This looks like an exercise that's building toward the idea of a derivative.
These calculations are done best with a calculator, but here's how the first interval is used:
Average velocity = (position at 2 - position at 1) / (2 - 1) It's really distance divided by time!
Position at t = 2:
Position at t = 1:
So over the interval [1, 2] the average velocity is
I used a spreadsheet to calculate the average velocity over the other intervals and a couple of shorter ones, too. (See attached image.)
As these intervals get shorter (the right endpoint is approaching 1), the average velocity gets closer and closer to the instantaneous velocity. An estimate would be -12.6.
Answer:
Step-by-step explanation:
<u>Given</u>
<u>Solving for n</u>
- 4(0.5n) - 4(3) = n - 0.25(12) + 0.25(8n)
- 2n - 12 = n - 3 + 2n
- -12 = n - 3
- n = 3 - 12
- n = -9
Answer:
The third choice
Step-by-step explanation:
We need to find the slope and y-intercept of the line and then put it into y = mx = b form. To find the slope, pick a point on the line; I will use (-2, 5); count how many units up you need to go to get to the next point on the line, which in this case it would be 3. The count how many to the right or left you would need to go, which is 1 to the left. Moving left means a negative, so it is -1. Your slope fraction would be , since slope is rise over run. You can sub this fraction in for m in y = mx + b, which will give you a revised equation of y = -3x = b. To find the y intercept, or b, just find the point where the line crosses the y-axis, which is -1. So, the equation is now y = -3x - 1.The correct answer is third choice.