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

Four point charges are positioned on the rim of a circle. The charge on each of the four (in micro Coulombs) is +0.5, +1.5, -1.0,and -0.5. If we are told that the electrical potential at the center of the circle due to the +0.5 charge is $4.5\times {10}^4$ V, what is the potential at the center due to the four charges combined?

1. For each of the following polyatomic ions, provide a Lewis structure, including resonance and formal charge. 

a)BH4–

b) HCO2–

 c)AsCl4–

d) ICl2–

Two basketball players are essentially equal in all respects. In particular, by jumping they can raise their centers of mass the same vertical distance, H. The first player,Arabella, wishes to shoot over the second player, Boris, and forthis she needs to be as high above Boris as possible. Arabella Jumps at time t=0, and Boris jumps later, at time ${\displaystyle t_R}$(his reaction time). Assume that Arabella has not yet reached her maximum height when Boris jumps.
Part A.) Find the vertical displacement ${\displaystyle D\left(t\right)=h_A\left(t\right)-h_B\left(t\right)}$, as a function of time for the interval ${\displaystyle 0<t<t_R}$, where ${\displaystyle h_A\left(t\right)}$ is the height of the raised hands of Arabella, while ${\displaystyle h_B\left(t\right)}$ is the height of the raised hands of Boris. (Express thevertical displacement in terms of H,g,and t.)
Part B.) Find the vertical displacement D(t) between the raised hands of the two players for the time period after Boris has jumped (${\displaystyle t>t_R}$) but before Arabella has landed. (Express youranswer in terms of t,${\displaystyle t_R}$, g,and H)
Part C.) What advice would you give Arabella To minimize the chance of her shot being blocked?

Find the Laplace transforms of the following
$L\left\{\frac{e^{-6t}\sinh \left(2t\right)}{e^{-6t}\cosh \left(2t\right)}\right\}$

A ski gondola is connected to the top of a hill by a steelcable of length 620m and diameter 1.5cm. As teh gondola comes tothe end of its run, it bumps into the terminal and sends a wavepulse along the cable. It is observed that it took 16 seconds forthe pulse to return. a) What is the speed of the pulse? b)What isthe tension in the cable?
I believe to find the speed of the pulse all I ahve to do is V=distancetravelled timetake $(V=\frac{\mathrm{△}X}{\mathrm{△}t})$ so it would equal 77.5 m/s
To find tension i would use $V^2=F_T÷(m÷L)$
After manipulating it I get $F_T=V^2\times (\frac{m}{L})$
i know V=77.5 and L = 620 but i dont know how to find m.Please help! I dont even know if I did the rest of the problemright please help as soon as possible. Thanks

Use Taylor's theorem to evaluate the following limits. $\underset{x\to 0}{lim}\frac{x\sin (x)-x^2}{\cos (x)-1+\frac{x^2}{2}}$

Please provide steps
The inverse Laplace transform for
${\displaystyle F\left(s\right)=\frac{8}{s+9}-\frac{6}{s^2-\sqrt{3}}}$ is
a) ${\displaystyle 8e^{-9t}-6\sin h\left(3t\right)}$
b) ${\displaystyle 8e^{-9t}-6\cos h\left(3t\right)}$
c) ${\displaystyle 8e^{9t}-6\sin h\left(3t\right)}$
d) ${\displaystyle 8e^{9t}-6\cos h\left(3t\right)}$

Consider the equation:
${\displaystyle 2\sqrt{3}{x}^2-6xy+\sqrt{3}x+3y=0}$
a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola?
b) Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies ${\displaystyle 0\le \phi \le \pi \text{/}2}$)