Answer:
The answer is below
Step-by-step explanation:
a) The maximum capacity of he tank is 6 L and initially it contains 11 mg of salt dissolved in 3 L of water. Solution enters the tank at a rate of 3 L/hr, therefore in x hours, the amount of water that have entered the tank = 3x.
Solution also leaves the tank at a rate of 2L/hr, therefore in x hours, the amount of water that have left the tank = 2x
Hence the amount of water present in the tank at x hours is given as:
3 + 3x - 2x = 3 + x
The time taken to full the tank can be gotten from:
3 + x = 6
x = 6 - 3
x = 3 hr
b)
![\frac{dQ}{dx}=3-\frac{2Q}{3+x}\\ \\\frac{dQ}{dx}+\frac{2Q}{3+x}=3\\\\let\ u'=\frac{2u}{3+x}\\\\\frac{u'}{u}=\frac{2Q}{3+x}\\\\ln(u)=2ln(3+x)\\\\u=(3+x)^2\\\\(3+x)^2Q]'=3(3+x)^2\\\\(3+x)^2Q=(3+x)^3+c\\\\Q(0)=11\\\\(3+0)^2(11)=(3+0)^3+c\\\\x=72\\\\Q=x+3+\frac{72}{(x+3)^2}\\ \\Q(3)=3+3+\frac{72}{(3+3)^2}=8\ mg](https://tex.z-dn.net/?f=%5Cfrac%7BdQ%7D%7Bdx%7D%3D3-%5Cfrac%7B2Q%7D%7B3%2Bx%7D%5C%5C%20%20%5C%5C%5Cfrac%7BdQ%7D%7Bdx%7D%2B%5Cfrac%7B2Q%7D%7B3%2Bx%7D%3D3%5C%5C%5C%5Clet%5C%20u%27%3D%5Cfrac%7B2u%7D%7B3%2Bx%7D%5C%5C%5C%5C%5Cfrac%7Bu%27%7D%7Bu%7D%3D%5Cfrac%7B2Q%7D%7B3%2Bx%7D%5C%5C%5C%5Cln%28u%29%3D2ln%283%2Bx%29%5C%5C%5C%5Cu%3D%283%2Bx%29%5E2%5C%5C%5C%5C%283%2Bx%29%5E2Q%5D%27%3D3%283%2Bx%29%5E2%5C%5C%5C%5C%283%2Bx%29%5E2Q%3D%283%2Bx%29%5E3%2Bc%5C%5C%5C%5CQ%280%29%3D11%5C%5C%5C%5C%283%2B0%29%5E2%2811%29%3D%283%2B0%29%5E3%2Bc%5C%5C%5C%5Cx%3D72%5C%5C%5C%5CQ%3Dx%2B3%2B%5Cfrac%7B72%7D%7B%28x%2B3%29%5E2%7D%5C%5C%20%5C%5CQ%283%29%3D3%2B3%2B%5Cfrac%7B72%7D%7B%283%2B3%29%5E2%7D%3D8%5C%20mg)
8 mg/ 6 L = 4/3 mg/L
Answer:
35 in²
Step-by-step explanation:
The irregular shaped can be divided into two squares and one rectangle, so the area will be the additions of the area of the squares and the rectangle
area of square A = L *B = 3 *3 = 9in²
area of square B = L * B = 4*4 = 16in²
area of rectangle C = L * B = 5 *2 = 10in²
th area of the irregular shape = 9 in² + 16 in² + 10 in² = 35 in²
The rule is that the angle is half the measure of the intercepted arc. So it's 110.
Answer:
- a) 11, d) 25, e) 14, b) 25, c) 28, f) 33
Step-by-step explanation:
<h3>Given</h3>
- ΔBDF, with H is the centroid of BDF, DF = 50, CF = 42, and BH = 22
<h3>To find</h3>
<h3>Solution</h3>
As per definition of the centroid, the points C, E and G are midpoints of respective sides and the length of short and long distances from the centroid have ratio of 1/3 and 2/3 of median
- a) HE = 1/2BH = 1/2(22) = 11
- d) DE = 1/2DF = 1/2(50) = 25
- e) CH = 1/3CF = 1/3(42) = 14
- b) EF = DE = 25
- c) HF = 2/3CF = 2/3(42) = 28
- f) BE =BH + HE = 22 + 11 = 33
16, first you need to add on the four he lost to the 18 he ended with.
