1 2 4 5 6 r(1) 2 10 24 36 46 54 60 3.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Suppose that a volcano is erupting and readings of the rate r(t)
at which solid materials are spewed into the atmosphere
are given in the table. The time t is measured in seconds and
the units for r(t) are tonnes (metric tons) per second.
(a) Give upper and lower estimates for the total quantity Q(6)
of erupted materials after 6 seconds.
(b) Use the Midpoint Rule to estimate Q(6) .
Given:
| t | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| r(t) | 2 | 10 | 24 | 36 | 46 | 54 | 60 |
To find:
(a) Upper and Lower estimates.
(b)Midpoint Rule estimate.
| t | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| r(t) | 2 | 10 | 24 | 36 | 46 | 54 | 60 |
(a) Upper and Lower estimates.
The right endpoint estimate,
The upper estimate is 172 tonnes.
The left endpoint estimate,
Lower estimate is
The lower estimate is 230 tonnes.
Step by step
Solved in 3 steps
