Answer:
18.75 feet of steel pipe weighs 237 pounds
explanation:
find out how much 1 feet weighs than u can find out how much 18.75 feet.
by doing it like this
158÷ 12.5
=12.64
1 feet equals 12.64 pounds
12.64× 18.75
=237 pounds this is the answer
i do apologize if it wrong
The position function of a particle is given by:
![X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t](https://tex.z-dn.net/?f=X%5Cmleft%28t%5Cmright%29%3D%5Cfrac%7B2%7D%7B3%7Dt%5E3-%5Cfrac%7B9%7D%7B2%7Dt%5E2-18t)
The velocity function is the derivative of the position:
![\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%28t%29%3D%5Cfrac%7B2%7D%7B3%7D%283t%5E2%29-%5Cfrac%7B9%7D%7B2%7D%282t%29-18%20%5C%5C%20%5Ctext%7BSimplifying%3A%7D%20%5C%5C%20V%28t%29%3D2t%5E2-9t-18%20%5Cend%7Bgathered%7D)
The particle will be at rest when the velocity is 0, thus we solve the equation:
![2t^2-9t-18=0](https://tex.z-dn.net/?f=2t%5E2-9t-18%3D0)
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
![t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Substituting:
![\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81-4%282%29%28-18%29%7D%7D%7B2%282%29%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81%2B144%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B225%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm15%7D%7B4%7D%20%5Cend%7Bgathered%7D)
We have two possible answers:
![\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B9%2B15%7D%7B4%7D%3D6%20%5C%5C%20t%3D%5Cfrac%7B9-15%7D%7B4%7D%3D-%5Cfrac%7B3%7D%7B2%7D%20%5Cend%7Bgathered%7D)
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Answer
Let t be number of minutes since tap is opened
water is increased by 20 gallons of water per minute.
sugar increase rate of 3 pounds per minute
water :- W(t) = 350 + 10 t
sugar :- S(t) = 10 + 3 t
concentration
C(t) = ![\dfrac{S(t)}{W(t)}](https://tex.z-dn.net/?f=%5Cdfrac%7BS%28t%29%7D%7BW%28t%29%7D)
at t = 15 minutes
C(15) = ![\dfrac{S(15)}{W(15)}](https://tex.z-dn.net/?f=%5Cdfrac%7BS%2815%29%7D%7BW%2815%29%7D)
C(15) = ![\dfrac{10 + 3\times 15 }{350 + 10\times 15}](https://tex.z-dn.net/?f=%5Cdfrac%7B10%20%2B%203%5Ctimes%2015%20%7D%7B350%20%2B%2010%5Ctimes%2015%7D)
C(15) = 0.11
at beginning t = 0 minutes
C(0) = ![\dfrac{S(0)}{W(0)}](https://tex.z-dn.net/?f=%5Cdfrac%7BS%280%29%7D%7BW%280%29%7D)
C(0) = ![\dfrac{10 + 3\times 0}{350 + 10\times 0}](https://tex.z-dn.net/?f=%5Cdfrac%7B10%20%2B%203%5Ctimes%200%7D%7B350%20%2B%2010%5Ctimes%200%7D)
C(0) = 0.0286
C(15) > C(0)
hence, concentration is increasing as time is passing.
Answer:
93107
Step-by-step explanation:
add all of the numbers together
divide by 5 since there are 5 numbers
you would get 92106.8
so round that up since you cannot have 1/8 of a squirrel
Hope this helps!!