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faltersainse [42]
3 years ago
9

10 points please answer thx

Mathematics
1 answer:
Ann [662]3 years ago
5 0

Answer:

B

Step-by-step explanation:

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A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is add
RUDIKE [14]

Salt flows into the tank at a rate of

(1/2 lb/gal) * (6 gal/min) = 3 lb/min

and flows out at a rate of

(Q(t)/60 lb/gal) * (6 gal/min) = 6Q(t) lb/min

The net rate of change of the amount of salt in the tank at time t is then governed by

\dfrac{\mathrm dQ}{\mathrm dt}=3-6Q

Solve for Q:

\dfrac{\mathrm dQ}{\mathrm dt}+6Q=3

e^{6t}\dfrac{\mathrm dQ}{\mathrm dt}+6e^{6t}Q=3e^{6t}

\dfrac{\mathrm d}{\mathrm dt}[e^{6t}Q]=3e^{6t}

e^{6t}Q=\dfrac{e^{6t}}2+C

\implies Q=\dfrac12+Ce^{-6t}

The tank starts with 10 lb of salt, so that Q(0) = 10. This gives us

10=\dfrac12+C\implies C=\dfrac{19}2

so that the amount of salt in the tank at time t is given by

\boxed{Q(t)=\dfrac{1+19e^{-6t}}2}

4 0
3 years ago
Which of the following math statements contain variable(s)? Check all that
DochEvi [55]

Answer:

A. and C.

Step-by-step explanation:

Hope this helps :)

8 0
3 years ago
Somebody please help me with this
Sedaia [141]

Answer:

E and F= 54 Degrees D is 90 degrees

Step-by-step explanation:

6 0
3 years ago
Help me with this question if you don’t mind
vampirchik [111]

Answer:

D

Step-by-step explanation:

if AB is congruent to AC that means both are 76 degrees so subtract that from the total degrees of a whole triangle which is 180 that gives you A which is 28.

Hope it helps :)

5 0
3 years ago
7. An example for using estimation would be:
Aliun [14]
Guessing the number of pennies in a jar
4 0
3 years ago
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