A carton of mass 10 kg is at rest on a rough plane inclined at an angle of 25° to the horizontal. Calculate the magnitude of the friction force, in newtons, to two significant figures. (Take the magnitude of the acceleration due to gravity, g, to be 9.8 ms 2.) The magnitude of the friction force is N (to 2.s.f.).

Let W be the subspace of R³ spanned by the vectors 1 and Find the projection matrix P that projects vectors in R³ onto W. 18881 P = 10

A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the​ house, the base is moving away at the rate of 24 ​ft/sec. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​then? c. At what rate is the angle between the ladder and the ground changing​ then? A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta. θ x(t)y(t)010-ft ladderxy   a. The rate of change of the height of the top of the ladder is nothing ​ft/sec. ​(Simplify your​ answer.)   b. The area is changing at…

It takes a force of 21,882 lb to compress a coil spring assembly from its free height of 6 inches to its fully compressed height of 3 inches. a. What is the assembly's force constant? b. How much work does it take to compress the assembly the first half inch? the second half inch? Answer to the nearest in-lb. a. k= lb/in