Answer:0.28divide by7
Step-by-step explanation:
50 miles, t=0 is the start
45 miles each 1 hour
A. d= 45•t+50
Answer:
Rate of change in height of the water level is 2.91 cm per second.
Step-by-step explanation:
Height of the inverted pyramid = 10 cm
Length of the square base = 7 cm
If water is filled up to the level of h cm then the volume of water up to height h will be
V = ![\frac{1}{3}(\text {Area of the base})\times (h)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Ctext%20%7BArea%20of%20the%20base%7D%29%5Ctimes%20%28h%29)
V = ![\frac{1}{3}(x^{2} )\times (h)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28x%5E%7B2%7D%20%29%5Ctimes%20%28h%29)
It is given that rate of water is filling with 70 cubic centimeters per second.
![\frac{dV}{dt}=70](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D70)
From two similar triangles in the figure attached,
![\frac{x}{h}=\frac{7}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bh%7D%3D%5Cfrac%7B7%7D%7B10%7D)
![x=\frac{7h}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7h%7D%7B10%7D)
By replacing the value of h,
V = ![\frac{1}{3}(\frac{7h}{10})^{2}h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cfrac%7B7h%7D%7B10%7D%29%5E%7B2%7Dh)
V = ![\frac{1}{3}(\frac{49h^{2} }{100})h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cfrac%7B49h%5E%7B2%7D%20%7D%7B100%7D%29h)
V = ![\frac{1}{3}(\frac{49h^{3}}{100})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Cfrac%7B49h%5E%7B3%7D%7D%7B100%7D%29)
Now we integrate the equation with respect to time 't'
![\frac{dV}{dt}=\frac{d}{dt}(\frac{1}{3}\times \frac{49h^{3} }{100})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%28%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5Cfrac%7B49h%5E%7B3%7D%20%7D%7B100%7D%29)
70 = ![\frac{49h^{2} }{100}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7B49h%5E%7B2%7D%20%7D%7B100%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{100\times 70}{49h^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B100%5Ctimes%2070%7D%7B49h%5E%7B2%7D%7D)
For h = 7 cm
![\frac{dh}{dt}=\frac{70\times 100}{49\times 49}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B70%5Ctimes%20100%7D%7B49%5Ctimes%2049%7D)
![\frac{dh}{dt}=2.91](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D2.91)
Therefore, rate of change in height of the water level is 2.91 cm per second.