According to Kate Raworth and her Doughnut Economics model, a order to achieve a humanity. and economy are required in and space for
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Economics is a social science which deals with human behavior as a relationship between ________. a. unlimited buyers and limited sellers b. consumption and production c. unlimited wants and scarce resources d. unending wants and limited people
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a. A torus of revolution (doughnut) is obtained by rotating a circle $C$ in the $x z$ -plane about the $z$ -axis in space. (See the accompa- nying figure.) If $C$ has radius $r>0$ and center $(R, 0,0),$ show that a parametrization of the torus is $$\begin{aligned} \mathbf{r}(u, v)=&((R+r \cos u) \cos v) \mathbf{i} \\ &+((R+r \cos u) \sin v) \mathbf{j}+(r \sin u) \mathbf{k} \end{aligned}$$ where $0 \leq u \leq 2 \pi$ and $0 \leq v \leq 2 \pi$ are the angles in the figure. b. Show that the surface area of the torus is $A=4 \pi^{2} R r$
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