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Some of the geometric formulas we take for granted today were first derived by methods that anticipate some of the methods of calculus. The Greek mathematician Archimedes (ca. 287—212; BCE) was particularly inventive, using polygons inscribed within circles to approximate the area of the circle as the number of sides of the
We can estimate the area of a circle by computing the area of an inscribed regular polygon. Think of the regular polygon as being made up of n triangles. By taking the limit as the vertex angle of these mangles goes to zero, you can obtain the area of the circle. To see this, carry out the following steps:
1. Express the height h and the base b of the isosceles triangle in Figure 2.31 in terms of
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- After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year and he will earn $63,417 for his tenth year of work. Complete each of the 2 activities for this Task. Activity 1 of 2 Part A: To the nearest dollar, what is Herbert's starting salary? O A. $94,244 O B. $42,674 O C. $40,836 D. $98,485arrow_forwardThe machined plate distances shown in Figure 41-3 are dimensioned, in millimeters, in terms of x. Determine dimensions A-G.arrow_forwardThe figure shows two circles C and D of radius 1 that touch at P. The line T is a common tangent line; C, is the circle that touches C, D, and T; C, is the circle that touches C, D, and C;; C3 is the circle that touches C, D, and C3. This procedure can be continued indefinitely and produces an infinite sequence of circles {C,}. Find an expression for the diameter of C, and thus provide another geometric demonstration of Example 8. In[n+1] dn = 1 C Tarrow_forward
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- please show work 5.1 #3arrow_forwardPlease answer part a and b. Show work! Thank you.arrow_forwardMany smartphones are now able to use information sent out by GPS satellites (of which there are about nine overhead at any one time) in a similar way. Since the satellites are moving around in space, and therefore can’t be located on a two-dimensional map of the Earth, we now need to consider three-dimensional geometry. How many satellites are needed to be sure of the location of a smartphone? Explain your findingsarrow_forward
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