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Mathematical steps

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.

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

s, 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 always a way to try to avoid it, like sanctions or appeasement, showing Vittola’s theory is flawed. Fourthly, Vittola questions upon whose authority can demand a declaration of war, where he implies any commonwealth can go to war, but more importantly, “the prince” where he has “the natural order” according to Augustine, and all authority is given to him. This is further supported by Aristotle’s Politics ((1996), Page 28): ‘a king is the natural superior of his subjects.’ However, he does later emphasise to put all faith in the prince is wrong and has consequences; a thorough examination of the cause of war is required along with the willingness to negotiate rival party (Begby et al (2006b), Page 312& 318). This is supported by the actions of Hitler are deemed unjustly. Also, in today’s world, wars are no longer fought only by states but also non-state actors like Al-Queda and ISIS, showing Vittola’s normative claim on authority is outdated. This is further supported by Frowe’s claim that the leader needs to represent the people’s interests, under legitimate authority, which links on to the fourth condition: Public declaration of war. Agreed with many, there must be an official announcement on a declaration of war (Frowe (2011), Page 59-60&63). Finally, the most controversial condition is that wars should have a reasonable chance of success. As Vittola reiterated, the aim of war is to establish peace and security; securing the public goo
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