If you're asking the difference between 14 ft and 21 ft your answer is 7 ft, just subtract 14 from 21
144 inches. 12 feet in one hour
12 inches per feet
12feet x 12 inches per foot= 144 inches
Answer:
x=14
Step-by-step explanation:
First bring the 6 to the other side and then bring the 4x to the other side to have 5x-4x=6+8 and combine the like terms and x equals 14.
a) Acceleration is the derivative of velocity. By the fundamental theorem of calculus,
![v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du](https://tex.z-dn.net/?f=v%28t%29%3Dv%280%29%2B%5Cdisplaystyle%5Cint_0%5Eta%28u%29%5C%2C%5Cmathrm%20du)
so that
![v(t)=\left(-11\frac{\rm m}{\rm s}\right)+\int_0^t9\sin u\,\mathrm du](https://tex.z-dn.net/?f=v%28t%29%3D%5Cleft%28-11%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%2B%5Cint_0%5Et9%5Csin%20u%5C%2C%5Cmathrm%20du)
![\boxed{v(t)=-\left(2+9\cos t)\right)\frac{\rm m}{\rm s}}](https://tex.z-dn.net/?f=%5Cboxed%7Bv%28t%29%3D-%5Cleft%282%2B9%5Ccos%20t%29%5Cright%29%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%7D)
b) We get the displacement by integrating the velocity function like above. Assume the object starts at the origin, so that its initial position is
. Then its displacement over the time interval [0, 3] is
![s(0)+\displaystyle\int_0^3v(t)\,\mathrm dt=-\int_0^3(2+9\cos t)\,\mathrm dt=\boxed{-6-9\sin3}](https://tex.z-dn.net/?f=s%280%29%2B%5Cdisplaystyle%5Cint_0%5E3v%28t%29%5C%2C%5Cmathrm%20dt%3D-%5Cint_0%5E3%282%2B9%5Ccos%20t%29%5C%2C%5Cmathrm%20dt%3D%5Cboxed%7B-6-9%5Csin3%7D)
c) The total distance traveled is the integral of the absolute value of the velocity function:
![s(0)+\displaystyle\int_0^3|v(t)|\,\mathrm dt](https://tex.z-dn.net/?f=s%280%29%2B%5Cdisplaystyle%5Cint_0%5E3%7Cv%28t%29%7C%5C%2C%5Cmathrm%20dt)
for
and
for
, so we split the integral into two as
![\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}-v(t)\,\mathrm dt+\int_{\cos^{-1}\left(-\frac29\right)}^3v(t)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B%5Ccos%5E%7B-1%7D%5Cleft%28-%5Cfrac29%5Cright%29%7D-v%28t%29%5C%2C%5Cmathrm%20dt%2B%5Cint_%7B%5Ccos%5E%7B-1%7D%5Cleft%28-%5Cfrac29%5Cright%29%7D%5E3v%28t%29%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}(2+9\cos t)\,\mathrm dt-\int_{\cos^{-1}\left(-\frac29\right)}^3(2+9\cos t)\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B%5Ccos%5E%7B-1%7D%5Cleft%28-%5Cfrac29%5Cright%29%7D%282%2B9%5Ccos%20t%29%5C%2C%5Cmathrm%20dt-%5Cint_%7B%5Ccos%5E%7B-1%7D%5Cleft%28-%5Cfrac29%5Cright%29%7D%5E3%282%2B9%5Ccos%20t%29%5C%2C%5Cmathrm%20dt)
![\displaystyle=\boxed{2\sqrt{77}-6+4\cos^{-1}\left(-\frac29\right)-9\sin3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D%5Cboxed%7B2%5Csqrt%7B77%7D-6%2B4%5Ccos%5E%7B-1%7D%5Cleft%28-%5Cfrac29%5Cright%29-9%5Csin3%7D)
Answer: 2.25
Step-by-step explanation: This is because 2.25*40 is 90
Hope this helps and brainliest would be appreciated