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Mashcka [7]
3 years ago
14

-11=-11a+33 what is the answer I’m stuck

Mathematics
1 answer:
Gnesinka [82]3 years ago
5 0
A=4

The work behind it

-11a+33= -11
-33 -33

-11a=-44
Divide both sides by -11
-44/-11=a
A=4
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A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter
faltersainse [42]

At the start, the tank contains

(0.02 g/L) * (1000 L) = 20 g

of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.

Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of

(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s

In case it's unclear why this is the case:

The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.

So the amount of chlorine in the tank changes according to

\dfrac{\mathrm dc(t)}{\mathrm dt}=-\dfrac{5c(t)}{200-3t}

which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):

\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{200-3t}=0

\dfrac1{(200-3t)^{5/3}}\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{(200-3t)^{8/3}}=0

\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0

\dfrac{c(t)}{(200-3t)^{5/3}}=C

c(t)=C(200-3t)^{5/3}

There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :

20=C(200)^{5/3}\implies C=\dfrac1{200\cdot5^{1/3}}

\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}

7 0
3 years ago
if francisco drinks 2 2/3 ounces of water every 1/2 hours.How many ounces of water does francisco drink in one hour?
masha68 [24]

Answer:

5 1/3  Please mark me brainlliest

Step-by-step explanation:

2 2/3 every half-hour so for 1 full hour 2 2/3+2 2/3 = 5 1/3

8 0
3 years ago
Find the missing Side of the triangle
sammy [17]

Answer:

2√15

Step-by-step explanation:

Use the Pythagorean theorem.

2² + x² = 8²

x² + 4 = 64

x² = 60

x² = 4 * 15

x = 2√15

3 0
2 years ago
A certain hybrid car has a mileage rating of 57 miles per gallon. if the car makes a trip of 293 miles, how many gallons of gaso
dlinn [17]
To determine the number of gallons of gasoline that is used, we need to know the rate of usage of gasoline. This rate would describe the number of gasoline in units of volume that is being used per distance in units of length. In this case, we need the rate in units of miles per gallon. From what is asked and the given values, we simply divide the rate to the the total distance that was traveled by the car. We calculate as follows:

Gallons of gasoline = 293 miles / 57 miles / gallon
Gallons of gasoline = 5.14 gallons

Therefore, about 5 gallons of gasoline was consumed by the hybrid car for a distance of 57 miles.
4 0
3 years ago
A salesman is paid $450 a week, plus a commission of 35 cents for every item that he sells. Write a linear function where the pa
Ratling [72]

Answer:

Step-by-step explanation:

1400×0.35

490+450

940

3 0
2 years ago
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