If you get stuck, you can post your partial work as a comment. Check back, and I will occasionally post hints!
You can post your solution any time you like, but it is due Sunday, January 4 by 5pm. At 5pm, all comments will be posted and no further homework will be accepted.
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The problem:
Santa is in trouble! He has a dozen houses to visit, and if he wants to get to them all on Christmas Eve he needs to do it in the right order. However, he has lost his directions! Help Santa find the correct order in which he needs to visit each house so he can make it in time.
There are 12 houses total. Santa only needs to fly over each house to make the delivery. It's a common misconception that Santa actually goes down the chimney: he actually just flies overhead and drops them down. What actually takes up the most time is changing direction. His reindeer fly at nearly light-speed in straight lines, but they have poor handling at such high speeds. In order to turn, they need to slow down to regular speed, turn, and then speed up again. So, since Santa needs to use the least amount of time as possible, he wants to turn as few times as he can.
Here are the basic requirements:
1) Santa can only travel in straight lines.
2) Santa wants to have as few lines as possible.
3) Santa needs to start and end at the North Pole (the origin).
Part 1)
Let the letter t be the number of turns he has to make. It takes Santa's reindeer 10 minutes to make each turn.
Write an expression for the amount of time it takes Santa to make all his deliveries.
Part 2)
Find Santa's path!
Find the co-ordinate location (x, y) for each of the 12 houses. Then, tell which order Santa travels to each house. Give your answer as a list. How many different lines does Santa need?
Part 3)
For each line that you drew, find the equation of this line in slope-intercept form.
y = mx + b
m is the slope, and b is the y-intercept.
Part 4)
Santa has one hour to make all his deliveries in this part of the world. (He goes to bed early. He's old, you know.) Write an inequality relating your expression from part (1) to this time limit.
Part 5)
Solve the inequality. Then, check your answer with the number of turns you found in part (3). Does Santa make it in time?
Hint: It is possible to connect all the points with less than 10 lines.
ReplyDeleteHint: You can have fewer lines if each line goes through more points.
ReplyDeleteMerry X-Mass
ReplyDeleteHappy New Year
-maria
Sarah-hi
ReplyDeletehi merry christmass
ReplyDeletePart1
ReplyDeleteAnswer-t10+12=time spent delivering gifts
Part2
Answer-
A=(-6,3)
B=(-3,2)
C=(-2,-3)
D=(-2,-5)
E=(1,0)
F=(-6,0)
G=(2,2)
H=(2,0)
I=(-1,-2.5)
J=(2,-3)
K=(3,3)
L=(6,-1)
ORDER=H-G-K-A-E-I-C-D-F-J-L-H
#lines=11 counting the line back to the North Pole
Part3
Answer-
H-G= y=2x+2
G=K= y=1x+1
K-A= y=0x+8
A-E= y=2x+6
E-I= y=3.5x+1
I-C= y=1x+2
C-D= y=2x+2
D-F= y=1x+2
F-J= y=3x+2
J-L= y=2x+6
L-H= y=1x+4
Part4
Answer-t10+12=1hr
part5
Answer-10*10+12=112
-Maria
hi
ReplyDeleteHint: The first line goes through G to K. That way, with only one line, you hit two houses!
ReplyDeleteheii guys
ReplyDelete(Part 1)
ReplyDelete110=10+T
(Part 2)
(points)(X,Y)
G.(2,2)
k.(3,3)
L.(6,-1)
J.(2,-3)
F.(-0,-6)
D.(-2,-5)
C.(-2,-3)
A.(-6,3)
B.(-3,2)
E.(0,1)
(Part 3)Slope and Y-intercept
G and K.Y=0x+o
L and F.Y=-6x+1
F and D.Y=-6x+5
C and A.Y=-4x+2
B and E.Y=-1x+-1
(Part 4) make an inequality.
80>60+10.
(Part 5)
M+60=80 (it equals 1.3)
Santa would make it on times because he made all his stops in,one hour and tree minutes. Santa needed to complet all his stops in one hour and tree minutes is nothing
graph
ReplyDeleteI connected from the north pole to point G from point G to K from K to A from A to B from B to E from E to L from L to J from J to H from H to I from I to C from C to D from D to F
Part 1
y=10t
Part 2
point a:<-6,3> point b:<-3,2> point c:<-2,-3> point d:<-2,-3> point e:<0,1> point f:<0,-6> point g:<2,2> point h:<2,0> point i:<-1,-2.5>
point j:<2,-3> point k:<3,3> NEXT QUESTION IS AT THE VERY BEGINGING...
There are 8 lines
Part 4
y=12m+1
Part 5
yes he does make it in time
Kensy
was up Mr.tsui
ReplyDeletepart 1
ReplyDelete10xT=90
part 2
from (0,0) to (3,3)
from (3,3) to (-6,3)
from (-6,3) to (0,1)
from (0,1) to (-2,-3)
from (-2,-3) to (2,0)
from (2,0) to (6,-1)
from (6,-1) t0 (-2,-5)
from (-2,-5) to(0,-6)
from (0,-6) to (0,0)
yaminel's homework packet
ReplyDeletehi mr.tsui happy new year this might be wrong b/c i didn' really get the problem but i tried.
[part 1]
t1o+12
[part 2]
the coordinates of the points are:
A-(-6,3)B-(-3,2)C-(-2,-3)D-(-2,-5)E-(0,1)F-(1,-6)
G-(2,2)H-(0,2)I-(-1,-2.5)J-(2,-3)K-(3,3)
[part 3]
A-B C-I D-F J-L E-H K-G
(1,3)(1,0)(1,1)(2,4) (1,2) (1,0)
Y=3X Y=1X Y=1X+-6 Y=2X y=2X+1 Y=1X
the other parts i didn't get but this might be wrong all the same but at least i tried
part 1)
ReplyDelete10t+60
part 2)[A] part 2) [B]
START AT THE NORTH POLE total lines:10
1.G=(2,2)
2.K=(3,3)
3.L=(6,-1)
4.H=(-2,0)
5.J=(2,-3)
6.F=(0,-6)
7.D=(-2,-5)
8.C=(-2,-3)
9.I=(-1,-3.5)
10.A=(-6,3)
11.B=(-3,2)
12.E=(0,1)
END AT NORTH POLE
Part 3)[y=mx+b]
2, 2 0=run 0
-- - = y intecept=none -- = slope
2,-3 5=rise 5x
3 ,3 0 4=rise 4
-- -- = -- y intercept=none -- = slope
6,-1 7 3=run 3x
-2, 0 -2=run -2
-- -- = -- y intercept=1 -- = slope
0, 1 -1=rise -1x+1
0, -6 -2
-- = -2 =run -- = -1 = rise -- = slope
-2 -5 -1x+6
-2, -3 1 = run 1
-- -- = -- ---= slope
-1,2.5 .5= rise .5x
-6, 3 -3=run -3
-- -- = -- = slope
-3, 2 -1= rise -1x
part 4)
10t=60
there are 6 turns he has to make
10*6 60
part 5)
10*6= 90 = 1 hour
Santa is going to be able to be in time for his bead time because he only has to make 6 turns. It will take him 10 minutes to do each turn wich means 10 minutes x 6 turns will give him 60 minutes in total just enough to go to bed.
Sweet dreams!!
-Erica