9. Show that the lines whose d.rs. are determined by the equations 1+m+ n 0 and...
a.Why are the lines whose equations are y+5 and y3x 1 perpendicular? b.Use a graphing utility to graph the equations in a- 10,10,1] by 10,10,1] viewing rectangle. Do the lines appear to be perpendicular? c. Now use the zoom square feature of your utility. Describe what happens to the graphs. Explain why this is so.
O LINES AND FUNCTIONS Identifying parallel and perpendicular lines from equations The equations of three lines are given below. 2 Line 1: y -x+6 Line 2: 3y 2x+7 Line 3: 4x-6y-4 For each pair of lines, determine whether they are parallel, perpendicular. Line 1 and Line 2: O Parallel O Perpendicular O Neither Line 1 and Line 3: O ParallelPerpendicular Neither Line 2 and Line 3: O Parallel ○ Perpendicular Neither Explanation Type here to s rch oward Cr。 mal...
56. Let Li and L2 be the lines whose parametric equations are L]: x = 41, y = 1 -21, z = 2 + 21 L2: x = 1+1, y = 1-1, Z=-1+ 41 (a) Show that Li and L2 intersect at the point (2,0, 3). (b) Find, to the nearest degree, the acute angle between L and L2 at their intersection. c) Find parametric equations for the line that is perpen- dicular to L, and L2 and passes through...
If two lines representing a system of equations have slopes whose product is - 1. then what can be said about the nature of its solutions? A. Infinitely many solutions B. Two rational solutions C One unique solution D. No solution
Exercises for Chapter 9 1. Consider a convex polyhedron, all of whose faces are squares or regular pentagons. Say there are m squares and n pentagons. Assume that each vertex lies on exactly 3 edges. (a) Show that for this polyhedron, the following equations hold: 3V = 2E, 4m + 5n = 2E, m+n=F. (b) Using Euler's formula, deduce that 2m+n=12. (C) Find examples of such polyhedra for as many different values " as you can.
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine all such triangles. b. Find the smallest two such triangles. 8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine...
. If σnσm((x, y)) = (x+6, y-3), find equations for lines m and n, in the form y = ax+b. Hint: What is this transformation and how does it decompose as a product of two reflections?
50° po m 9° so 1° n Do uº 65. In the figure above, if lines m and n are parallel, all of the following statements are true except I A. t= 130 B. 9+u= 100 C. V + 50 = 180 D. S = 150
The equations of three lines are given below. Line 1: y=-3x+7 Line 2: 8x-6y=-4 Line 3: 4y=-3x+5 For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither
Writing equations of lines parallel and perpendicular to a given... Consider the line y=-6x+5. Find the equation of the line that is parallel to this line and passes through the point (8, -4). Find the equation of the line that is perpendicular to this line and passes through the point (8, -4). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of parallel line: e X Equation of perpendicular line: 1 ? Explanation Check 20:20...