Other Problem Solutions: Expert Help and Step-by-Step Explanation

A fair coin is flipped four times in a row independently. Let X denote the number of heads obtained. Plot the probability mass function ofthe random variable $X-2$

Refer to the following matrices.
$A=\left[\begin{array}{cccc}2& -3& 7& -4\\ -11& 2& 6& 7\\ 6& 0& 2& 7\\ 5& 1& 5& -8\end{array}\right]B=\left[\begin{array}{ccc}3& -1& 2\\ 0& 1& 4\\ 3& 2& 1\\ -1& 0& 8\end{array}\right],C=\left[\begin{array}{ccccc}1& 0& 3& 4& 5\end{array}\right],D=\left[\begin{array}{c}1\\ 3\\ -2\\ 0\end{array}\right]$
Identify the row matrix. Matrix C is a row matrix.

Two cords support a chandelier in the manner shown in the diagram with the upper wire making an angle of 45 degrees with the ceiling. If the cords can sustain a force of 1300 N without breaking, what is the maximum chandelier weight that can be supported?

A 10-km-long underground cable extends from east to west and consists of two parallel wires, each of which has resistance13? /km. An electrical short develops at distance x from the west end when a conducting path of resistance R connects the wires. The resistance of the wires and the short is then100? when measured for the east end and 200? when measured from the west end. What are (a) x and (b)R?

Find the solution of limit ${\displaystyle \underset{(x,y)\to 0,0}{lim}\frac{\sqrt{x^2+y^2}}{x^2+y^2}}$ by using the polar coordinates system.

In Figure, one block has mass M = 500 g, theother has mass m = 460 g, and the pulley, which is mountedin horizontal frictionless bearings, has a radius of 5.00 cm. Whenre leased from rest, the more massive block falls 80.9 cm in 2.78 s (without the cord slipping on the pulley).

a) What is the magnitude of the block's acceleration?
b) What is the tension in the part of the cord that supports the heavier block?
c) What is the tension in the part of the cord that supporst the lighter block?
d) What is the magnitude of the pulley's angular acceleration?
e) What is its rotational inertia?

f(x)=x−3 and ${\displaystyle g\left(x\right)=4x^2-3x-9g\left(x\right)=4x^2-3x-9}$. Find composite function ${\displaystyle f\circ g}$ and ${\displaystyle g\circ f}$

Simplify each expression
(a) ${\displaystyle \sqrt[4]{3^2}}$
(b) ${\displaystyle \sqrt[6]{{(x+1)}^4}}$

Show: a) that the motion equation's solution, x = asin wt:
${\displaystyle m\dot{\frac{d^{2}x}{{ dt }^2}}=-k\dot{x}}$ of the harmonic oscillator. 
b) that ${\displaystyle w=\sqrt{k}\left\{m\right\}}$ 
c) that the momentum is given by p = ${\displaystyle mwA\cos wt}$ 
d) the particle is stationary if and only if x = A 
(To get the time when x = A, use the formula x = A sinwt. Then, use this time in an expression for the velocity.) 
e) that the energy of a harmonic oscillator is ${\displaystyle \frac{1}{2}k{A}^2}$

A noisy grinding machine in a factory produces a soundintensity of $1.0\cdot 10-5W/m2$ . What is thesound level of this machine? A second identical machine is brought into the factory. Whatis the new sound intensity? What is the new sound level?

Prove that for $n\ge 2,2\cdot \left(\begin{array}{c}n\\ 2\end{array}\right)+\left(\begin{array}{c}n\\ 1\end{array}\right)=n^2$