Answer:
here you go I hope this is right
The rate of change of the depth of water in the tank when the tank is half
filled can be found using chain rule of differentiation.
When the tank is half filled, the depth of the water is changing at <u>1.213 × </u>
<u>10⁻² ft.³/hour</u>.
Reasons:
The given parameter are;
Height of the conical tank, h = 8 feet
Diameter of the conical tank, d = 10 feet
Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.
Required:
The rate at which the depth of the water in the tank is changing when the
tank is half full.
Solution:
The radius of the tank, r = d ÷ 2
∴ r = 10 ft. ÷ 2 = 5 ft.
Using similar triangles, we have;
The volume of the tank is therefore;
Therefore;
By chain rule of differentiation, we have;
Which gives;
When the tank is half filled, we have;
Solving gives;
h³ = 256
h = ∛256
Which gives;
![\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B3%7D%7B5%7D%20%5Ctimes%20%5Cdfrac%7B64%7D%7B25%20%5Ccdot%20%28%5Csqrt%5B3%5D%7B256%7D%29%20%5E2%20%5Ccdot%20%5Cpi%7D%20%5Capprox%20%5Cmathbf%7B1.213%5Ctimes%2010%5E%7B-2%7D%7D)
When the tank is half filled, the depth of the water is changing at <u>1.213 × 10⁻² ft.³/hour</u>.
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Answer:
Step-by-step explanation:
It really depends on how much the family is moving, what company they are using, or if they are using their own vehicle, and how much trips they want to make.
By car, it takes 17 hrs and 26 minutes to travel the 1152.9 miles via I-95 S. This does not include traffic, any stops for meals, rest, or restrooms. If you are making multiple trips, this could amount to even longer time that can extend over weeks or months.
if you want to see what the mile per gallon is, you can go to fueleconomy. This would tell you average miles per gallons for fairly new (?) cars. This is IMPORTANT, because you want to see how much it will cost your family to gas up certain cars. Also keep in mind that different gas companies have different prices.
Also depending on which restruants you go too, it can be fairly expensive, so usually you would stick with fast foods (once in awhile, cuz they are unhealthy) or places with MRE. (no not talking about the military food, just like already cooked food that you only need to heat up food).
Another factor you want to know is the route you are taking. The route you take can is crucial because it not only can save you or extend the time it takes for you to go from your starting point to your destination, it also can give you some other things as well, including scenery, etc.
These are just a few things that you have to find out before you do anything, as they can greatly impact any outcomes and the amount of time, money, and effort you need to put in to move to Florida.
hope this helps
There is a difference of 14 units between -2 and 12. To find the coordinate in the middle, just add 7, half the distance between -2 and 12, to -2 and subtract 7 from 12. That gives you the coordinate 5.
