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NationalTutoringObservatory
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MathEd-PII

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student
is it 3,5 again?
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volunteer
So because the combined line never ends (all points are included in the union), the interval is (-∞,∞)
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student
ok
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volunteer
Does that make sense?
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student
so for the steps we
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student
combine the two intervals into one?
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volunteer
Yes, that is a great way to look at it
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student
step 2. see if any numbers are not included in the line
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volunteer
Yep, and the answer is the interval of numbers which ARE on the line
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student
step 3 every # is included
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volunteer
For this problem, all numbers are included
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student
yep
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student
i have one more left
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student
if you Ben have time
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[ { "pii_type": "PERSON", "surrogate": "Ben", "start": 7, "end": 10 } ]
volunteer
Of course!
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student
ok
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student
lets work on A first
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volunteer
Sounds good! Do you want to try to draw the intervals on the number line for this one?
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student
sure
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student
done
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volunteer
The second interval should go to positive ∞ actually
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student
-4?
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student
oh i see
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volunteer
from -4 to positive ∞
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student
so this way?
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student
and closed circle?
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volunteer
Yes
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student
ok
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volunteer
Now, this question is asking for union again. Try to solve it using our steps!
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student
[-4,-1]
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volunteer
That is correct, but that is for intersection which is problem b
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student
ohhhh
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student
so combine the intervals
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student
into one
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student
?
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volunteer
yes, and then look to see if there are any places not covered by the line
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student
kk
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student
all covered
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student
so negative infinity, positive infiny
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volunteer
exactlu!
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student
and thats it?
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student
for a?
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volunteer
yes
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student
now B
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volunteer
For b, we look at the overlap, which you correctly said was the interval [-4,-1].
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student
find where they overlap
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student
mhm
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student
starts at -4 ends at -1?
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student
?
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volunteer
Yes
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student
thanks so much for your help! :)
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volunteer
Of course, great job with that material!
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volunteer
Hi, how can I help you today?
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student
hi!
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student
I need help with this one problem
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volunteer
Great!
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volunteer
What's confusing to you?
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student
everything
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volunteer
Ok, let's see if we can find a starting point!
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volunteer
Are these two images part of the same question?
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student
yes
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volunteer
Okay, let's start by defining the question
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volunteer
What is the problem asking?
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student
to find the angles of m<a, m<B, and m<C
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student
and to round our answers to one decimal place
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volunteer
Okay, and we have all the side lengths
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volunteer
Sorry, do you mind if I ask what the dropdown menu says on the first image>
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volunteer
?
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student
oh yea
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student
Law of Cosine or Law of Sine
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volunteer
Ok! Can you tell me the difference between sine and cosine?
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volunteer
If you can't, that's okay, we'll go over it together!
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student
I got it
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student
I'm typing them rn
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volunteer
Sounds good!
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student
Sine (0) = opposite/ hypotenouse
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student
Cosine (0)= adjacent/ hypotenuse
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volunteer
Ok, those are perfect!
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volunteer
I'm a little confused because the triangle in the picture doesn't have a right angle, so it wouldn't have a hypotenuse
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volunteer
We can't use either theorem because there isn't a hypotenuse
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student
could we use Pythagoras
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volunteer
The trigonometric functions only work on right triangles!
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student
oh
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volunteer
So sine, cosine, tangent, etc, don't work unless there's a right angle
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volunteer
I'm not sure what your teacher wants us to do here, did they ever bring up triangles with no right angle?
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student
no
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student
I'm doing geometry online through University of Phoenix
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[ { "pii_type": "SCHOOL", "surrogate": "University of Phoenix", "start": 34, "end": 55 } ]
volunteer
Hmm
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volunteer
You said the first and second images are part of the same question?
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student
yes
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volunteer
Then I think the answer is going to have to be no solutions
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student
ok
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volunteer
Wait, actually, hold on one minute!
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student
ok
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volunteer
Okay, I was mistaken about the Law of Cosines, sorry!
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volunteer
The law states:
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volunteer
a^2 = b^2 + c^2 - 2bc * cos(A)
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volunteer
b^2 = a^2 + c^2 - 2ac * cos(B)
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student
ok
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volunteer
c^2 = a^2 + b^2 - 2ab * cos(c)
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