a. The
component tells you the particle's height:
![3t=16\implies t=\dfrac{16}3](https://tex.z-dn.net/?f=3t%3D16%5Cimplies%20t%3D%5Cdfrac%7B16%7D3)
b. The particle's velocity is obtained by differentiating its position function:
![\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20v%28t%29%3D%5Cdfrac%7B%5Cmathrm%20d%5Cvec%20r%28t%29%7D%7B%5Cmathrm%20dt%7D%3D-%5Csin%20t%5C%2C%5Cvec%5Cimath%2B%5Ccos%20t%5C%2C%5Cvec%5Cjmath%2B3%5C%2C%5Cvec%20k)
so that its velocity at time
is
![\vec v\left(\dfrac{16}3\right)=-\sin\dfrac{16}3\,\vec\imath+\cos\dfrac{16}3\,\vec\jmath+3\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20v%5Cleft%28%5Cdfrac%7B16%7D3%5Cright%29%3D-%5Csin%5Cdfrac%7B16%7D3%5C%2C%5Cvec%5Cimath%2B%5Ccos%5Cdfrac%7B16%7D3%5C%2C%5Cvec%5Cjmath%2B3%5C%2C%5Cvec%20k)
c. The tangent to
at
is
![\vec T(t)=\vec r\left(\dfrac{16}3\right)+\vec v\left(\dfrac{16}3\right)t](https://tex.z-dn.net/?f=%5Cvec%20T%28t%29%3D%5Cvec%20r%5Cleft%28%5Cdfrac%7B16%7D3%5Cright%29%2B%5Cvec%20v%5Cleft%28%5Cdfrac%7B16%7D3%5Cright%29t)
Answer:
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form:
61 / 10
Decimal Form:
6.1
Mixed Number Form:
6 1/10
Answer:
90°
Step-by-step explanation:
90
Thales Theorem
Answer:
14!
Step-by-step explanation:
The actual question is 2^4 + 3^2, so 2+2+2+2=8 and 3+3=6. So, 8+6= 14