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3 years ago

Which month has the colder average temperatures?

Mathematics

2 answers:

Dima020 [189]3 years ago

7 0

I think january or december

amid [387]3 years ago

7 0

The month has the colder average temperature is that December

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Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

aliya0001 [1]

Answer:

$A=1500-1450e^{-\dfrac{t}{250}}$

Step-by-step explanation:

The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.

Volume = 500 gallons

Initial Amount of Salt, A(0)=50 pounds

Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min

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

$=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}$

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

Concentration c(t) of the salt in the tank at time t

Concentration, $C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}$

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

$=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}$

Now, the rate of change of the amount of salt in the tank

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

$\dfrac{dA}{dt}=6-\dfrac{A}{250}$

We solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}$

Recall that when t=0, A(t)=50 (our initial condition)

$50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}$

4 0

3 years ago

If f(x)=x^2-3x,find f(-18). Show work

scoundrel [369]

Answer: 378

-------------------------------------
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Work Shown:

f(x) = x^2 - 3x
f(x) = ( x )^2 - 3*( x )
f(-18) = ( -18 )^2 - 3*( -18 ) ... replace every x with -18; now use PEMDAS
f(-18) = 324 - 3*( -18 )
f(-18) = 324 + 54
f(-18) = 378

6 0

3 years ago

What is the product of -8(9) show your work to the problem

Daniel [21]

-72 just do 8*9 and add a negative sign

8 0

2 years ago

Read 2 more answers

Please help me out with this

Travka [436]

Either B or C.
Im thinking more C.....

6 0

2 years ago

jonny [76]

Answer:

1. False; 2. False; 3. False.

Step-by-step explanation:

1. Mode

False.

The mode, mean, and media are all measures of central tendency.

The mean is the best measure for normally distributed data.

The median is the best measure for skewed data.

The mode is the least used, because it's the only measure you can apply to nominal data.

2. Median

False.

The mean is the average of a set of scores or list of numbers.

3. Frequency distribution table

False.

It is not necessary to put the numbers in order.

For example, assume that you wanted to count the frequency of occurrence of each number in the list: 3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3, 1, 2, 1, 1, 3.

If you are doing this manually, you would go through the list and use tally marks to record the appearance of each number in its category.

If you are using a computer, it will do the sorting for you.

8 0

2 years ago