MA005: Calculus I

1. (a) $(10)(12) + (8)(4) = 152$  (b)$(10)(20) – (3)(8) = 176$

3. $\mathrm{bh}+\frac{1}{2} \mathrm{~b}(\mathrm{H}-\mathrm{h})=\mathrm{bh}+\frac{1}{2} \mathrm{bH}-\frac{1}{2} \mathrm{bh}=\mathrm{b}\left(\frac{\mathrm{h}+\mathrm{H}}{2}\right)$

5. (a) $(1)(3) + (1)(2) = 5$  (b) {area of shaded region in Fig. 24b} < 5

7. $\mathrm{A}(1)=1, \mathrm{~A}(2)=2.5, \mathrm{~A}(3)=4.5, \mathrm{~A}(4)=6, \mathrm{~A}(5)=7$

9. $\mathrm{C}(1)=1.5, \mathrm{C}(2)=4, \mathrm{C}(3)=7.5$ and $\mathrm{C}(\mathrm{x})=\text { rect. }+\text { triangle areas }=\mathrm{x}+\frac{1}{2} \mathrm{x}^{*} \mathrm{x}=\mathrm{x}+\frac{1}{2} \mathrm{x}^{2}$

11. Distance = "area" = $(20)(30)+\frac{1}{2}(10)(30)=600+150=750 \text { feet. }$

13. (a) A: 20 seconds to stop. B: 40 seconds to stop.
      (b) A: $\text { A: } \frac{1}{2}(20)(80)$ feet to stop B: $\frac{1}{2}(40)(40)=800$ feet to stop

15. miles, dollars, cubic feet, kilowatt. hours, people, square meals