The average velocity of the car for the whole journey is 69.57 km/h.
The given parameters:
- <em>Length of the road, L = 320 km</em>
- <em>Distance covered = 240 km at 75 km/h</em>
- <em>time spent refueling, t₂ = 0.6 hr</em>
- <em>Final velocity, = 100 km/hr</em>
The time spent by the before refueling is calculated as follows;
![t = \frac{d}{v} \\\\t_1 = \frac{240}{75} \\\\t_1 = 3.2 \ hours](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bd%7D%7Bv%7D%20%5C%5C%5C%5Ct_1%20%3D%20%5Cfrac%7B240%7D%7B75%7D%20%5C%5C%5C%5Ct_1%20%3D%203.2%20%5C%20hours)
The time spent by the car for the remaining journey;
![t_3 = \frac{320 - 240}{100} \\\\t_3 = 0.8 \ hr](https://tex.z-dn.net/?f=t_3%20%3D%20%5Cfrac%7B320%20-%20240%7D%7B100%7D%20%5C%5C%5C%5Ct_3%20%3D%200.8%20%5C%20hr)
The total time of the journey is calculated as follows;
![t = t_1 + t_2 + t_3\\\\t = 3.2 \ hr \ + \ 0.6 \ hr \ + \ 0.8 \ hr\\\\t = 4.6 \ hours](https://tex.z-dn.net/?f=t%20%3D%20t_1%20%2B%20t_2%20%2B%20t_3%5C%5C%5C%5Ct%20%3D%203.2%20%5C%20hr%20%5C%20%2B%20%5C%200.6%20%5C%20hr%20%5C%20%2B%20%5C%200.8%20%5C%20hr%5C%5C%5C%5Ct%20%3D%204.6%20%5C%20hours)
The average velocity of the car for the whole journey is calculated as follows;
![v = \frac{total \ distance }{total \ time} \\\\v = \frac{320}{4.6} \\\\v = 69.57 \ km/h](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Btotal%20%5C%20distance%20%7D%7Btotal%20%5C%20time%7D%20%5C%5C%5C%5Cv%20%3D%20%5Cfrac%7B320%7D%7B4.6%7D%20%5C%5C%5C%5Cv%20%3D%2069.57%20%5C%20km%2Fh)
Learn more about average velocity here: brainly.com/question/6504879
Answer:
dV/dt = 9 cubic inches per second
Explanation:
Let the height of the cylinder is h
Diameter of cylinder = height of the cylinder = h
Radius of cylinder, r = h/2
dh/dt = 3 inches /s
Volume of cylinder is given by
![V = \pi r^{2}h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E%7B2%7Dh)
put r = h/2 so,
![V = \pi \frac{h^{3}}{4}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Cfrac%7Bh%5E%7B3%7D%7D%7B4%7D)
Differentiate both sides with respect to t.
![\frac{dV}{dt}=\frac{3h^{2}}{4}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B3h%5E%7B2%7D%7D%7B4%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Substitute the values, h = 2 inches, dh/dt = 3 inches / s
![\frac{dV}{dt}=\frac{3\times 2\times 2}{4}\times 3](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B3%5Ctimes%202%5Ctimes%202%7D%7B4%7D%5Ctimes%203)
dV/dt = 9 cubic inches per second
Thus, the volume of cylinder increases by the rate of 9 cubic inches per second.
Answer: ![\theta=cos^{-1}0.991=7.69^o](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D0.991%3D7.69%5Eo)
The following vectors have been given: ![\vec{a}=3.0\widehat{i}+3.0\widehat{j}+3.0\widehat{k}\\ \vec{b}=5.0\widehat{i}+7.0\widehat{j}+6.0\widehat{k}](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%3D3.0%5Cwidehat%7Bi%7D%2B3.0%5Cwidehat%7Bj%7D%2B3.0%5Cwidehat%7Bk%7D%5C%5C%20%5Cvec%7Bb%7D%3D5.0%5Cwidehat%7Bi%7D%2B7.0%5Cwidehat%7Bj%7D%2B6.0%5Cwidehat%7Bk%7D)
The angle between these two vectors can be found by:
![cos\theta=\frac{\vec{a}.\vec{b}}{||\vec{a}|| ||\vec{b}||}\\ ||\vec{a}=\sqrt{a_x^2+a_y^2+a_z^2}](https://tex.z-dn.net/?f=cos%5Ctheta%3D%5Cfrac%7B%5Cvec%7Ba%7D.%5Cvec%7Bb%7D%7D%7B%7C%7C%5Cvec%7Ba%7D%7C%7C%20%7C%7C%5Cvec%7Bb%7D%7C%7C%7D%5C%5C%0A%7C%7C%5Cvec%7Ba%7D%3D%5Csqrt%7Ba_x%5E2%2Ba_y%5E2%2Ba_z%5E2%7D)
![\vec{a}.\vec{b}=a_xb_x+a_yb_y+a_zb_z\\ \vec{a}.\vec{b}=3\times5+3\times7+3\times6=15+21+18=54](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D.%5Cvec%7Bb%7D%3Da_xb_x%2Ba_yb_y%2Ba_zb_z%5C%5C%20%5Cvec%7Ba%7D.%5Cvec%7Bb%7D%3D3%5Ctimes5%2B3%5Ctimes7%2B3%5Ctimes6%3D15%2B21%2B18%3D54)
![||\vec{a}||=\sqrt{3^2+3^2+3^2}=\sqrt{27}\\ ||\vec{b}||=\sqrt{5^2+7^2+6^2}=\sqrt{110}](https://tex.z-dn.net/?f=%7C%7C%5Cvec%7Ba%7D%7C%7C%3D%5Csqrt%7B3%5E2%2B3%5E2%2B3%5E2%7D%3D%5Csqrt%7B27%7D%5C%5C%20%7C%7C%5Cvec%7Bb%7D%7C%7C%3D%5Csqrt%7B5%5E2%2B7%5E2%2B6%5E2%7D%3D%5Csqrt%7B110%7D)
![cos\theta=\frac{54}{\sqrt{27}\times\sqrt{110}}\\=0.991\\ \Rightarrow \theta=cos^{-1}0.991=7.69^o](https://tex.z-dn.net/?f=cos%5Ctheta%3D%5Cfrac%7B54%7D%7B%5Csqrt%7B27%7D%5Ctimes%5Csqrt%7B110%7D%7D%5C%5C%3D0.991%5C%5C%20%5CRightarrow%20%5Ctheta%3Dcos%5E%7B-1%7D0.991%3D7.69%5Eo)
<span>reflection, rotation, translation</span>