a. Find the arc length of the curve y = ln(x) on [1,5] b. A force of 5 pounds compresses a 15-inch spring 3 inches. How much work is required to compress the spring a total of 7 inches.

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.

A piece of round stock is being turned to a 17.86-millimeter diameter. A machinist measures the diameter of the piece as 18.10 millimeters.What depth of cut should be made to turn the piece to the required diameter?

Calculate the force (in Newtons) required to push a 50kg wagon up a 0.2 radian inclined plane. One Newton (N) is equal to 1 kg-m and the g2 force due to gravity on the wagon is F = m * g, where m is the mass of the wagon, and g is the acceleration due to gravity (9.8 ). Please ignore friction in this problem. Hint: draw a picture, and express the forces on the wagon as vectors. Force N

A shell of mass 4 kg is shot upward with an initial velocity of 200 m/sec. The magnitude of the force on the shell due to air resistance is 20 the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m/s². When will the shell reach its maximum height above the ground? The shell will reach maximum height after 18.16 seconds. (Round to two decimal places as needed.) What is the maximum height? The maximum height is 1747 m. (Round to the nearest whole number as needed.) 3 (...) When will the shell reach its maximum height above

A 50 N force is applied at the end of a 20 cm wrench and makes an angle of 30° with the handle of the wrench. Find the magnitude of the torque. b. What is the maximum torque that can be exerted by a 50 N force on the wrench and а. how it can be achieved?

solve fast ,within 20 min

Answer: 750 Newtons

Part E: Vectors MindBook decides to diversify their portfolio and invest in the "RoboMap" technology which is a robot that maps different types of territories. The new CEO is trying to make some drastic changes to some of the software and hardware systems in the new version of the robot. You have been hired by the opposing faction in the board to lead an investigation on how the performance of the robot is affected by the new proposed changes. a) The first system that you will test is the navigation system. The robot maps the territory by calculating distances and angles whilst moving between various locations. It then stores on its system the shortest direct path from initial location to the intended target. During the test the robot navigates around a muddy surface in the following path: 55cm [NW] and then moves 45cm [S30°W]. The robot sends back to the server the following overall shortest path: 70cm [W10°S]. Use triangle or parallelogram method to verify the precision of the…

Suppose a spring with spring constant 8 N/m is horizontal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 1.4 Hz (cycles per second). What is the mass? Assume there is no friction. Mass= help (units)