The rate at which pollution escapes a scrubbing process at a manufacturing plant increases over time as filters and other technologies become less effective. For this particular example, assume that the rate of pollution (in tons per week) is given by the following table. days 0| 4| 7| 10 | 14| 20 pollution rate (tons/week) || 43 | 51 | 74 93 122 | 235 (a) Write a left Riemann sum that estimates the amount of pollution emitted over the first four weeks. (Notes: (1) You must include at least two terms in your sum. (2) You do not need to evaluate the sum. (3) The units for time and pollution rate are correct.) (b) How does your left Riemann sum compare to the actually amount of pollutant emitted? Can you tell if your Riemann sum is an overestimate or an underesti- mate?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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