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3 years ago

-4(2p + 5) + 8p = -11

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

6 0

Answer:

There are no values of P to make it true

Step-by-step explanation:

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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

Round number to the nearest hundred 293

Mrac [35]

300 is your answer

293 the 2 looks at the neighbor and says are you 5 or more or are you 4 or less and 9 is bigger than 5 so then you round 9 and your answer turns into 300 okay.

3 0

3 years ago

Read 2 more answers

If a child younger than the age of about 4 or 5 was to have a large portion of their brain removed in a necessary surgery, _____

ohaa [14]

Answer:

their brains are plastic enough that cells intended to serve one function could be turned into cells that serve another function

Step-by-step explanation:

3 0

2 years ago

Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the

ss7ja [257]

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

The correct question is

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

$x+2(x+1)+3(x+2)=-76$

solve for x

apply distributive property

$x+2x+2+3x+6=-76$

Combine like terms

$6x+8=-76$

subtract 8 both sides

$6x=-76-8$

$6x=-84$

Divide by 6 both sides

$x=-14$

$x+1=-14+1=-13$

$x+2=-14+2=-12$

therefore

The numbers are -14,-13 and -12

3 0

3 years ago

Patrick counts on to solve 9+?=16 Explain how he can do this. What is the missing addend? Enter your answers in the boxes. Patri

Ipatiy [6.2K]

Answer:

Step-by-step explanation:

9+7=16

Hope this helps

6 0

3 years ago