Answer:
C. -24
Step-by-step explanation:
![5k + m \\ k = - 3 \\ m = - 9](https://tex.z-dn.net/?f=5k%20%2B%20m%20%5C%5C%20k%20%3D%20%20-%203%20%5C%5C%20m%20%3D%20%20-%209)
Plug in values into the given equation
![5( - 3) + ( - 9) \\ - 15 - 9 \\ = - 24](https://tex.z-dn.net/?f=5%28%20-%203%29%20%2B%20%28%20-%209%29%20%5C%5C%20%20-%2015%20-%209%20%5C%5C%20%20%3D%20%20-%2024)
All methods are supposed to be correct in most if not all situations and it should not matter if you use a different method given the options
Answer:
![\frac{225}{16} cm/s](https://tex.z-dn.net/?f=%5Cfrac%7B225%7D%7B16%7D%20cm%2Fs)
Step-by-step explanation:
We are given that
![\frac{dV}{dt}=25cm^3/s](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D25cm%5E3%2Fs)
Side of base=4 cm
l=w=4 cm
Height,h=12 cm
We have to find the rate at which the water level rising when the water level is 4 cm.
Volume of pyramid=![\frac{1}{3}lwh=\frac{1}{3}l^2h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dlwh%3D%5Cfrac%7B1%7D%7B3%7Dl%5E2h)
![\frac{l}{h}=\frac{4}{12}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bl%7D%7Bh%7D%3D%5Cfrac%7B4%7D%7B12%7D%3D%5Cfrac%7B1%7D%7B3%7D)
![l=\frac{1}{3}h](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B1%7D%7B3%7Dh)
Substitute the value
![V=\frac{1}{27}h^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B27%7Dh%5E3)
Differentiate w.r.t t
![\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B3%7D%7B27%7Dh%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
Substitute the values
![25=\frac{1}{9}(4^2)\frac{dh}{dt}](https://tex.z-dn.net/?f=25%3D%5Cfrac%7B1%7D%7B9%7D%284%5E2%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B25%5Ctimes%209%7D%7B16%7D%3D%5Cfrac%7B225%7D%7B16%7D%20cm%2Fs)