Answer:
Step-by-step explanation:
Given that tank has the shape of inverted circular cone
Height = 10 feet and radius = 4 feet
After water pumped out height = 5 ft
Hence volume of water pumped out = ![\frac{1}{3} \pi R^2 h-\frac{1}{3} \pi r^2 h'](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20R%5E2%20h-%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%27)
Here we have r/h is constant always
Hence ![\frac{r}{h'} =\frac{R}{h} \\r=Rh'/h = 4(5)/10 = 2](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%27%7D%20%3D%5Cfrac%7BR%7D%7Bh%7D%20%5C%5Cr%3DRh%27%2Fh%20%3D%204%285%29%2F10%20%3D%202)
Substitute to get volume of water pumped out = ![\frac{1}{3} \pi (10*16-4*5)=\frac{140\pi}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%2810%2A16-4%2A5%29%3D%5Cfrac%7B140%5Cpi%7D%7B3%7D)
Mass of water = density x volume = ![62.4(\frac{140\pi}{3})\\= 2912\pi lbs](https://tex.z-dn.net/?f=62.4%28%5Cfrac%7B140%5Cpi%7D%7B3%7D%29%5C%5C%3D%202912%5Cpi%20lbs)
Work done = force x displacement
= mass x accen x displacement
Here acceleration = gravity = 32.2 ft/sec^2
Displaement = height reduced = 5 ft
W=2912(32.2)(5)\pi =468832\pi foot -pound
Answer:
x = 4 or D
Step-by-step explanation:
3x - 6 = 6
Solve for x
3x = 12
x = 4
A common tangent is a line that happens to be tangent ("touching but not intersecting a curve or curved surface") to two different coplanar ("in the same plane) circles. I do hope that helped you.
Answer:
dI/dt = 0.0001(2000 - I)I
I(0) = 20
![I(t)=\frac{2000}{1+99e^{-0.2t}}](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7B2000%7D%7B1%2B99e%5E%7B-0.2t%7D%7D)
Step-by-step explanation:
It is given in the question that the rate of spread of the disease is proportional to the product of the non infected and the infected population.
Also given I(t) is the number of the infected individual at a time t.
![\frac{dI}{dt}\propto \textup{ the product of the infected and the non infected populations}](https://tex.z-dn.net/?f=%5Cfrac%7BdI%7D%7Bdt%7D%5Cpropto%20%5Ctextup%7B%20the%20product%20of%20the%20infected%20and%20the%20non%20infected%20populations%7D)
Given total population is 2000. So the non infected population = 2000 - I.
![\frac{dI}{dt}\propto (2000-I)I\\\frac{dI}{dt}=k (2000-I)I, \ \textup{ k is proportionality constant.}\\\textup{Since}\ k = 0.0001\\ \therefore \frac{dI}{dt}=0.0001 (2000-I)I](https://tex.z-dn.net/?f=%5Cfrac%7BdI%7D%7Bdt%7D%5Cpropto%20%282000-I%29I%5C%5C%5Cfrac%7BdI%7D%7Bdt%7D%3Dk%20%282000-I%29I%2C%20%5C%20%5Ctextup%7B%20k%20is%20proportionality%20constant.%7D%5C%5C%5Ctextup%7BSince%7D%5C%20k%20%3D%200.0001%5C%5C%20%5Ctherefore%20%5Cfrac%7BdI%7D%7Bdt%7D%3D0.0001%20%282000-I%29I)
Now, I(0) is the number of infected persons at time t = 0.
So, I(0) = 1% of 2000
= 20
Now, we have dI/dt = 0.0001(2000 - I)I and I(0) = 20
![\frac{dI}{dt}=0.0001(2000-I)I\\\frac{dI}{(2000-I)I}=0.0001 dt\\\left ( \frac{1}{2000I}-\frac{1}{2000(I-2000)} \right )dI=0.0001dt\\\frac{dI}{2000I}-\frac{dI}{2000(I-2000)}=0.0001dt\\\textup{Integrating we get},\\\frac{lnI}{2000}-\frac{ln(I-2000)}{2000}=0.0001t+k \ \ \ (k \text{ is constant})\\ln\left ( \frac{I}{I-222} \right )=0.2t+2000k](https://tex.z-dn.net/?f=%5Cfrac%7BdI%7D%7Bdt%7D%3D0.0001%282000-I%29I%5C%5C%5Cfrac%7BdI%7D%7B%282000-I%29I%7D%3D0.0001%20dt%5C%5C%5Cleft%20%28%20%5Cfrac%7B1%7D%7B2000I%7D-%5Cfrac%7B1%7D%7B2000%28I-2000%29%7D%20%5Cright%20%29dI%3D0.0001dt%5C%5C%5Cfrac%7BdI%7D%7B2000I%7D-%5Cfrac%7BdI%7D%7B2000%28I-2000%29%7D%3D0.0001dt%5C%5C%5Ctextup%7BIntegrating%20we%20get%7D%2C%5C%5C%5Cfrac%7BlnI%7D%7B2000%7D-%5Cfrac%7Bln%28I-2000%29%7D%7B2000%7D%3D0.0001t%2Bk%20%5C%20%5C%20%5C%20%28k%20%5Ctext%7B%20is%20constant%7D%29%5C%5Cln%5Cleft%20%28%20%5Cfrac%7BI%7D%7BI-222%7D%20%5Cright%20%29%3D0.2t%2B2000k)
![\frac{I}{I-2000}=Ae^{0.2t}\\\frac{I-2000}{I}=Be^{-0.2t}\\\frac{2000}{I}=1-Be^{-0.2t}\\I(t)=\frac{2000}{1-Be^{-0.2t}}\textup{Now we have}, I(0)=20\\\frac{2000}{1-B}=20\\\frac{100}{1-B}=1\\B=-99\\ \therefore I(t)=\frac{2000}{1+99e^{-0.2t}}](https://tex.z-dn.net/?f=%5Cfrac%7BI%7D%7BI-2000%7D%3DAe%5E%7B0.2t%7D%5C%5C%5Cfrac%7BI-2000%7D%7BI%7D%3DBe%5E%7B-0.2t%7D%5C%5C%5Cfrac%7B2000%7D%7BI%7D%3D1-Be%5E%7B-0.2t%7D%5C%5CI%28t%29%3D%5Cfrac%7B2000%7D%7B1-Be%5E%7B-0.2t%7D%7D%5Ctextup%7BNow%20we%20have%7D%2C%20I%280%29%3D20%5C%5C%5Cfrac%7B2000%7D%7B1-B%7D%3D20%5C%5C%5Cfrac%7B100%7D%7B1-B%7D%3D1%5C%5CB%3D-99%5C%5C%20%5Ctherefore%20I%28t%29%3D%5Cfrac%7B2000%7D%7B1%2B99e%5E%7B-0.2t%7D%7D)
Y = -4x -8
Slope = -4 where it’s the coefficient of the variable x
Y-intercept = -8 where it is b