Compute \(\oint_{C}{\bf F}\cdot d{\bf r}\) where \(C\) is the curve parametrized by \({\bf r}(t)= \langle \cos t,\sin t, \cos t+\sin t \rangle, \quad 0\leq t\leq 2\pi\) and where \({\bf F}=(xy+z){\bf i}+z^2{\bf j}+xyz{\bf k}\) [Hint: The curve lies on the surface \(z=x+y\)]
Read DetailsEvaluate the integral \(\int_{C} {\bf F} \cdot {\bf dr} \) where \({\bf F}=\left( \frac{1}{x}+y \right) {\bf i} + \left( \frac{1}{y} + x \right) {\bf j}\) and \(C\) is a smooth curve with starting point \((1,1)\) and end point \((2,3)\).
Read Details5.1 Poverty can be described as (1) A. the state of not having enough material possessions or income for a person’s basic needs. B. having enough material possessions to live comfortably. C. a condition that results from eating a diet which does not supply a healthy amount of nutrients. D. the condition of not having adequate housing.
Read Details3. Match column A with column B (5) COLUMN A COLUMN B 3.1. To have supreme power or authority. A. Electorate 3.2. Example of a non-sovereign state. B. Sovereignty 3.3. It is a system of government in which power and authority are controlled by a single person or party. C. Nation-state 3.4. A cultural group that is also a state. D. Hong Kong 3.5. All the people in a country who are allowed to vote. E. Totalitarian
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