1. Sry, I am confused by this one
2. Positive Integer factors of 196 = 2, 4, 7, 28, 196/2, 2, 7, 7, leaves it with no remainder.
3. Neither
4. Prime
5. Composite
6. 80, 96, 112 (pattern: add 16 each time)
7. 29, 36, 38 (pattern: add 7, add 2 and so on)
Hope this helped!!
Also, can I pls, pls, pls have brainliest? I need about 100 more points and 1 brainliest to lvl up to Ace!!
Q(-3,-3)
R(3,2)
S(5,2)
T(5,-4)
1.
a. 120+80+50+150= 400
2.
b. 250 of each game should the store order
3. this year 60 of each game should the store order
2.
a. 240 ounces of sugar water you need
b. none
Answer:
≥ and ≤ will both be solid dots, as it includes the number
x ≥ -7 is everything greater than -7; x ≤ 4 is everything less than 4.
to include both, you'd click -7, drag right, and stop at 4
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)