Precalculus:
Name:
1) The weight of 2000 pounds is suspended from two cables as shown in the figure. What are the tensions on
each cable?
2) A boat must head in the direction N20°W at 45 mph to get to its destination on time (This is B+C) . To adjust
for the current, the captain heads the boat at N40°W at 40 mph . Find the speed and direction of the current.
Please give vector components for all vectors.
3) Find each limit.
1
1+a) lim - x
x ->0 _ _!_
1
X
4) Determine the value of k that will make
the function continuous at 4.
x2 - 9
- - x<4
f(x) = x+3
{
kx+5 x>4
~
v
7) State whether the given vectors
6) Write the vector AB
in component form and
5) Draw the vector
. Include the prism.
= -2i -5} +4k
r. ..fY·C:.~~;'
..
as a position vector.
- ~kk_
(¥,-:J,i) . . .
.
are orthogonal, parallel or neither.
. \'
You must show work or explain your
answer.
·o...~~~ .
~ . •
a)
v = 2i + 4j
w=
. fT
.
• (:-;1·, :i.,-\)
b)
4i -2 j
v = 3i -4}
w = -12i +16}
Use the following vectors to answer each of the following questions.
v
= i - 5} - 2k
w
= -3i + j +4k
8) 2v-w
9)
llvll
10) The angle between vectors v and w.
Fill in the blank (#11-13):
11) Vectors are orthogonal if the angle between them is _ _ . This occurs when the dot product is _ __
12) Vectors are considered parallel if they have the same _ _ _ _ _ _ _ but different _ _ _ _ _ _ __
or if their directions are - - - - - - 13) a) Find the missing component that will make vectors v and w parallel. v = 3i - j
w = ai- 2}
b) Find at least two more vectors that are also parallel to v and w.
Draw each conic. Include the foci. (Some of the graphs will not fit, don't worry © )
14) (x-3i + (y - 1)2 =1
9
13
15) (y -
4
4i
2
(x+ 1) = 1
16
16) (y -3) 2 =-12(x+2)
Name:
Preca lculus :
1) Th e weight of 2000 pounds is suspended from t wo cables as shown in the figure. What are the tension s on
eac h cable?
JILl\
lltflSivt ll{O
(_oc;.\L£0 <., +-
J1 t-lt to~ 3o t,
II (Zt l ~: vt :SO~·
f-
;)_ CJLJD
J
1
I Lll cos ll(O +He..} Lc.o~ 30 :..()
I ( L/ \ = - fll<-\tc.o$1?
//L/{ Sin l'to rlfKLf..i Y130 -= d<Al7J
/1 R..ll
- co~ll{ L}
l · 1 31t ~\I
j.
c.s l~-t
II R\ I
c..
/t{(J
=I~ 3D . 4 I
I bs
II L/ I ·-: . 1 <t c.r 1 . .).. 1 tlos
2) A boat must head in the direction N20°W at 45 mph to get to its destination on time (This is B+C) . To adjust
for the current, the captain heads the boat at N40°W at 40 mph. Find the speed a;ld direction of the current.
Please give vector components for all vectors.
4) Determine the value of k that will make
3) Find each limit.
( X? J.. 'y:_,. r-~)
1
1+ - . ~
a) lim--x
x--.0 1 - _!_
'i.
b) lim x- x--.2 •
)( - 1
pLu.j ~
)(-;..()
.
x 3- 8
.
(>.~ )
X
X. ·H
the function continuous at 4.
4
~
- - :: -1
·-j
/ k /[')_2 .
~
{
,\
•Jf...d) f(x)
,f
)...
l
(_f ;
=
D1
?
x- - 9
-x +3
x:s;4
kx + 5 x > 4
'
"~~'
lw -'-4
t r.l,
,. ;
1
I
..:.:;:_.J
-= 1 ~
/( ,. tj rS
1h
f
lr
::~'
L
l
v = - 2i- 5 j + 4k
Cov, - elt:
v
.:_)
.
k.. ·~+tv-
-
"'-. .
\l e_S ~ (W-thO~() ~
1~
a)
w=4i-2J
·x "'
I
~
I,
'-......./
~
.L ~
sD v
v =3i-4j - 5l'?': - "'J.J '\
w= -12i+16j SIMI~ ..!J'..: _.;t )
b)
1
-
I"
~
- ,,_
~(Uf-/1 .'
<...i.o/-'-11~)
r;;r1
~
ros-e
Use the following vectors to answe r each of the following questions.
w = -3i + j +4k
- ltJO
- ,;J;, • iJ y
-.v v ':' - -~
/lv/1/lwll ~~~
- .-
.:. ... I t..e
I
c..o s~ -; - \ s<t.._e ;- FdJ ~;;o =10} The angle between vectors v and w .
\l
.3
L)
·,J ~ 1 I~~~~_
{;J:; tel:.-(( - I_~ .=.
Fill in the blank (#11-13}:
11) Vectors are orthogonal if the angle between them is
D ~·~
.
slop
/7 -t o(2_,
13) a) Find the missing component that will make
but different
,/"
s0
//
f
_ --------.,
-J J;)_ '-/, 9 S 0
~-ectors v and w parallel.
(x + 1) 2
.j
16
. .~ • .
·
. . o'.t , - --
-·
--;1
Ill....
= 1 0 Jd
.... c~~?o
\
Th-~
= 3i- j w = ai- 2} [;._ ~
SI¥L· · 1~
-~:: • ..l
v
Draw each conic. Include the foci. (Some of the graphs will not fit, don't worry©)
(y - 4) 2
VV\-..0.-'fl"\
._)
b) Find at least two more vectors that are also parallel to v and w.
15l
\.
D
\f'JO·~~
-~ - _!lQ_. This occurs when the do.iproduct is 0 .
12) Vectors are considered parallel if they have the same
or if their directions are
r.
-
1 -ct
u i.-4J-r~L
v = i -Sj -2k
~
V , "'-J
..\::. 0)
SD ca~e
v=2i+4].
tf -
v ·•
.
~
You must show w.ork or explain your
J
1J.
- .r- /
.
tv,
~;~pv~£ s.wer.
I
'.
.
IJ y- ·• s, vv;. . ~'
_ · f'~ . ·,~
·\
-
are orthogonal, parallel or neither .
as a pos1tion vector.
(v, ··::., ·s: ,
...
7) State whether the given vectors
6) Write the vector AB
in component form and
5) Draw the vector
. Include the prism.
16)
,!,
,