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Paladinen [302]

3 years ago

12

There are 56 fourth graders going on a field trip. The teacher wants to divide them evenly into groups of 4 students and no more

than 8 students. What are ways to divide the students evenly into groups

1 answer:

AleksAgata [21]3 years ago

8 0

56 ÷14 =4

Step-by-step explanation:

dividing

56÷7=8

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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}}$

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Jeanette purchased a concert ticket on a website. The original price of the ticket was $75. She use a coupon code to receive a 2

devlian [24]

The remaining cost is $66 after 20% discount and 10% service fee

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4 years ago

The perimeter of the rectangle below is 158 units. find the length of side ad

seraphim [82]

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Find the area of a parallelogram ABCD with AB =7 m. AD = 20 m and BAD = 62°.

nikklg [1K]

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Answer:

123.6 m²

Step-by-step explanation:

The area is given by the formula ...

A = (AB)(AD)sin(∠A)

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You have 40 grams of a radioactive kind of tellurium. If it's half life is 9 hours, how much will be left after 18 hours

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Answer:

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Step-by-step explanation:

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