Solve for w 3w-3+4=1-5w

A tank contains 3,000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is

Shalnov [3]

Answer:

Step-by-step explanation:

Volume of tank is 3000L.

Mass of salt is 15kg

Input rate of water is 30L/min

dV/dt=30L/min

Let y(t) be the amount of salt at any time

Then,

dy/dt = input rate - output rate.

The input rate is zero since only water is added and not salt solution

Now, output rate.

Concentrate on of the salt in the tank at any time (t) is given as

Since it holds initially holds 3000L of brine then the mass to volume rate is y(t)/3000

dy/dt= dV/dt × dM/dV

dy/dt=30×y/3000

dy/dt=y/100

Applying variable separation to solve the ODE

1/y dy=0.01dt

Integrate both side

∫ 1/y dy = ∫ 0.01dt

In(y)= 0.01t + A, .A is constant

Take exponential of both side

y=exp(0.01t+A)

y=exp(0.01t)exp(A)

exp(A) is another constant let say C

y(t)=Cexp(0.01t)

The initial condition given

At t=0 y=15kg

15=Cexp(0)

Therefore, C=15

Then, the solution becomes

y(t) = 15exp(0.01t)

At any time that is the mass.

5 0

3 years ago

987÷z=164.5

AveGali [126]

Answer:

z=6

Step-by-step explanation:

987/z=164.5

multiply both sides by z

4 0

3 years ago

Manuel bought 2kg of jelly beans and 2kg of gummy worms for a total of $26. Danny bought 2kg of jelly beans and 3kg of gummy wor

charle [14.2K]

Answer:

Jelly beans: $6 for 1 kg

Gummy worms: $7 for 1 kg

Step-by-step explanation:

In this question, we need to find the cost of 1kg of jelly beans and gummy worms.

To do this, make equations for both scenarios and solve:

2j + 2g = 26

2j + 3g = 33

Turn the bottom equation negative, as we will first solve for gummy worms (g).

2j + 2g = 26

-2j - 3g = -33

Solve:

-g = -7

Divide both sides by -1.

g = 7

We now know that gummy worms cost $7 for 1 kg

To solve for jellybeans (j), plug in 7 to g in one of the equations and solve:

2j + 2(7) = 26

2j + 14 = 26

Subtract 14 from both sides.

2j = 12

Divide both sides by 2.

j = 6

Jellybeans cost $6 for 1 kg.

Check answer by plugging in values to one of the equations:

2(6) + 2(7) = 26

12 + 14 = 26

26 = 26

3 0

3 years ago

A bicycle normally sells for 239.99 dollars. It is now on sale for 25% off. As an employee, Baron is able to save an extra 10% o

Mekhanik [1.2K]

239.99 x 75%(75/100) ~ $180
$180 x 90%(90/100) = $162

8 0

3 years ago

Pleaseee helppp with thissss asapppp

Natasha2012 [34]

As we know that the standard equation of circle is ${\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}$ , where r is the radius of circle and centre at (h,k) 

Now , as the circle passes through (2,9) so it must satisfy the above equation after putting the values of h and k respectively

${:\implies \quad \sf \{2-(-1)\}^{2}+(9-5)^{2}=r^{2}}$