A linkage mechanism of a machine is subjected to three forces F1 = 68 N, F2 = 20 N, and F3 exerted by other machine parts as shown in the figure. The two rods shown
in the linkage are light weight compared to the forces and their masses can be
neglected. The 6.0 cm rod makes an angle 0 = 36° with the horizontal as shown.
Which force F3 will set the linkage system in equilibrium? Keep your answer to the
nearest newton. (Do not include units in your answer)

Cameron indoor stadium at duke university is one of the most revered sites in all of college basketball, as well as in all of sports period. duke’s men’s and women’s basketball programs have attained quite a few wins in the building over the last seventy years. cameron indoor stadium is capable of seating 9,460 people. for each game, the amount of money that the duke blue devils’ athletic program brings in as revenue is a function of the number of people in attendance. if each ticket costs $45.50, find the domain and range of this function.

Suppose that a households monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, hcf). when graphed, the function gives a line with slope of 1.65. if the monthly cost for 13 hcf is $46.10 what is the monthly cost for 19 hcf?

Find the perimeter of the triangle with vertices  d(3, 4),  e(8, 7), and  f(5, 9). do not round before calculating the perimeter. after calculating the perimeter, round your answer to the nearest tenth.