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Perfected a method for the perfect glazed icing

Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk to confectioner’s sugar while exposed to low heat. Your mixing tank starts with 10 fluid ounces of milk and 10 ounces of sugar. You continue adding sugar at a rate of 10 ounces per minute and milk at 2 ounces per minute, as depicted by the two equations below:

S=10+10t

M=10+2t

Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes.

Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes.

Assessment Instructions
Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Part 1: Create a rational equation to represent the concentration (C) in ounces of sugar per ounce of milk.

Part 2: Find the domain of the concentration equation.

Part 3: Will we ever encounter a time where the rational equation is undefined? Explain your reasoning.

Part 4: Calculate the concentration after five minutes.

Part 5: How long does it take to reach a concentration of 4 ounces of sugar per ounce of milk?

Sample Solution

Begby et al (2006b), Page 314). Frowe, however, argues the idea of “just cause” based on “Sovereignty” which refers to the protection of political and territorial rights, along with human rights. In contemporary view, this view is more complicated to answer, given the rise of globalisation. Similarly, it is difficult to measure proportionality, particularly in war, because not only that there is an epistemic problem in calculating, but again today’s world has developed (Frowe (2011), Page 54-6). Furthermore, Vittola argues war is necessary, not only for defensive purposes, ‘since it is lawful to resist force with force,’ but also to fight against the unjust, an offensive war, nations which are not punished for acting unjustly towards its own people or have unjustly taken land from the home nation (Begby et al (2006b), Page 310&313); to “teach its enemies a lesson,” but mainly to achieve the aim of war. This validates Aristotle’s argument: ‘there must be war for the sake of peace (Aristotle (1996), Page 187). However, Frowe argues “self-defence” has a plurality of descriptions, seen in Chapter 1, showing that self-defence cannot always justify one’s actions. Even more problematic, is the case of self-defence in war, where two conflicting views are established: The Collectivists, a whole new theory and the Individualists, the continuation of the domestic theory of self-defence (Frowe (2011), Page 9& 29-34). More importantly, Frowe refutes Vittola’s view on vengeance because firstly it empowers the punisher’s authority, but also today’s world prevents this action between countries through legal bodies like the UN, since we have modernised into a relatively peaceful society (Frowe (2011), Page 80-1). Most importantly, Frowe further refutes Vittola through his claim that ‘right intention cannot be used as an excuse to wage war in response to anticipated wrong,’ suggesting we cannot just harm another just because they have done something unjust. Other factors need to be considered, for example, Proportionality. Thirdly, Vittola argues that war should be avoided (Begby et al (2006b), Page 332) and that we should proceed circumstances diplomatically. This is supported by the “last resort” stance in Frowe, where war should not be permitted unless all measures to seek diplomacy fails (Frowe (2011), Page 62). This means war shouldn’t be declared until one party has no choice but to declare war, in order to protect its territory and rights, the aim of war. However, we can also argue that the war can never be the last resort, given there is
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