Choose all options that apply. In the US Customary System, which of the following terms is used to measure volume? a) Cup b) Tab
2 answers:
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To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling
at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
with each of being either 1 or 2.
Then the integral of over
is approximated by the Riemann sum,
(compare to the actual value of about 4.159)
Format of my answer:
[Problem letter] Parallel Lines
- Converse / Reason
!! I am not sure which / what converses you are using, but I gave the reasoning for it. If you see something similar, use the converses you know !!
[a] j & k
- If two lines intersected by a transversal form congruent alternate interior angles, then the lines are parallel
[b] m & n
- If angles are supplementary in this placement, the lines are parallel
[c] l & n
- If angles are equal when they are corresponding, the lines are parallel
[d] l & m
- If two angles that are congruent are vertical, the lines are parallel
[e] j & k
- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel
[f] l & n
- If angles are supplementary in this placement, the lines are parallel
[g] l & n
- If two angles that are congruent are vertical, the lines are parallel
[h] -------
[i] l & n
- If two angles that are congruent are vertical, the lines are parallel
[j] -------
[k] -------
[l] j & k
- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel
[m] -------
[n] j & k
- If angles are supplementary in this placement, the lines are parallel
[o] -------
-> See attached for more information
Have a nice day! - hopefully these are mostly correct, been awhile since I've done this
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
