Answer:
3
Step-by-step explanation:
look for the greatest exponent
Answer:
Step-by-step explanation:
k(k+1)(k+2) - 3k(k+1)
k and (k+1) are common to both terms.
k(k+1)(k+2) - 3k(k+1) = k(k+1)[(k+2) - 3] = k(k+1)(k-1)
Answer:
5.0 ft-lbf
Step-by-step explanation:
The force is
![F = \dfrac{9}{6^x}](https://tex.z-dn.net/?f=F%20%3D%20%5Cdfrac%7B9%7D%7B6%5Ex%7D)
This force is not a constant force. For a non-constant force, the work done, <em>W</em>, is
![W = \int\limits^{x_2}_{x_1} {F(x)} \, dx](https://tex.z-dn.net/?f=W%20%3D%20%5Cint%5Climits%5E%7Bx_2%7D_%7Bx_1%7D%20%7BF%28x%29%7D%20%5C%2C%20dx)
with
and
the initial and final displacements respectively.
From the question,
and
.
Then
![W = \int\limits^{12}_0 {\dfrac{9}{6^x}} \, dx](https://tex.z-dn.net/?f=W%20%3D%20%5Cint%5Climits%5E%7B12%7D_0%20%7B%5Cdfrac%7B9%7D%7B6%5Ex%7D%7D%20%5C%2C%20dx)
Evaluating the indefinite integral,
![\int\limits \dfrac{9}{6^x} \, dx =9 \int\limits\!\left(\frac{1}{6}\right)^x \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%20%5Cdfrac%7B9%7D%7B6%5Ex%7D%20%5C%2C%20dx%20%20%3D9%20%5Cint%5Climits%5C%21%5Cleft%28%5Cfrac%7B1%7D%7B6%7D%5Cright%29%5Ex%20%5C%2C%20dx)
From the rules of integration,
![\int\limits a^x\, dx = \dfrac{a^x}{\ln a}](https://tex.z-dn.net/?f=%5Cint%5Climits%20a%5Ex%5C%2C%20dx%20%3D%20%5Cdfrac%7Ba%5Ex%7D%7B%5Cln%20a%7D)
![9 \int\limits \left(\frac{1}{6}\right)^x \, dx = 9\times\dfrac{(1/6)^x}{\ln(1/6)} = -5.0229\left(\dfrac{1}{6}\right)^x](https://tex.z-dn.net/?f=9%20%5Cint%5Climits%20%5Cleft%28%5Cfrac%7B1%7D%7B6%7D%5Cright%29%5Ex%20%5C%2C%20dx%20%3D%209%5Ctimes%5Cdfrac%7B%281%2F6%29%5Ex%7D%7B%5Cln%281%2F6%29%7D%20%3D%20-5.0229%5Cleft%28%5Cdfrac%7B1%7D%7B6%7D%5Cright%29%5Ex)
Returning the limits,
![\left.-5.0229\left(\dfrac{1}{6}\right)^x\right|^{12}_0 = -5.0229(0.1667^{12} - 0.1667^0) = 5.0229 \approx 5.0 \text{ ft-lbf}](https://tex.z-dn.net/?f=%5Cleft.-5.0229%5Cleft%28%5Cdfrac%7B1%7D%7B6%7D%5Cright%29%5Ex%5Cright%7C%5E%7B12%7D_0%20%3D%20-5.0229%280.1667%5E%7B12%7D%20-%200.1667%5E0%29%20%3D%205.0229%20%5Capprox%205.0%20%5Ctext%7B%20ft-lbf%7D)
18?
-18 divided by [-1/6]
is 18
hopefully that's what you were looking for.?!!