Consider the equation of the tractrix y = a sech−1(x/a) − a2 − x2 , a > 0. (a) find dy/dx. dy dx = − a2 x√x+a√−x+a+ x √a2−x2 (b) let l be the tangent line to the tractrix at the point p. when l intersects the y-axis at the point q, show that the distance between p and q is a.

Acable company wants to provide cell phone service for residents on an island. the function for the cost of laying the cable from the island to the mainland is c(x)= 6.500 square root x2+4, where x represents the length of the cable in feet. what are the domain and range of the function? a) domain: all real numbers range: all real numbers greater than or equal to 17,000 b) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 17,000 c) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 13,000 d) domain: all real numbers greater than or equal to 13,000 range: all real numbers greater than or equal to 0

Hardest math question of all time can you solve the equation. check for extraneous solutions.9∣9-8x∣ = 2x+3

Ariel is working at a meat packing plant for 5 nights a week. her regular wage is $11 an hour. she earns tine and a half for any overtime hours. this week she worked 9 hours of over time .how much will ariel earn for overtime this week ?