<span>Vector Equation (Line)</span>(x,y) = (x,y) + t(a,b);tERParametric Formx = x + t(a), y = y + t(b); tERr = (-4,-2) + t((-3,5);tERFind the vector equation of the line passing through A(-4,-2) & parallel to m = (-3,5)<span>Point: (2,5) Create a direction vector: AB = (-1 - 2, 4 - 5) = (-3,-1) or (3,1)when -1 (or any scalar multiple) is divided out. r = (2,5) + t(-3,-1);tER</span>Find the vector equation of the line passing through A(2,5) & B(-1,4)<span>x = 4 - 3t y = -2 + 5t ;tER</span>Write the parametric equations of the line passing through the line passing through the point A(4,-2) & with a direction vector of m =(-3,5)<span>Create Vector Equation first: AB = (2,8) Point: (4,-3) r = (4,-3) + (2,8); tER x = 4 + 2t y = -3 + 8t ;tER</span>Write the parametric equations of the line through A(4,-3) & B(6,5)<span>Make parametric equations: x = 5 + 4t y = -2 + 3t ; tER For x sub in -3 -3 = 5 + 4t (-8 - 5)/4 = t -2 = t For y sub in -8 -8 = -2 + 3t (-8 + 2)/3 = t -2 = t Parameter 't' is consistent so pt(-3,-8) is on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (-3,-8) on the line?<span>Make parametric equations: x = 5 + 4t y = -2 + 3t ; tER For x sub in 1 -1 = 5 + 4t (-1 - 5)/4 = t -1 = t For y sub in -7 -7 = -2 + 3t (-7 + 2)/3 = t -5/3 = t Parameter 't' is inconsistent so pt(1,-7) is not on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (1,-7) on the line?<span>Use parametric equations when generating points: x = 5 + 4t y = -2 + 3t ;tER X-int: sub in y = 0 0 = -2 + 3t solve for t 2/3 = t (this is the parameter that will generate the x-int) Sub t = 2/3 into x = 5 + 4t x = 5 + 4(2/3) x = 5 + (8/3) x = 15/3 + (8/3) x = 23/3 The x-int is (23/3, 0)</span>What is the x-int of the line r = (5,-2) + t(4,3); tER?Note: if they define the same line: 1) Are their direction vectors scalar multiples? 2) Check the point of one equation in the other equation (LS = RS if point is subbed in)What are the two requirements for 2 lines to define the same line?
If order mattered, then there would be 6*5*4*3 = 30*12 = 360 different ways to form the committee. However, no single member outranks the other. Each member has equal ranking. So order does not matter.
Since order does not matter, we must consider all of the ways to arrange a single group of 4 people. That is 4! = 4*3*2*1 = 24 ways. We overcount by a factor of 24 when order doesn't matter which is why we divide the previous result (360) by 24 to get 360/24 = 15
Answer: 15
Note: you can use the combination formula n C r = (n!)/(r!*(n-r)!) with n = 6 and r = 4 to get the same answer
Roni did not make use of the equation for a proportional relationship.
Step-by-step explanation:
For some constant of proportionality k, y is proportional to x if x and y satisfy the equation ...
y = kx
Roni knows k=7/25, but she did not use this equation. She added instead of multiplying, so did not end with an equation expressing a proportional relation.