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2 years ago

What is the coefficient of the second term of the polynomial? (In other words, what is B?

Mathematics

1 answer:

Scrat [10]2 years ago

7 0

Answer: The coefficient of the second term of the polynomial is B=5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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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}}$

3 0

3 years ago

The letter or number on each side indicates the side's measure and the letter or number in the interior of each angle of each tr

Travka [436]

Answer:

$\beta , \alpha , \gamma$

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Can you help me with this question please? I will reward 20 points for best answer.

swat32

Answer:

Demand: q = -50p + 1200

Supply: q = 40p

Step-by-step explanation:

First let's define our variables.

q = quantity of T-shirts

p = price

We know that when p = 12, q = 600. When p increases by 1, q decreases by 50. So this is a line with slope -50 that passes through the point (12, 600). Using point-slope form to write the equation:

q - 600 = -50 (p - 12)

Converting to slope-intercept form:

q - 600 = -50p + 600

q = -50p + 1200

Similarly, we know that when p = 9.75, q = 600 - 210 = 390. When p increases by 1, q increases by 40. So this is a line with slope 40 that passes through the point (9.75, 390). Using point-slope form to write the equation:

q - 390 = 40 (p - 9.75)

Converting to slope-intercept form:

q - 390 = 40p - 390

q = 40p

5 0

3 years ago

the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t

777dan777 [17]

Answer:

ratio: 2/3
sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

a2 = a1·r^(2-1) = a1·r

a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

a2 = 18 = a1·(2/3)

a1 = (3/2)·18 = 27

The sum of the first 6 terms is ...

Sn = a1·(r^n -1)/(r -1)

S6 = 27·((2/3)^6 -1)/(2/3 -1)

S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

8 0

3 years ago

25 less than twice a number is equal to the number. What is the number?

belka [17]

Step-by-step explanation:

x = the number

2x - 25 = x

2x = x + 25

x = 25

8 0

3 years ago