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3 years ago

Please help me on this! my homework is hard :(

Mathematics

1 answer:

Marat540 [252]3 years ago

8 0

Answer:

Step-by-step explanation:

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At 57 degrees fahrenheit, a certain insect chirps at a rate of 100 times per minute, and at 65 degrees, they chirp 156 times per

Elan Coil [88]

Answer:

57= 100 65=156-8=158

Step-by-step explanation:

5 0

3 years ago

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

$R_{in}=$ (concentration of salt in inflow)(input rate of fluid)

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

$R_{out}=$ (concentration of salt in outflow)(output rate of fluid)

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

3 years ago

Half of a pizza was broccoli and half was mushroom. george ate 1/3 of the broccoli part and 1/4 of the mushroom part. how much o

butalik [34]

1/3x1/4=1/16 I think

5 0

3 years ago

Find the new amount. explain 200 books; 75% decrease 160 bananas; 20% decrease

prohojiy [21]

Answer:

75% of 200 = 50; 20% of 160 = 128

Step-by-step explanation:

200 (0.75) = 150

200 - 150 = 50

160 (0.20) = 32

160 - 32 = 128

8 0

3 years ago

Oil is pumped into a tank at a rate of Q(t)=45-t gallons per minute where time is t is measured in minutes how many gallons are

FinnZ [79.3K]

Answer:

15 gallons

Step-by-step explanation:

Given that:

Pumping rate is modeled by the equation :

Q(t)=45-t gallons per minute ; where t is in minutes

Number of gallons in tank after 30 minutes ;

Q(t)=45-t

Q(30) = 45 - 30

Q(30) = 15

Hence, Number of gallons in tank after 30 minutes is 15 gallons

5 0

3 years ago