Chapter 2.4, Problem 29E

A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a. Compute the area of the piece to be cut. Round the answer to the nearest square millimeter. b. After cutting the piece, determine the percentage of the plate that will be wasted.

aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

Area under the curve x + y = 3 and the coordinate axis

A boat leaves a port traveling due east at 12 mi/hr. At the same time, another boat leaves the same port traveling northeast at 15 mi/hr. The angle 8 of the line between the boats is measured relative to due north (see the figure to the right). What is the rate of change of this angle 30 min after the boats leave the port? 3 hr after the boats leave the port? X= Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat. Write an equation relating x, z, and 0. √√2 √2 2 (Type an exact answer. Type any angle measures in radians.) Z+ -z tan 0 2 C The rate of change of this angle 30 min after the boats leave the port is (Round to the nearest thousandth as needed.) Port 15 mi/h 12 mi/h ----191

An airplane flies at an altitude of  y = 4  miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation ? is changing when the angle is  ? = 45°,   ? = 60°,  and  ? = 80°.   (a)    ? = 45°  rad/min(b)    ? = 60°  rad/min(c)    ? = 80° (Round your answer to two decimal places.)  rad/min

Water is leaking out the bottom of a hemispherical tank of radius 9 feet at a rate of 3 cubic feet per hour. the tank was full at a certain time. how fast is the water level changing when its height h is 5 feet? note​: the volume of a segment of height h in a hemisphere of radius r is pi h squared left bracket r minus left parenthesis h divided by 3 right parenthesis right bracket.

The radius r of a sphere is increasing at a rate of 5 inches per minute. Find the rate of change of the volume when r = 9 inches and r = 16 inches. (a) r = 9 inches in3/min (b) r = 16 inches in3/min

please be quick