Complete the sentences. Be prepared to explain your reasoning.
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1
1
1
Han and Clare walk towards each other at a constant rate, meet up, and then continue past each other in opposite directions. We will call the position where they meet up 0 feet and the time when they meet up 0 seconds.
Han's velocity is 4 feet per second.
Clare's velocity is -5 feet per second.
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1
It is possible to make a new number system using only the numbers 0, 1, 2, and 3. We will write the symbols for multiplying in this system like this: 1\otimes2=2. The table shows some of the products.
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1
1
1
1
A water well drilling rig has dug to a height of -60 feet after one full day of continuous use.
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1
1
Question 1
1.
Is the solution to this equation positive or negative?
Question 2
2.
Is \frac{35}{27} a solution to the equation?
Question 3
3.
Is -\frac{35}{27} a solution to the equation?
Question 4
4.
-3\cdot4=?
Question 5
5.
-3\cdot?=12
Question 6
6.
3\cdot?=12
Question 7
7.
?\cdot-4=12
Question 8
8.
?\cdot4=-12
Question 9
9.
Rewrite the unknown factor problems as division problems.
Question 10
10.
The sign of a positive number divided by a positive number is always:
Question 11
11.
The sign of a positive number divided by a negative number is always:
Question 12
12.
The sign of a negative number divided by a positive number is always:
Question 13
13.
The sign of a negative number divided by a negative number is always:
Question 14
14.
Where is each person 10 seconds before they meet up?
Question 15
15.
When is each person at the position -10 feet from the meeting place?
Question 16
16.
In this system, 1\otimes3=3 and 2\otimes3=2. How can you see that in the table?
Question 17
17.
What do you think 2\otimes1 is?
Question 18
18.
What about 3\otimes3?
Question 19
19.
What do you think the solution to 3\otimes n=2 is?
Question 20
20.
What about 2\otimes n=3?
Question 21
21.
Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours?
Question 22
22.
If the rig has been running constantly and is currently at a height of -147.5 feet, for how long has the rig been running?
Use the coordinate grid in the applet to show the drill’s progress: