Two ways of solving it:
The angle beside the 71 is equal to
180 - 71 = 109
so a triangle angles sums up to 180
so the reminaing is
x = 180 - 109 - 28 = 43
solution (2):
the exterior angle = sum of interior angles except the one near it.
28 + x = 71
x = 43
Answer:
Step-by-step explanation:
the lat answer for the first picture correct just plug it in the hihger number for x and then try a larger number y decreases. The same answer for the second one 2
Answer:
![1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=1%5C%20%5Cfrac%7B%5Ctext%7Bcal%7D%7D%7Bm%5E2%5Ctimes%20sec%5Ctimes%20%5E%5Ccirc%20C%7D%3D0.03926%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
Step-by-step explanation:
To find : Convert
into ![\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
Solution :
We convert units one by one,
![1\text{ m}^2=10.7639\text{ ft}^2](https://tex.z-dn.net/?f=1%5Ctext%7B%20m%7D%5E2%3D10.7639%5Ctext%7B%20ft%7D%5E2)
![1\text{ sec}=\frac{1}{3600}\text{ hour}](https://tex.z-dn.net/?f=1%5Ctext%7B%20sec%7D%3D%5Cfrac%7B1%7D%7B3600%7D%5Ctext%7B%20hour%7D)
![1\text{ cal}=0.003968\text{ BTU}](https://tex.z-dn.net/?f=1%5Ctext%7B%20cal%7D%3D0.003968%5Ctext%7B%20BTU%7D)
Converting temperature unit,
![^\circ C\times \frac{9}{5}+32=^\circ F](https://tex.z-dn.net/?f=%5E%5Ccirc%20C%5Ctimes%20%5Cfrac%7B9%7D%7B5%7D%2B32%3D%5E%5Ccirc%20F)
![1^\circ C\times \frac{9}{5}+32=33.8^\circ F](https://tex.z-dn.net/?f=1%5E%5Ccirc%20C%5Ctimes%20%5Cfrac%7B9%7D%7B5%7D%2B32%3D33.8%5E%5Ccirc%20F)
So, ![1^\circ C=33.8^\circ F](https://tex.z-dn.net/?f=1%5E%5Ccirc%20C%3D33.8%5E%5Ccirc%20F)
Substitute all the values in the unit conversion,
![1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{10.7639\times \frac{1}{3600}\times 33.8}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=1%5C%20%5Cfrac%7B%5Ctext%7Bcal%7D%7D%7Bm%5E2%5Ctimes%20sec%5Ctimes%20%5E%5Ccirc%20C%7D%3D%5Cfrac%7B0.003968%7D%7B10.7639%5Ctimes%20%5Cfrac%7B1%7D%7B3600%7D%5Ctimes%2033.8%7D%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
![1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{0.101061}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=1%5C%20%5Cfrac%7B%5Ctext%7Bcal%7D%7D%7Bm%5E2%5Ctimes%20sec%5Ctimes%20%5E%5Ccirc%20C%7D%3D%5Cfrac%7B0.003968%7D%7B0.101061%7D%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
![1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=1%5C%20%5Cfrac%7B%5Ctext%7Bcal%7D%7D%7Bm%5E2%5Ctimes%20sec%5Ctimes%20%5E%5Ccirc%20C%7D%3D0.03926%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
Therefore, The conversion of unit is ![1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}](https://tex.z-dn.net/?f=1%5C%20%5Cfrac%7B%5Ctext%7Bcal%7D%7D%7Bm%5E2%5Ctimes%20sec%5Ctimes%20%5E%5Ccirc%20C%7D%3D0.03926%5Cfrac%7B%5Ctext%7BBTU%7D%7D%7Bft%5E2%5Ctimes%20hr%5Ctimes%20%5E%5Ccirc%20F%7D)
Answer:
Her centripetal acceleration during the turn at each end of the track is ![0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
Step-by-step explanation:
Total distance covered in one round , D= 400 m
Time taken to cover one round , T = 1 min 40 s = 100 sec
Speed of runner , ![V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BD%7D%7BT%7D%3D%5Cfrac%7B400%7D%7B100%7D%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D%3D%204.0%5C%2C%20%5Cfrac%7Bm%7D%7Bs%7D)
Now centripetal acceleration is given by
![a_c=\frac{V^{2}}{R}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7BV%5E%7B2%7D%7D%7BR%7D)
where ![V= 4.0\frac{m}{s}](https://tex.z-dn.net/?f=V%3D%204.0%5Cfrac%7Bm%7D%7Bs%7D)
![Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m](https://tex.z-dn.net/?f=Radius%2C%20R%3D%20%5Cfrac%7BDiameter%7D%7B2%7D%3D%5Cfrac%7B74%7D%7B2%7Dm%3D37%5C%2C%20m)
![\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=%5Ctherefore%20a_c%3D%5Cfrac%7B4%5E%7B2%7D%7D%7B37%7D%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%3D0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
Thus her centripetal acceleration during the turn at each end of the track is ![0.432\, \frac{m}{s^{2}}](https://tex.z-dn.net/?f=0.432%5C%2C%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)