Wednesday, February 6: Here are the answers to the Vector concepts .
Thursday, February 7: Happy E-Day!!
Monday, February 11: We worked problem #79 using both the law of cosines and using vector components. Here is that problem:
Thursday, February 7: Happy E-Day!!
Monday, February 11: We worked problem #79 using both the law of cosines and using vector components. Here is that problem:
Tuesday, February 12: Here is the projection PPT and here are the answers to the projection worksheet. Here are the Valentine's Day Project directions as determined by ASE, etc.
Wednesday, February 13: Bad news! I like all the application problems. However, if you don't have time to do all of them tonight, just complete page 435 tonight and work 446 by Monday, February 25.
Thursday, February 14: Today we will look at vector equations of lines. Here are the answers to the Vector Equations of a Line Worksheet.
And problem #85 from today is worked out below.
Friday, February 15: Today we looked at how to find the distance between a point (P) and a line (l) using projections. This is our summary:
1. Write a vector perpendicular to the line. (This is called the normal vector and often called n.)
2. Locate a point on that line. (I'm going to call that point P1.)
3. Write the vector from P to P1. (This joins our point to the line.)
4. Find the scalar projection from the vector in part 3 onto the normal vector. And example of that is worked out below.
Here are possible answers to the "Distance between a point and a line" worksheet.
Wednesday, February 13: Bad news! I like all the application problems. However, if you don't have time to do all of them tonight, just complete page 435 tonight and work 446 by Monday, February 25.
Thursday, February 14: Today we will look at vector equations of lines. Here are the answers to the Vector Equations of a Line Worksheet.
And problem #85 from today is worked out below.
Friday, February 15: Today we looked at how to find the distance between a point (P) and a line (l) using projections. This is our summary:
1. Write a vector perpendicular to the line. (This is called the normal vector and often called n.)
2. Locate a point on that line. (I'm going to call that point P1.)
3. Write the vector from P to P1. (This joins our point to the line.)
4. Find the scalar projection from the vector in part 3 onto the normal vector. And example of that is worked out below.
Here are possible answers to the "Distance between a point and a line" worksheet.
Monday, February 25: The answers to the 2D vector review are here. "2D Vector Review"
Tuesday, February 26: We did have a quiz today. Hopefully you did well. I felt it was an easy quiz to pass, but a hard one to ace. (But remember, it was out of 110 points, so if you struggled with the last two, consider them bonus problems...)
Wednesday, February 27: Can you do these efficiently?
Given points A: (3, -7), B: (-4, -3) and C: (2, 4)
Thursday, February 28: Today we reviewed and here are the odd answers to the problems we got in class. Note that the forces are bold and in brown but should have arrows over them.
49. a) F = <7, 2> b) G = -F = <-7, -2>
51. a) F =<-5.86, 1.13> b) G = -F = <5.86, -1.13>
**53. The tugboats are to the north and south of a horizontal line and the smaller tugboat makes a 30 degree angle with the horizontal line. Arcsin(.4) = 23.6 degrees
55. 56 degrees, 232 miles/hour
57. 420 miles per hour, 244 degrees
59. N 22 degrees W
29. 7
31. 28
Back
61. v1 = 4.1 i - 7.10 j; v2 = .98 i - 3.67 j
63. a) (24.51, 20.57) b) (-24.57, 18.10)
41. 1000sqrt(3) or 1732 ft-lb
Administration Notes:
Registration for School Year 2019-2020
Our students continue to challenge themselves, grow academically and reflect on the competitive admission requirements that colleges expect from graduates. We know that our students are among the best in the country and our instructional data confirms it! Please gather information during registration and set curriculum expectations for yourself that challenge you to meet your goals. We want you to be successful and set yourself apart from others after high school.
Rising Juniors and Seniors (current 10th and 11th graders):
Core Recommendations and Elective Registration materials for next school year will come home with your child on Friday, March 1st. Students will also receive AP Potential letters that are generated by College Board based on PSAT scores. Please look over the materials and make course selections very carefully. The directions and procedures will be included in the information. Registration closes at 2:30 p.m. on Friday, March 8, so the required documents (parent waivers, minimum day forms, specific program applications) need to be returned prior to that time to the student’s advisement teacher or to the Lassiter Room during lunch periods on March 7 and 8. The Master Schedule is created and teachers are hired based on this registration. Please select courses very carefully. The courses are for the entire school year. Thank you for your attention to this important step in your child’s schedule for School Year 2019-2020.
Rising Sophomores (current 9th graders):
Students will register for core classes and electives during their individual 9th advisement appointment on March 4 or 5. Core recommendations will be included in materials given at this appointment and will also be mailed home the first week of March for your review prior to the registration and advisement appointment. Registration closes at the end of your 9th advisement appointment. The Master Schedule is created and teachers are hired based on this registration. Please select courses very carefully. The courses are for the entire school year. Thank you for your attention to this important step in your child’s schedule for School Year 2019-2020.
Rising Freshman:
Please contact the appropriate middle school.
These were done hastily. Let me know quickly if you find errors.
1. Given points A: (3, -7), B: (-4, -3) and C: (2, 4) Write the line through A and B in point-slope form, slope-intercept form, standard form
and vector form.
helpful.=?)
1. Write y = (2/3)x - (7/3) in standard and in vector form.
Tuesday, February 26: We did have a quiz today. Hopefully you did well. I felt it was an easy quiz to pass, but a hard one to ace. (But remember, it was out of 110 points, so if you struggled with the last two, consider them bonus problems...)
Wednesday, February 27: Can you do these efficiently?
Given points A: (3, -7), B: (-4, -3) and C: (2, 4)
- Write the line through A and B in point-slope form, slope-intercept form, standard form and vector form.
- Write the line through A and C in vector form and in standard form.
- Write the perpendicular bisector of AB in point-slope form and in vector form.
- Write the median of BC in slope-intercept and in vector form.
- Write, in any form, the equation of the line through C that divides AB in a 2:3 ratio. (What form of the line in problem #1 was the most helpful.=?)
- Write, in any form, the equation of the line through the altitude from B to AC.
- Write y = (2/3)x - (7/3) in standard and in vector form.
- Write y - 3 = -4(x + 5) in standard and in vector form.
- Write 5x + 8y = 10 in slope-intercept and in vector form.
- Write r = <2, 6> + d<-5, 3> in point-slope, slope-intercept and standard form.
Thursday, February 28: Today we reviewed and here are the odd answers to the problems we got in class. Note that the forces are bold and in brown but should have arrows over them.
49. a) F = <7, 2> b) G = -F = <-7, -2>
51. a) F =<-5.86, 1.13> b) G = -F = <5.86, -1.13>
**53. The tugboats are to the north and south of a horizontal line and the smaller tugboat makes a 30 degree angle with the horizontal line. Arcsin(.4) = 23.6 degrees
55. 56 degrees, 232 miles/hour
57. 420 miles per hour, 244 degrees
59. N 22 degrees W
29. 7
31. 28
Back
61. v1 = 4.1 i - 7.10 j; v2 = .98 i - 3.67 j
63. a) (24.51, 20.57) b) (-24.57, 18.10)
41. 1000sqrt(3) or 1732 ft-lb
Administration Notes:
Registration for School Year 2019-2020
Our students continue to challenge themselves, grow academically and reflect on the competitive admission requirements that colleges expect from graduates. We know that our students are among the best in the country and our instructional data confirms it! Please gather information during registration and set curriculum expectations for yourself that challenge you to meet your goals. We want you to be successful and set yourself apart from others after high school.
Rising Juniors and Seniors (current 10th and 11th graders):
Core Recommendations and Elective Registration materials for next school year will come home with your child on Friday, March 1st. Students will also receive AP Potential letters that are generated by College Board based on PSAT scores. Please look over the materials and make course selections very carefully. The directions and procedures will be included in the information. Registration closes at 2:30 p.m. on Friday, March 8, so the required documents (parent waivers, minimum day forms, specific program applications) need to be returned prior to that time to the student’s advisement teacher or to the Lassiter Room during lunch periods on March 7 and 8. The Master Schedule is created and teachers are hired based on this registration. Please select courses very carefully. The courses are for the entire school year. Thank you for your attention to this important step in your child’s schedule for School Year 2019-2020.
Rising Sophomores (current 9th graders):
Students will register for core classes and electives during their individual 9th advisement appointment on March 4 or 5. Core recommendations will be included in materials given at this appointment and will also be mailed home the first week of March for your review prior to the registration and advisement appointment. Registration closes at the end of your 9th advisement appointment. The Master Schedule is created and teachers are hired based on this registration. Please select courses very carefully. The courses are for the entire school year. Thank you for your attention to this important step in your child’s schedule for School Year 2019-2020.
Rising Freshman:
Please contact the appropriate middle school.
These were done hastily. Let me know quickly if you find errors.
1. Given points A: (3, -7), B: (-4, -3) and C: (2, 4) Write the line through A and B in point-slope form, slope-intercept form, standard form
and vector form.
- Point-slope is easiest: y + 7 = (4/-7)(x - 3). Distribute and solve for y to get slope-intercept: y = (-4/7)x -37/7. I usually work from point-slope to get standard. Multiply both sides by -7 and distribute to clear the fractions. Then move terms to get it into Ax+By=C form where A is positive, and A, B and C have no common factors. Since we had slope-intercept form already, you could use that as well. 4x + 7y = -37 And vector is as easy as point-slope: r = <3, -7> + d<-7, 4>.
- Vector form: r = <3, -7> + d<-1, 11>. Standard form: 11x + y = 26
- The midpoint of AB is (-0.5, -5), and the slope is the opposite reciprocal of -4/7, so the point-slope form is y + 5 = 7/4(x + 0.5) and the vector form is r = <-0.5, -5> + d<4, 7>
- The median joins the midpoint of a side to the opposite vertex. The midpoint of BC is (-1, 0.5) and A = (3, -7), so the vector equation is r = <3, -7> + d<-4, 7.5> or r = <-1, 0.5> + d<4, -7.5> and the slope-intercept is y = -15/8x - 11/8
helpful.=?)
- Using the vector equation, let d = 2/5, since we want the point 2/5 of the way from A to B. r = <3, -7> + 2/5<-7, 4> or r = <3, -7> + 0.4<-7, 4> = <3, -7> + <-2.8, 1.6> = <0.2, -5.4>, which points to (0.2, -5.4). Since C = (2, 4), a vector equation would be: r = <2, 4> + d<1.8, 9.4> (and there are many other forms of this answer).
- An altitude is perpendicular to a side, so a vector form of this altitude would be r = <-4, 3> + d<11, 1> and a point-slope form is y - 3 = (1/11)(x + 4)
1. Write y = (2/3)x - (7/3) in standard and in vector form.
- Standard: 2x - 3y = 7 Since (2, -1) lies on this line, a vector equation could be r = <2, -1> + d<3, 2> (and there are many others).
- Standard form: 4x + y = -17 and vector form: r = <-5, 3> + d<1, -4>
- Slope-intercept: y = (-5/8)x +5/4 and vector form: r = <2, 0> + d<8, -5>
- Point-slope is easiest: y - 6 = (-3/5)(x - 2)
- Slope-intercept: y = (-3/5)x +36/5
- Standard: 3x + 5y = 36