A 20 kg box is being pulled across a floor by a horizontal rope. The tension in the rope is 99 Newtons. The coefficient of friction is 0.25. What is the force of friction on the box? What is the acceleration of the box?

You are given two vectors a⃗ =−3.00ι^ 5.00j^ and b⃗ =5.00ι^ 2.00j^. let the counterclockwise angles be positive.

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j

The horizontal blue line through the middle of the lens is called the optical axis. as the lamp is moved above or below the axis, keeping the horizontal distance to the center of the lens constant, how does the horizontal distance from the lens to the image change?