Question Solved1 Answer Written Homework 1 - Math 116 1. The cost in dollars to a company to produce x bronze medals is given by C(x) = 12x + 39. Suppose the company sells each medal for 25 dollars. a. How much does it cost for the company to produce 75 bronze medals? b. Determine the profit function P(x). Simplify your answer. c. Find the average cost when 10 bronze medals are produced.

6. (06.02 HC) A continuously-decreasing function that is concave up on the interval [2,6] is represented by the table. х 2 3.3 4.4 5.5 6 f(x) 0.5 0.303 0.227 0.182 0.167 x) Part A: Find the left Reimann sum estimate of sºf(x)dx , based on the subintervals given in the table. (4 points) Part B: Write the midpoint Reimann sum that estimates do x(x)dx, based on the subintervals given in the table. (4 points) Part C: Determine whether the left Reimann sum estimate is an overestimate or an underestimate, based on the properties of the function. (2 points)

A model for the change in the number of woodland caribou in Manitoba can be given by dP dt = 6(400 - P), P(0) = 403 where t is measured in months and 1 = 0 represents January 1st, 2017. (a) True or False: The number of Caribou is increasing when t = 0. (b) True or False: P(1) 3e 6+ + 403 is a solution to this initial value problem. (C) Use Euler's method with the step size Al = 1 to estimate the number of woodland caribou in Manitoba on February 1st, 2017.

Consider the function f(x) = 4 1 - 12 dt. We want to find its degree two Taylor polynomial T, (3) near = First, we calculate l'(a). We get: Then, we calculate F"(x). We get: f"(a) = Futting this together, we can construct the degree two Taylor polynomial T2 (2) near == T2(x) = 15

In the figure two identical plastic rods are bent to form a circle of a 10.0 cm radius, one of charge +q and the other of charge −q. The charge is distributed uniformly on both rods. If q = 10 pC, what is the electric field at P, the center of the circle? 2. In the figure two identical plastic rods are bent to form a circle of a 10.0 cm radius, one of charge +q and the other of charge -q. The charge is distributed uniformly on both rods. If q = 10 pC, what is the electric field at P, the center of the circle? +9 ТР -9

Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite is first released from a space shuttle, which is in a circular orbit at an altitude of 185 mi, and is then propelled by an upper-stage booster to its final altitude. As the satellite passes through A, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. The booster is again fired at Bto insert the satellite into a geosynchronous orbit. The second firing increases the speed of the satellite by 4850 ft/s. 29.240 mi 185 mi R-3960 mi Determine the speed of the satellite as it approaches B on the elliptic transfer orbit. (You must provide an answer before moving to the next part.) The speed of the satellite as it approaches Bis ft/s.

6. (20 pts) Eurostar is a high speed rail service that connects London to Paris. The distance from London to the English Channel Tunnel is 108.0 km. The English Channel Tunnel is 50.5 km long. The distance from the English Channel Tunnel to Paris is 316.0 km. The train travels at a maximum speed of 300 km/hr except within the English Channel Tunnel, where a 6. (20 pts) Eurostar is a high speed rail service that connects London to Paris. The distance from London to the English Channel Tunnel is 108.0 km. The English Channel Tunnel is 50.5 km long. The distance from the English Channel Tunnel to Paris is 316.0 km. The train travels at a maximum speed of 300 km/hr except within the English Channel Tunnel, where a reduced speed of 160 km/hr is required for safety reasons. a. How long does the journey from London to Paris take? Give you answer in s. b. If the resistance between the train and the track at maximum speed is 120 kN and air resistance adds an additional 20.5 kN (Note: Power = force x velocity), what is the power in horsepower required to power the engine?