.) dvdu van de integral as: JJ 2 actually salane te imeni)
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
4. Find the equation of the line that is symmetric to line l:y=x-3 with JOT1 to welve9! 1 respect to line m: y 3 3 3. Find k for which the two given lines are perpendicular. (1) 3y-7kx-4=0, 7y+x+2= telgibroqo nit dio (2) 4y r+1 = 0, 2y+4x-3=0 4. Find the equation of the line that is symmetric to line l:y=x-3 with JOT1 to welve9! 1 respect to line m: y 3 3 3. Find k for which the two...
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....
For the following specifications of lines find the equation of the line in (a) General form (b) Point-gradient form (c) Gradient intercept form i. Passing through (2,2) with gradient 3 ii. Passing through (-3,7) parallel to the line 38-4y+1=0 Passing through (1.1) perpendicular to the line 7x+3y-5=0
15. Find the equation of the line parallel to y = -5/2 x + 6 that passes through the point (-2,1) 16. Find the equation of the line that passes through (4,5) and that is perpendicular to the line y = 3/2 x -4 17. The figure to the side represents a sidewalk structure. measurements are in meters. If beam A is perpendicular to beam B, find the size of beam C. 18. For each of the following equations, determine...
Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find the distance between them. If they are not parallel, but are intersecting (at a single point), find the point of intersection. If they are none of the above, draw a cat. 4. The line r(t) = 〈1, 1,1〉 +t(1,3,-1) and the plane...
The equation of the line that goes through the point ( 3 ,5 ) and is parallel to the line 2 x + 4 y = 2 can be written in the form y = mx+b where m is and where b is?
D.E (1) y"+2y'+y=x2-1-3, y(0)=-2, y'(0)=1 (2) + y'= -8cos2x+6sin 2 x (3) y*- 3y + 2 y =e" (x2 + 2x - 1)