I got 2 but this could be wrong. Hope this helps ;D
Answer:
C
Step-by-step explanation:
Total Work hours = 3 1/2 hours
One routine physical routine requires: 1/3 hours.
Number of routines can be completed = Total work hours / Time required for one physical routine
= ![3\frac{1}{2} / \frac{1}{3}\\=\frac{7}{2} /\frac{1}{3} \\=\frac{7}{2} *3\\](https://tex.z-dn.net/?f=3%5Cfrac%7B1%7D%7B2%7D%20%20%2F%20%5Cfrac%7B1%7D%7B3%7D%5C%5C%3D%5Cfrac%7B7%7D%7B2%7D%20%2F%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%3D%5Cfrac%7B7%7D%7B2%7D%20%2A3%5C%5C)
= 10.5 routines.
In this case, we are unable to complete half a routine (0.5), so we will choose the highest possible whole number, in this case, its 10 routines.
25% of 64 is 16
![\frac{25}{100} = \frac{x}{64} \\ x = \frac{64 \times 25}{100} = \frac{1600}{100} = 16](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%7D%7B100%7D%20%20%3D%20%20%5Cfrac%7Bx%7D%7B64%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B64%20%5Ctimes%2025%7D%7B100%7D%20%20%3D%20%20%5Cfrac%7B1600%7D%7B100%7D%20%20%3D%2016)
it will work properly 16 times
![64 - 16 = 48](https://tex.z-dn.net/?f=64%20-%2016%20%3D%2048)
it will not work 48 times
hope this helps
Answer:
![\frac{dy}{dt} = 102](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%20%3D%20102)
Step-by-step explanation:
<u>step(i)</u>
Given function y = 3 x³ - 2 x ... (i)
Differentiating equation (i) with respective to 'x'
![\frac{dy}{dx} = 3 (3 x^{2} ) - 2(1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%203%20%283%20x%5E%7B2%7D%20%29%20-%202%281%29)
Given x = -2
![(\frac{dy}{dx} ) x_{=-2} = 3 (3 (-2)^{2} ) - 2(1)](https://tex.z-dn.net/?f=%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29%20x_%7B%3D-2%7D%20%3D%203%20%283%20%28-2%29%5E%7B2%7D%20%29%20-%202%281%29)
![(\frac{dy}{dx} ) x_{=-2} = 36 -2 =34](https://tex.z-dn.net/?f=%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29%20x_%7B%3D-2%7D%20%3D%2036%20-2%20%3D34)
<u><em>Step(ii):-</em></u>
<u><em>we know that </em></u>
![\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B%5Cfrac%7Bdy%7D%7Bdt%7D%20%7D%7B%5Cfrac%7Bdx%7D%7Bdt%7D%20%7D)
Given ![\frac{dx}{dt} = 3 and \frac{dy}{dx} = 34](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%203%20%20and%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%2034)
![\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B%5Cfrac%7Bdy%7D%7Bdt%7D%20%7D%7B%5Cfrac%7Bdx%7D%7Bdt%7D%20%7D)
substitute values
⇒ ![34 = \frac{\frac{dy}{dt} }{3 }](https://tex.z-dn.net/?f=34%20%3D%20%5Cfrac%7B%5Cfrac%7Bdy%7D%7Bdt%7D%20%7D%7B3%20%7D)
cross multiplication , we get
![\frac{dy}{dt} = 34( 3 ) = 102](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%2034%28%203%20%29%20%3D%20102)
<u><em>Final answer</em></u>:-
![\frac{dy}{dt} = 34( 3 ) = 102](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%2034%28%203%20%29%20%3D%20102)