Answer:
a) 54.6
b) 140
Step-by-step explanation:
7644 ÷ 140 = 54.6
so;
7644 ÷ 54.6 = 140
Answer:13.5 inches
Step-by-step explanation:
Given diagonal as 15.6inches
Width is unknown
Height is 7.8 inches
From the diagram attached it forms a right angle solved using Pythagoras theorem
Ie
15.6^2=width^2+7.8^2
Width= ✓(15.6^2-7.8^2)=13.5inches
![\int e^{x/2} /(e^{x/3} +1) dx](https://tex.z-dn.net/?f=%5Cint%20e%5E%7Bx%2F2%7D%20%2F%28e%5E%7Bx%2F3%7D%20%2B1%29%20dx)
start with substituting z=e^x
![z=e^x\\dz=e^x dx\\\int \frac{dz}{z^{5/6}+z^{1/2}}](https://tex.z-dn.net/?f=z%3De%5Ex%5C%5Cdz%3De%5Ex%20dx%5C%5C%5Cint%20%5Cfrac%7Bdz%7D%7Bz%5E%7B5%2F6%7D%2Bz%5E%7B1%2F2%7D%7D)
then substitute u = z^(1/6):
![u=z^{1/6}\\dz=6 z^{5/6}du\\6 \int \frac{u^2}{u^2+1}du](https://tex.z-dn.net/?f=u%3Dz%5E%7B1%2F6%7D%5C%5Cdz%3D6%20z%5E%7B5%2F6%7Ddu%5C%5C6%20%5Cint%20%5Cfrac%7Bu%5E2%7D%7Bu%5E2%2B1%7Ddu)
that integral has a standard form that can be looked up in integral tables, it has the following solution:
![6(u - \tan^{-1} u) + \mbox{constant}](https://tex.z-dn.net/?f=6%28u%20-%20%5Ctan%5E%7B-1%7D%20u%29%20%2B%20%5Cmbox%7Bconstant%7D)
substituting back the the variable z and then x you get the final solution:
![6 e^{x/6} - 6 \tan^{-1}(e^{x/6}) + \mbox{constant}](https://tex.z-dn.net/?f=6%20e%5E%7Bx%2F6%7D%20-%206%20%5Ctan%5E%7B-1%7D%28e%5E%7Bx%2F6%7D%29%20%2B%20%5Cmbox%7Bconstant%7D)
Answer:
8w^2 - 7w + 6
Step-by-step explanation:
We can add the co-efficients of variable with the same power.