Question

chapter 2 performance task (continued)

1. given the load inequality below, describe what appliances could be running, and calculate how many watts you can still add. provide an example of other appliances that could be running without overloading this system.

1100 + 600 + 1150 + 1800 + 5000 + 500 + 8(60)+70 + 240 ≤ 18,000
10,150+480 + 310 ≤ 18,000
10,440 ≤ 18,000

1. refer to your scenarios in exercise 2. increase the total number of watts in each situation by 40%. the additional 40% compensates for the surge wattage required at the startup of an appliance. express your answer as an inequality.

scenario 1: original scenario 1 inequality:
new inequality:
scenario 2: original scenario 2 inequality:
new inequality:
scenario 3: original scenario 3 inequality:
new inequality:

1. use the information you created from your three scenarios to produce an inequality to represent the maximum number of watts you might need to have available at any given time in your dream home. explain how you arrived at your decision.

inequality:
i decided that i would need ____ watts because ____

Explanation:

Step1: Analyze the problem

We need to work with inequalities and watt - age calculations.

Step2: For Scenario 1 (assuming original inequality is \(x\leq y\))

The new inequality with a 40% increase for startup wattage would be \(x(1 + 0.4)\leq y\).

Step3: For Scenario 2 and 3 (similarly)

If the original inequalities are \(a\leq b\) and \(c\leq d\) respectively, the new inequalities are \(a(1 + 0.4)\leq b\) and \(c(1 + 0.4)\leq d\).

Step4: For question 5

To find the maximum number of watts needed, we consider the highest value among the new inequalities from the three scenarios. Let the watt - age values from the three scenarios after 40% increase be \(W_1\), \(W_2\), \(W_3\). The inequality for the maximum number of watts \(M\) is \(M=\max\{W_1,W_2,W_3\}\).

Answer:

Since the original inequalities for Scenarios 1 - 3 are not given, we can't provide specific inequalities. But for Scenario 1, if the original inequality is \(x\leq y\), the new one is \(1.4x\leq y\). Similarly for Scenario 2 and 3 with new inequalities \(1.4a\leq b\) and \(1.4c\leq d\) respectively. For question 5, the inequality is \(M = \max\{W_1,W_2,W_3\}\) where \(W_1\), \(W_2\), \(W_3\) are the watt - age values after 40% increase in each scenario.