WEBVTT
Kind: captions
Language: en
00:00:20.040 --> 00:00:21.960
heres a fun practice problem
00:00:27.000 --> 00:00:29.880
you originally have 500 grams of an element
00:00:30.800 --> 00:00:32.880
8 hours later you have 400 grams
00:00:33.680 --> 00:00:37.360
if you split this up you get 250 grams, so whats half life
00:00:37.800 --> 00:00:39.880
how are we gonna find that, well
00:00:40.400 --> 00:00:41.200
the easiest
00:00:42.080 --> 00:00:44.560
you set up basic exponetial equation
00:00:48.540 --> 00:00:51.580
y=a times b to the x, now put the thought in here
00:00:51.960 --> 00:00:53.880
the original amount will be a
00:00:53.880 --> 00:00:56.400
if youre not sure you can always figure that out
00:00:58.520 --> 00:01:00.680
you can say, when x is 0, i have 500
00:01:01.960 --> 00:01:02.460
so 500
00:01:04.400 --> 00:01:05.600
is a times b to the 0
00:01:07.340 --> 00:01:08.140
b to the 0 is 1
00:01:08.140 --> 00:01:10.540
anything to the zero is one besides 0
00:01:13.580 --> 00:01:14.080
a is 500
00:01:17.060 --> 00:01:19.860
so now we know a, you can take this equation
00:01:21.460 --> 00:01:22.260
and prove it
00:01:25.260 --> 00:01:26.220
y=500b to the x
00:01:26.980 --> 00:01:28.020
now you say okay
00:01:28.960 --> 00:01:30.720
and after 8 hours i have 400
00:01:32.500 --> 00:01:33.000
so 400
00:01:34.820 --> 00:01:35.320
equals
00:01:35.960 --> 00:01:36.460
500
00:01:37.380 --> 00:01:38.340
times b to the 8
00:01:40.540 --> 00:01:42.540
so you divide by 400 you get 4/5
00:01:48.240 --> 00:01:48.740
so b
00:01:49.840 --> 00:01:50.800
to the 8th root
00:01:52.060 --> 00:01:52.560
of 4
00:01:53.460 --> 00:01:53.960
5
00:01:57.380 --> 00:01:59.380
or write it in a better way, 4/5
00:01:59.620 --> 00:02:00.260
to the 1/8
00:02:05.780 --> 00:02:08.020
understand how im getting there?
00:02:08.020 --> 00:02:10.500
you start with your two pieces of information
00:02:11.300 --> 00:02:11.860
at time 0
00:02:13.140 --> 00:02:14.500
you have 500 at time 8
00:02:14.880 --> 00:02:15.680
you have 400
00:02:16.120 --> 00:02:17.880
so first you can use the 500
00:02:19.680 --> 00:02:20.960
and 0 to find a is 500
00:02:21.080 --> 00:02:23.400
and then you plug in a and do it again
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i know when x is 8 y is 400
00:02:27.580 --> 00:02:28.700
now i can get for b
00:02:28.940 --> 00:02:31.100
that means my equationis really
00:02:32.040 --> 00:02:32.540
y is 500
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times
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4/5
00:02:36.520 --> 00:02:37.160
to the 1/8
00:02:38.160 --> 00:02:38.660
to the x
00:02:39.620 --> 00:02:41.460
you are just saying that 500
00:02:44.440 --> 00:02:45.720
times 4/5 to the x/8
00:02:49.040 --> 00:02:50.000
so far so good?
00:02:52.040 --> 00:02:52.680
last step
00:03:11.720 --> 00:03:13.480
now that i know that y is 500
00:03:15.060 --> 00:03:15.700
times 4/5
00:03:17.280 --> 00:03:17.920
to the x/8
00:03:19.020 --> 00:03:22.540
i want to find the half life so i want to find when y=250
00:03:23.140 --> 00:03:24.660
cause 250 is half of 500
00:03:26.660 --> 00:03:27.160
so 250
00:03:28.280 --> 00:03:28.780
is 500
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times 4/5
00:03:32.500 --> 00:03:33.000
x/8
00:03:34.720 --> 00:03:36.480
divide 250/500 you get 1/2
00:03:42.020 --> 00:03:44.260
and now you just have to solve for x
00:03:45.460 --> 00:03:48.180
the easiest way to solve for x is with logs
00:03:48.200 --> 00:03:53.240
you can use natural logs, you can use common logs you can use any log youd like
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log of 1/2
00:04:01.080 --> 00:04:01.880
is log of 4/5
00:04:04.840 --> 00:04:05.340
and x/8
00:04:11.400 --> 00:04:11.900
3x/8
00:04:20.880 --> 00:04:22.480
then you just solve for x
00:04:24.160 --> 00:04:24.720
you get 8
00:04:26.220 --> 00:04:27.340
times a log of 1/2
00:04:30.740 --> 00:04:31.940
over the log of 4/5
00:04:35.780 --> 00:04:38.660
equals x, howd we do on the half life problem
00:04:40.680 --> 00:04:41.320
good, bad
00:04:44.120 --> 00:04:44.760
you okay?
00:04:45.180 --> 00:04:46.460
practice one more?
00:04:47.560 --> 00:04:49.080
lets practice one more
00:04:52.980 --> 00:04:54.500
ill leave that up there
00:04:56.860 --> 00:04:58.380
ill make up another one
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you originally have a 1000 grams of an element
00:06:03.020 --> 00:06:07.340
6 hours later you have 200 grams, the half life is less then 6 hours
00:06:08.120 --> 00:06:10.200
after 6 hours you only have a 5th
00:06:11.140 --> 00:06:12.660
so what is its half life
00:06:19.120 --> 00:06:20.000
so we have y is
00:06:21.880 --> 00:06:22.920
a times b tot he x
00:06:23.740 --> 00:06:27.020
and you should know that a is 1000, but just in case
00:06:28.540 --> 00:06:29.820
start off with 1000
00:06:33.640 --> 00:06:34.140
x is 0
00:06:35.520 --> 00:06:36.880
and anything to 0 is 1
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a is 1000
00:06:40.600 --> 00:06:42.760
we rewrite this equation as 1000
00:06:44.200 --> 00:06:44.700
yes
00:06:46.040 --> 00:06:48.920
further more we would have 200 after 6 hours
00:06:50.120 --> 00:06:50.620
so 200
00:06:52.020 --> 00:06:52.520
1000
00:06:54.400 --> 00:06:54.960
b to the 6
00:06:56.840 --> 00:06:58.680
divide it by 1000 you get 1/5
00:07:00.480 --> 00:07:01.040
b to the 6
00:07:03.460 --> 00:07:03.960
b is 1/5
00:07:05.800 --> 00:07:06.440
to the 1/6
00:07:07.320 --> 00:07:08.120
the 6th root
00:07:10.140 --> 00:07:11.100
so far so good?
00:07:12.520 --> 00:07:15.320
easy, alright now we can take our equation
00:07:15.940 --> 00:07:16.900
you get y=1000
00:07:19.600 --> 00:07:20.240
times 1/5
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to the x/5
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you take the x
00:07:24.640 --> 00:07:25.920
and multiply by 1/6
00:07:25.980 --> 00:07:26.780
you get that
00:07:27.340 --> 00:07:30.060
and then you substitute in a you solve for
00:07:31.140 --> 00:07:32.340
you have 500 grams
00:07:32.440 --> 00:07:33.240
the half life
00:07:34.340 --> 00:07:34.840
so 500
00:07:36.440 --> 00:07:36.940
is 1000
00:07:38.400 --> 00:07:39.040
times 1/5
00:07:40.420 --> 00:07:41.060
to the x/6
00:07:41.920 --> 00:07:43.760
divided by a 1000 you get 1/2
00:07:45.600 --> 00:07:46.100
1/5
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to the x/6
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take the log of both sides
00:07:56.820 --> 00:07:57.940
you get log of 1/2
00:08:01.660 --> 00:08:02.160
log of
00:08:03.400 --> 00:08:03.900
1/5
00:08:05.880 --> 00:08:06.520
to the x/6
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bring the x of 6 in front
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and solve for x and you get 6
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log of 1/2
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over log of 1/5
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equals x howd we do?
00:08:33.940 --> 00:08:34.900
you get it? yay
00:08:35.960 --> 00:08:36.520
alright
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second set of things
00:09:47.440 --> 00:09:48.400
tan of a is 9/13
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and cosine of b is -5/11
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where a is between pi and 3pi/2
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and b is between pi/2 and pi
00:09:59.940 --> 00:10:01.380
find the sin of a plus b
00:10:02.300 --> 00:10:02.800
cos2a
00:10:03.800 --> 00:10:04.920
and tan of a plus b
00:10:12.200 --> 00:10:16.040
this is mostly formulas and figure out where the angles go
00:10:19.080 --> 00:10:21.800
so i tell you that a is between pi and 3pi/2
00:10:22.100 --> 00:10:23.220
that means that a
00:10:24.460 --> 00:10:26.940
somewhere here in the third quadrant
00:10:31.580 --> 00:10:32.220
this is pi
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this is 3pi/2
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the tangent of a is 9/13
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sohcahtoa
00:10:41.100 --> 00:10:41.980
thats 9 and 13
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you do pythagorean theorem and find that this is 250
00:10:47.540 --> 00:10:48.740
square root of 250
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howd we do on that
00:11:08.460 --> 00:11:09.980
b is between pi/2 and pi
00:11:14.640 --> 00:11:15.600
so this is pi/2
00:11:18.440 --> 00:11:19.320
and this is pi
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cosine is -5/11
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little pythagorean theorem
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and then this is 96 and the square root of 96
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so far so good
00:11:33.740 --> 00:11:38.700
so now we just have to remmeber the formulas we will not give them on the test
00:11:38.700 --> 00:11:40.540
we might give you like one of them
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to help jog your memory
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what can i say
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i suggest you keep it in your head until youre done with math
00:11:55.280 --> 00:11:57.540
otherwise youre just gonna have to memorize it again
00:12:04.080 --> 00:12:04.960
sin of a plus b
00:12:11.420 --> 00:12:12.300
sin of a plus b
00:12:20.780 --> 00:12:21.660
sin of a plus b
00:12:31.200 --> 00:12:32.160
sin of a cos of b
00:12:33.440 --> 00:12:34.080
plus cos a
00:12:35.220 --> 00:12:35.720
sin of b
00:12:36.840 --> 00:12:39.960
if im motivate ill put the formula on instagram
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if im motivated
00:12:42.340 --> 00:12:44.980
its a two hour train trip either way well
00:12:47.660 --> 00:12:49.100
lets see what i can get
00:12:50.240 --> 00:12:50.960
the sin of a
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is -9/ the square root of 250
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how do we know its negative?
00:12:57.860 --> 00:13:00.020
because were in the 3rd quadrant
00:13:02.080 --> 00:13:03.040
the cosine of b
00:13:03.980 --> 00:13:06.380
why it told you what cosb is its -5/11
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cosA
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is -13/ square root of 250
00:13:23.880 --> 00:13:24.600
the sin of b
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is square root of 96/11
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and you can leave it right now
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i dont think you have to really simplify from there
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we dont really care if we multiply out
00:13:50.060 --> 00:13:51.500
now i have to fins cos2a
00:13:52.400 --> 00:13:53.680
well the cosin of 2a
00:13:58.120 --> 00:13:59.320
is cosin squared a
00:14:01.000 --> 00:14:02.200
minus sin square a
00:14:05.100 --> 00:14:06.780
you also can do cosa plus a
00:14:06.780 --> 00:14:11.100
you can memorize a couple of these formulas to figure out the rest
00:14:12.860 --> 00:14:13.580
the cos if a
00:14:15.820 --> 00:14:16.780
is negative 13
00:14:17.700 --> 00:14:19.460
over the square root of 250
00:14:21.400 --> 00:14:21.960
squared
00:14:23.000 --> 00:14:23.960
and the sin of a
00:14:25.380 --> 00:14:26.980
is -9/ square root of 250
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and you dont need to simplify that
00:14:36.660 --> 00:14:37.160
so 9
00:14:38.240 --> 00:14:38.800
minus 81
00:14:40.080 --> 00:14:41.520
over square root of 250
00:14:43.340 --> 00:14:44.960
which is 88/square root of 250
00:14:45.560 --> 00:14:48.440
i certainly dont expect you to rationalize
00:14:48.520 --> 00:14:51.640
and simplify from there its not important to me
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oh yea 250, thank you
00:15:12.140 --> 00:15:14.860
now we have to find the tqangent of a plus b
00:15:14.860 --> 00:15:19.140
to find the tangent of a plus b, the simple way is you already have the sin of a plus b
00:15:19.220 --> 00:15:21.540
find the cosin of a plus b and divide
00:15:30.920 --> 00:15:32.200
the cosin of a plus b
00:15:33.740 --> 00:15:34.240
is
00:15:35.420 --> 00:15:35.920
cosin a
00:15:37.840 --> 00:15:38.340
cosin b
00:15:39.520 --> 00:15:40.020
minus
00:15:42.700 --> 00:15:43.340
sinasinb
00:15:53.140 --> 00:15:54.740
so what are they? cosa is
00:15:58.060 --> 00:15:59.740
is -13/square root of 250
00:16:06.040 --> 00:16:06.540
cosb
00:16:07.620 --> 00:16:08.500
is minus 5/11
00:16:13.620 --> 00:16:14.340
and sin of a
00:16:16.560 --> 00:16:18.160
is -9/square root of 250
00:16:22.160 --> 00:16:23.120
and the sin of b
00:16:23.760 --> 00:16:25.280
is the square root of 96
00:16:25.860 --> 00:16:26.360
over 11
00:16:26.360 --> 00:16:30.520
and you take the top of sin and divde it by the cos and get the tangent
00:16:33.580 --> 00:16:34.380
so its messy
00:16:36.060 --> 00:16:37.420
now we have the cosin
00:16:37.420 --> 00:16:39.480
is we wanted to find the tangent
00:16:39.820 --> 00:16:41.180
you just take the sin
00:16:41.540 --> 00:16:42.980
which is on this board
00:16:45.980 --> 00:16:48.460
take the sin and divide it by the cosin
00:16:51.720 --> 00:16:54.120
the sin divided by the cos is tangent
00:17:00.720 --> 00:17:06.320
you can write the unsimplified expression over the other unsimplified expression
00:17:06.320 --> 00:17:07.680
that would be fine with me
00:17:09.540 --> 00:17:10.100
okay yes
00:17:15.380 --> 00:17:17.140
many professors dont care
00:17:26.240 --> 00:17:29.280
if you get to this step its usually good enough
00:17:30.940 --> 00:17:33.340
you have to remind the tas of that one
00:17:46.000 --> 00:17:47.600
lets do another problem
00:19:25.120 --> 00:19:26.320
you have two ships
00:19:28.060 --> 00:19:30.700
ship a leaves port at noon and sails 8 mph
00:19:34.920 --> 00:19:36.600
ship b leaves port at 6:30
00:19:37.680 --> 00:19:39.120
and sails about 10 mph
00:19:39.480 --> 00:19:44.200
if the angle between the ships is 60 degrees how far apart are they at 2pm
00:19:45.700 --> 00:19:48.260
and next semester youll learn how fast
00:19:48.700 --> 00:19:49.360
but not yet
00:19:56.420 --> 00:19:58.420
going this way, going that way
00:20:00.940 --> 00:20:02.060
60 degrees thats
00:20:10.320 --> 00:20:11.520
so how can we find c
00:20:13.760 --> 00:20:15.840
well we can use the law of cosine
00:20:17.180 --> 00:20:17.820
c sqyared
00:20:19.340 --> 00:20:21.100
is a squared plus b squared
00:20:23.400 --> 00:20:24.040
minus 2ab
00:20:25.980 --> 00:20:26.480
cos c
00:20:30.280 --> 00:20:31.880
and what else do we know?
00:20:32.920 --> 00:20:35.480
we know that a is how far the ship as gone
00:20:36.100 --> 00:20:36.600
at 2pm
00:20:37.600 --> 00:20:38.880
also 8mph in 2 hours
00:20:40.460 --> 00:20:41.180
so thats 16
00:20:43.120 --> 00:20:43.620
b
00:20:44.620 --> 00:20:45.580
is going 10 mph
00:20:45.580 --> 00:20:46.820
for an hour and a half
00:20:49.540 --> 00:20:50.100
thats 15
00:20:55.600 --> 00:20:56.560
so far so good?
00:20:57.420 --> 00:21:00.060
you know where those numbers come from?
00:21:02.180 --> 00:21:03.380
8mph for 2 hours is
00:21:04.240 --> 00:21:04.800
16 miles
00:21:06.380 --> 00:21:07.180
so this is 16
00:21:10.720 --> 00:21:11.220
10 mph
00:21:11.260 --> 00:21:12.300
per hour and 1/2
00:21:13.260 --> 00:21:13.980
is 15 miles
00:21:19.900 --> 00:21:21.660
10 mph for 1 hour is 10 miles
00:21:21.660 --> 00:21:22.680
plus an hour and 1/2
00:21:22.780 --> 00:21:24.300
you get another 5 miles
00:21:24.300 --> 00:21:25.280
you get 15 miles
00:21:28.420 --> 00:21:28.920
minus 2
00:21:31.200 --> 00:21:31.700
times
00:21:32.540 --> 00:21:33.660
2 times 16 imes 15
00:21:39.220 --> 00:21:40.180
cos60 degrees
00:21:45.500 --> 00:21:46.220
that is 256
00:21:49.260 --> 00:21:49.820
plus 225
00:21:52.820 --> 00:21:54.820
-480 times cos60 which is a 1/2
00:22:01.100 --> 00:22:02.700
2 times 16 times 15 is 480
00:22:03.480 --> 00:22:04.280
cos60 is 1/2
00:22:08.880 --> 00:22:09.380
481
00:22:10.260 --> 00:22:10.900
minus 240
00:22:12.140 --> 00:22:12.780
c squared
00:22:13.640 --> 00:22:14.440
c squared is
00:22:16.320 --> 00:22:17.040
241 and c is
00:22:18.360 --> 00:22:19.560
square root of 241
00:22:21.420 --> 00:22:22.620
that would be 15.7
00:22:26.700 --> 00:22:27.420
maybe 15.8
00:22:30.800 --> 00:22:32.240
howd we do on this one?
00:22:37.140 --> 00:22:38.020
so once again
00:22:38.420 --> 00:22:40.420
where do the 16 and 15 come from
00:22:41.140 --> 00:22:41.860
you go 8 mph
00:22:42.480 --> 00:22:43.200
for 2 hours
00:22:44.120 --> 00:22:46.600
so 8 miles per hour for 1 hour is 8 miles
00:22:46.820 --> 00:22:48.820
2 hours at another 8 is 16 miles
00:22:49.520 --> 00:22:51.280
10 mph for an hour and a half
00:22:51.780 --> 00:22:53.220
so 10 to the first hour
00:22:54.160 --> 00:22:55.920
five for the next hour is 15
00:23:01.840 --> 00:23:05.600
do we know the law of cosin or should we do another of those
00:23:09.720 --> 00:23:10.920
one more? alright
00:25:08.300 --> 00:25:09.980
airplane a and airplane b
00:25:11.460 --> 00:25:13.540
are initially at the same point
00:25:15.320 --> 00:25:17.800
a flies at 500 mph and b flies at 300mph
00:25:19.360 --> 00:25:20.560
the annually pi/6
00:25:21.260 --> 00:25:23.260
how far are they after 3 hours?
00:25:26.960 --> 00:25:29.520
alright well c squared is well lets see
00:25:31.160 --> 00:25:31.880
airplane a
00:25:32.980 --> 00:25:34.020
is going 200 mph
00:25:36.200 --> 00:25:36.920
for 200 mph
00:25:37.300 --> 00:25:38.020
for 3 hours
00:25:38.760 --> 00:25:39.560
is 600 miles
00:25:43.140 --> 00:25:45.700
everyone see where the 600 comes from?
00:25:47.620 --> 00:25:48.820
200 mph for 3 hours
00:25:50.900 --> 00:25:51.400
b
00:25:52.880 --> 00:25:55.920
b goes 300 mph for 3 hours so b is going 900 miles
00:26:01.360 --> 00:26:02.480
minus 2 times 600
00:26:03.120 --> 00:26:03.760
times 900
00:26:06.580 --> 00:26:07.620
cos150 degrees
00:26:12.940 --> 00:26:14.540
do scientific notation
00:26:32.900 --> 00:26:34.820
and you get 360,000+810,000
00:26:36.740 --> 00:26:37.860
minus 1,080,000
00:26:38.380 --> 00:26:40.220
times negative radical 3/2
00:26:42.100 --> 00:26:43.780
arent those fun numbers?
00:26:47.300 --> 00:26:49.300
why is it negative radical 3/2
00:26:49.300 --> 00:26:50.900
cos150 is negative degrees
00:26:50.900 --> 00:26:52.460
youre in the second quadrant
00:26:53.860 --> 00:26:55.220
its the same as cos30
00:26:56.720 --> 00:26:58.480
but where on the other side
00:26:59.600 --> 00:27:01.280
so you add those together
00:27:15.640 --> 00:27:19.000
and since square root of something awful like that
00:27:22.560 --> 00:27:25.200
i dont really care what numbers come out
00:27:45.640 --> 00:27:48.440
whats another kind of thing you need to use
00:27:52.240 --> 00:27:53.600
we can do one of those
00:27:57.940 --> 00:27:59.540
everyone set with this?
00:28:56.760 --> 00:28:58.120
piecewise function
00:28:58.120 --> 00:29:01.320
x squared minus 4 is greater then or equal to zero
00:29:02.660 --> 00:29:04.340
and 5 plus 3x is less then 0
00:29:05.380 --> 00:29:06.660
find all values of x
00:29:07.820 --> 00:29:09.100
where f of x equals 0
00:29:10.740 --> 00:29:15.220
this is very straight forward it will only take two or three minutes
00:29:18.640 --> 00:29:20.960
if we wanna know where f of x equals 0
00:29:24.140 --> 00:29:25.740
f of x is x squared minus 4
00:29:27.260 --> 00:29:29.580
x is positive 5 plus 3x s is negative
00:29:29.580 --> 00:29:33.180
so you shouold know where both of these parts equal to zero
00:29:34.940 --> 00:29:36.620
x squared minus 4 equals 0
00:29:39.460 --> 00:29:41.300
well when x squared equals 4
00:29:43.800 --> 00:29:45.000
s is plus or minus 2
00:29:47.920 --> 00:29:52.800
you would have to throw out the x is -2 becaues it has to be x is greater then 0
00:29:53.160 --> 00:29:55.480
so you have to throw one of those out
00:29:58.360 --> 00:29:59.560
so you only get x=2
00:30:00.900 --> 00:30:04.100
now for the second equation you find out what is 0
00:30:04.440 --> 00:30:04.940
so 5
00:30:05.980 --> 00:30:06.780
=3x equals 0
00:30:08.820 --> 00:30:10.180
and x is negative 5/3
00:30:12.360 --> 00:30:15.400
negative 5/3 is less than 0, so thats also true
00:30:56.360 --> 00:30:57.960
alright find the domain
00:31:00.500 --> 00:31:03.060
the numerator can be anything it wants
00:31:03.060 --> 00:31:05.240
we dont care whats in the numerator
00:31:05.420 --> 00:31:07.980
denominator what about the cubed root
00:31:08.640 --> 00:31:10.560
you can get a negative number
00:31:11.020 --> 00:31:11.520
sure
00:31:12.140 --> 00:31:14.780
the only problem in the denominator is 0
00:31:15.700 --> 00:31:17.620
the domain would be all reals
00:31:19.540 --> 00:31:20.340
except x is 5
00:31:21.720 --> 00:31:23.640
wen x is 5 the denominator is 0
00:31:26.200 --> 00:31:27.240
what if instead
00:31:30.400 --> 00:31:31.040
i gave you
00:31:37.820 --> 00:31:39.900
6-2x over the squrae root of x-5
00:31:54.020 --> 00:31:54.900
so once again
00:31:55.120 --> 00:31:57.680
the numerator can be anything it wants
00:31:58.020 --> 00:32:01.540
but the denominator, you cant have a negative number
00:32:01.540 --> 00:32:04.100
the denominator has to be greater then 0
00:32:04.600 --> 00:32:06.520
and that the denominator is 0
00:32:07.800 --> 00:32:09.000
x is greater then y
00:32:14.420 --> 00:32:17.380
interval notation, you want to d that again?
00:32:22.560 --> 00:32:24.720
thats 5 and infinity, thats 5 and
00:32:24.720 --> 00:32:26.300
negative infinity and 5
00:32:28.940 --> 00:32:29.980
and 5, infinity
00:32:39.640 --> 00:32:41.560
what i i turn this upside down
00:32:44.860 --> 00:32:45.580
and do h of x
00:32:47.440 --> 00:32:48.640
square root of x-5
00:32:50.820 --> 00:32:51.780
over 6 minus 2x
00:32:52.020 --> 00:32:54.980
interval notation is nice but not necessary
00:32:55.040 --> 00:32:57.680
only necassary when theres graph stuff
00:33:50.700 --> 00:33:51.200
now
00:33:52.940 --> 00:33:55.180
now we do care about the numerator
00:33:55.180 --> 00:33:58.480
because you cant do the square root of a negative number
00:33:59.200 --> 00:34:00.320
so the numerator
00:34:02.060 --> 00:34:05.900
x has to be greater than or equal to 5, whats the difference
00:34:05.940 --> 00:34:07.380
between here and here
00:34:08.140 --> 00:34:09.660
here x cant be 5 because
00:34:09.660 --> 00:34:11.560
because you have 5 in the denominator
00:34:11.980 --> 00:34:12.700
you put in 5
00:34:12.700 --> 00:34:14.040
and denominator you put 0
00:34:14.960 --> 00:34:15.600
thats bad
00:34:16.040 --> 00:34:19.560
of the numerator is 0, thats fine of the numerator is 0
00:34:21.300 --> 00:34:21.800
and
00:34:23.620 --> 00:34:24.500
6-2x cant be 0
00:34:25.360 --> 00:34:26.560
so x cannot equal 3
00:34:30.360 --> 00:34:33.000
you plug in 3 you get 0 in the denominator
00:34:33.400 --> 00:34:36.120
square root of x-5 in the numerator so you
00:34:36.120 --> 00:34:38.080
you can have 0 in the numerator
00:34:38.920 --> 00:34:40.200
x could be equla to 5
00:34:40.940 --> 00:34:45.340
or the middle one, you cant have 0 in the denominator so x cannot be 5
00:34:46.340 --> 00:34:47.140
got the idea
00:34:49.920 --> 00:34:50.420
yes no?
00:35:48.540 --> 00:35:50.460
how bout something like that
00:35:51.340 --> 00:35:52.860
sin cos negative 1 (3/7
00:35:52.860 --> 00:35:55.180
first of all you notice its a positive number
00:35:55.180 --> 00:35:56.780
and we are in the first quadrant
00:35:58.400 --> 00:36:00.400
that means we have some number
00:36:02.580 --> 00:36:04.340
the cos of this angle is 3/7
00:36:05.540 --> 00:36:08.980
and now were just trying to find the sin of that angle
00:36:12.380 --> 00:36:14.460
you just want to find the sin of x
00:36:14.560 --> 00:36:18.240
use the pythagorean theorem and thats square root of 40
00:36:24.060 --> 00:36:25.820
sinx is square root of 40/7
00:36:27.200 --> 00:36:28.320
that wasnt so bad
00:36:34.740 --> 00:36:36.100
one last one of these
00:37:05.260 --> 00:37:09.100
cos now we do negative, where do we do inverse cos negative
00:37:09.800 --> 00:37:11.160
the second quadrant
00:37:13.840 --> 00:37:14.640
we have sin x
00:37:15.900 --> 00:37:16.400
cos of x
00:37:17.520 --> 00:37:18.560
is negative 2/9
00:37:22.300 --> 00:37:24.300
so we use pythagorean theorem
00:37:25.320 --> 00:37:26.520
and that comes out
00:37:28.080 --> 00:37:29.360
square root 7 over 7
00:37:30.280 --> 00:37:31.880
9 square minus 2 squared
00:37:35.180 --> 00:37:37.260
this is gonna be the tangent of x
00:37:41.560 --> 00:37:42.120
which is
00:37:43.940 --> 00:37:46.100
negative square root of 77 over 2