Suppose that the random variables X and Y have joint p.d.f.f(x,y)=\begin

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.

A 17.8 kg flood light in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A cable connected to the beam helps to support the light. (In thefigure, ${\displaystyle \theta }$ = 34.2 degrees. Find (A) The tension in the cable and (B) the horizontal and (C) vertical forces exerted on the beamby the pole.

(A) 320 N
(B) 250 N
(C) 0

A stone hangs by a fine thread from the ceiling,and a section of the same thread dangles from the bottom of the stone.If a person gives a sharp pull on the dangling thread,where is the thread likely to break:below the stone or above it?

Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height of 13 m into 35 cm. of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass to be 72 kg, find the magnitudes of the impulse on him from the water.

Consider a solution ${\displaystyle x_1}$ of the linear system Ax=b. Justify the facts stated in parts (a) and (b):
a) If ${\displaystyle x_h}$ is a solution of the system Ax=0, then ${\displaystyle x_1+x_h}$ is a solution of the system Ax=b.
b) If ${\displaystyle x_2}$ is another solution of the system Ax=b, then ${\displaystyle x_2-x_1}$ is a solution of the system Ax=0

Find the inverse Laplace transform $f\left(t\right)=L^{-1}\left\{F\left(s\right)\right\}$ of each of the following functions.
$\left(i\right)F\left(s\right)=\frac{2s+1}{s^2-2s+1}$
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
$\left(ii\right)F\left(s\right)=\frac{3s+2}{s^2-3s+2}$
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.
$\left(iii\right)F\left(s\right)=\frac{3s^2+4}{(s^2+1)(s-1)}$
Hint – Use Partial Fraction Decomposition and the Table of Laplace Transforms.

To calculate:
To simplify the expression $\sqrt[3]{24}-\sqrt[3]{81}$.