Solve for n q= 2n+2w

A 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. Brine containing 3 lb of salt per

gulaghasi [49]

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is $\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow$

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank × flow rate

= x/250 × 9

= 9x/250 lb/s

∴

$\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}$

$\dfrac{dx}{dt} + \dfrac{9x}{250}= 21$

This is a 1st order linear differentiation,

The integrating factor if $e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}$

∴

$e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C$

$e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C$

$x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}$ at t = (0) and x(0) = 100 lb

Hence;

$100 = \dfrac{1750}{3}+C$

$C = \dfrac{1750}{3} -100$

$C = - \dfrac{1450}{3}$

∴ $x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}$

after time t = 1 minute i.e 60 s

$x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}$

$x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}$

x(t) = 581.66 lb

5 0

3 years ago

after selling three fifth of its books, a bookstore had 880 textbooks left. how many books were in the bookstore initially

sleet_krkn [62]

Answer:

yours answer is 1760

Step-by-step explanation:

he sold 3/5 of its books , that means 2/5 is left and 2/5 is 880

so 2/5=880

880/5 = 176

176x2=352

352x5=1760

5 0

3 years ago

How many solutions does this linear system have <br><br> y = 2x - 5<br><br> -8x - 4y = -20

Ray Of Light [21]

replace the 1st equation into the 2nd one for y

-8x-4(2x-5) = -20

-8x-8x+20 =-20

-16x+20 = -40

-16x=-40

x = 5/2 = 2.5

y = 2x-5 - 2(2.5) - 5 = 5-5 = 0

one solution (2.5,0)

8 0

3 years ago

Read 2 more answers

Colton earns $7 per hour plus $1.50 for each pizza delivery. The expression 7h+1.50d can be used to find the total earnings afte

Fed [463]

He would make $117 because 7x15=105 and 1.50x8=$12.00 add that together you get 117

4 0

3 years ago

Read 2 more answers

Rectangle ABCD has a perimeter of 32 units and will

AlladinOne [14]

Answer:

Check below

Step-by-step explanation:

1) Check the rectangle below with a line k, the axis of rotation in the center of the figure.

2) Since it has a perimeter of 32 units and it is to be rotated about the line, the solid to be created it is a cylinder. As you can see below.

3) Let's calculate its radius, based on the information given, i.e. the perimeter:

$2p=32\\2p=b+b+h+h\\2p=2(b+h)\\2(b+h)=32\\b+h=16\\b.h=60\\\\b=10\: and \:h=6$

Since the line of rotation is the center, and the radius is half the line segment of the basis, then the radius is 5.

4 0

3 years ago