Put the fish in another small bowl of water. Empty the tank, rinse it, and fill it with new water and the right amount of conditioner. Let it get to the right temperature for the fish, then gently put the fish back in it. And FAST ! All of this is very stressful for the fish.
A. 4% you divide 2000 to 500 and you get 4 which is your answer
![\textbf{A}×\textbf{B}= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%C3%97%5Ctextbf%7BB%7D%3D%2068%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%2052%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
Explanation:
Given:
![\textbf{A} = 5\hat{\textbf{i}} - 7\hat{\textbf{j}} - 3\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%20%3D%205%5Chat%7B%5Ctextbf%7Bi%7D%7D%20-%207%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%203%5Chat%7B%5Ctextbf%7Bk%7D%7D)
![\textbf{B} = -4\hat{\textbf{i}} + 4\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BB%7D%20%3D%20-4%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%204%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
The cross product
is given by
![\textbf{A}×\textbf{B} = \left|\begin{array}{ccc}\hat{\textbf{i}} & \hat{\textbf{j}} & \hat{\textbf{k}} \\\:\:5 & -7 & -3 \\ -4 & \:\:4 & -8 \\ \end{array}\right|](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%C3%97%5Ctextbf%7BB%7D%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%26%20%5Chat%7B%5Ctextbf%7Bj%7D%7D%20%26%20%5Chat%7B%5Ctextbf%7Bk%7D%7D%20%5C%5C%5C%3A%5C%3A5%20%26%20-7%20%26%20-3%20%5C%5C%20-4%20%26%20%5C%3A%5C%3A4%20%26%20-8%20%5C%5C%20%5Cend%7Barray%7D%5Cright%7C)
![= \left|\begin{array}{cc}-7 & -3\\\:4 & -8\\ \end{array}\right|\:\hat{\textbf{i}}\:+\:\left|\begin{array}{cc}-3 & \:\:5\\-8 & -4\\ \end{array}\right|\:\hat{\textbf{j}}\:+\: \left|\begin{array}{cc}\:\:5 & -7\\-4 & \:\:4\\ \end{array}\right|\:\hat{\textbf{k}}](https://tex.z-dn.net/?f=%3D%20%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D-7%20%26%20-3%5C%5C%5C%3A4%20%26%20-8%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bi%7D%7D%5C%3A%2B%5C%3A%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D-3%20%26%20%5C%3A%5C%3A5%5C%5C-8%20%26%20-4%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bj%7D%7D%5C%3A%2B%5C%3A%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D%5C%3A%5C%3A5%20%26%20-7%5C%5C-4%20%26%20%5C%3A%5C%3A4%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bk%7D%7D)
![= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%3D%2068%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%2052%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
Answer:
Incomplete question: The masses of the blocks m₂ = 1.5 kg and m₃ = 2 kg
Explanation:
Given data:
L₁ = length = 0.85 m
L₂ = 0.25 m
L₃ = 0.5 m
m₂ = 1.5 kg
m₃ = 2 kg
Question: Find the unknown mass of the block 1 needed to balance the bar, m₁ = ?
The torque is zero (intermediate point of the bar)
![-m_{1} gL_{1} +m_{2} gL_{2} +m_{3} gL_{3} =0](https://tex.z-dn.net/?f=-m_%7B1%7D%20gL_%7B1%7D%20%2Bm_%7B2%7D%20gL_%7B2%7D%20%2Bm_%7B3%7D%20gL_%7B3%7D%20%3D0)
Is negative because mass 1 is to the left of the coordinate system (see the diagram)
![m_{1} =\frac{m_{2} gL_{2}+m_{3} gL_{3} }{L_{1} } =\frac{(1.5*0.25)+(2*0.5)}{0.85} =1.6176kg](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%5Cfrac%7Bm_%7B2%7D%20gL_%7B2%7D%2Bm_%7B3%7D%20gL_%7B3%7D%20%20%7D%7BL_%7B1%7D%20%7D%20%3D%5Cfrac%7B%281.5%2A0.25%29%2B%282%2A0.5%29%7D%7B0.85%7D%20%3D1.6176kg)