Answer: ![40\ beats](https://tex.z-dn.net/?f=40%5C%20beats)
Step-by-step explanation:
Knowing the information provided in the exercise, you need to find the Least Common Multiple (L.C.M) in order to solve it.
You can follow these steps:
1- You must descompose 2, 5 and 8 into their prime factors:
![2=2\\5=5\\8=2*2*2=2^3](https://tex.z-dn.net/?f=2%3D2%5C%5C5%3D5%5C%5C8%3D2%2A2%2A2%3D2%5E3)
2- And finally, you must multiply the commons and non commons with the highest exponent:
![L.C.M=2^3*5=40](https://tex.z-dn.net/?f=L.C.M%3D2%5E3%2A5%3D40)
Therefore, the answer is: ![40\ beats](https://tex.z-dn.net/?f=40%5C%20beats)
Answer:
2.68
Step-by-step explanation:
25/67 = 2.68
Answer:
114.5 in³
Step-by-step explanation:
Volume of cone:
⅓ × 3.14 × 8² × 12
= 803.84 cm³
Volume of hemisphere:
⅔ × 3.14 × 8³
= 1071.786667 cm³
Total = 803.84 + 1071.786667
= 1875.626667 cm³
1 cm = 0.393701 inches
1 cm³ = 0.393701³ inches
Volume in in³:
1875.786667/0.393701³
= 114.4579471 in³
By definition of the derivative,
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{(s + h)^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cleft%28%5Cfrac%7B%28s%20%2B%20h%29%5E3%7D2%20%2B%201%5Cright%29%20-%20%5Cleft%28%5Cfrac%7Bs%5E3%7D2%20%2B%201%5Cright%29%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{s^3+3s^2h+3sh^2+h^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cleft%28%5Cfrac%7Bs%5E3%2B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D2%20%2B%201%5Cright%29%20-%20%5Cleft%28%5Cfrac%7Bs%5E3%7D2%20%2B%201%5Cright%29%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\frac{3s^2h+3sh^2+h^3}2}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%5Cfrac%7B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D2%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 \frac{3s^2h+3sh^2+h^3}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac12%20%5Cfrac%7B3s%5E2h%2B3sh%5E2%2Bh%5E3%7D%7Bh%7D)
![\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 (3s^2+3sh+h^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac12%20%283s%5E2%2B3sh%2Bh%5E2%29)
![\displaystyle\frac{dr}{ds} = \frac{3s^2}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdr%7D%7Bds%7D%20%3D%20%5Cfrac%7B3s%5E2%7D2)