Answer:
x= 3, 1
Step-by-step explanation:
Answer:
n = -5
Step-by-step explanation:
Solve for n:
n + 2 = 4 n + 17
Hint: | Move terms with n to the left hand side.
Subtract 4 n from both sides:
(n - 4 n) + 2 = (4 n - 4 n) + 17
Hint: | Combine like terms in n - 4 n.
n - 4 n = -3 n:
-3 n + 2 = (4 n - 4 n) + 17
Hint: | Look for the difference of two identical terms.
4 n - 4 n = 0:
2 - 3 n = 17
Hint: | Isolate terms with n to the left hand side.
Subtract 2 from both sides:
(2 - 2) - 3 n = 17 - 2
Hint: | Look for the difference of two identical terms.
2 - 2 = 0:
-3 n = 17 - 2
Hint: | Evaluate 17 - 2.
17 - 2 = 15:
-3 n = 15
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 n = 15 by -3:
(-3 n)/(-3) = 15/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
n = 15/(-3)
Hint: | Reduce 15/(-3) to lowest terms. Start by finding the GCD of 15 and -3.
The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):
n = 5/(-1)
Hint: | Simplify the sign of 5/(-1).
Multiply numerator and denominator of 5/(-1) by -1:
Answer: n = -5
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:
the answer is 24.
Step-by-step explanation:
