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3 years ago

Please help me I’ll give you a thanks :-)

Mathematics

2 answers:

sergejj [24]3 years ago

6 0

(4,10) x = 4 y = 10

Sonbull [250]3 years ago

4 0

Answer:

I love algebra anyways

The ans is in the picture with the steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

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Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

I just need help finding h pleasww

SCORPION-xisa [38]

Answer:

h = (2/3)√3
b = 3√2

Step-by-step explanation:

It is useful to remember the ratios between the side lengths of these special triangles.

30°-60°-90° ⇒ 1 : √3 : 2

45°-45°-90° ⇒ 1 : 1 : √2

h is the shortest side, and the given length is the intermediate side. This means ...

h/1 = 2/√3

h = 2/√3 = (2/3)√3 . . . . . . simplify, rationalize the denominator

b is the longest side, and the given length is the short side. This means ...

b/√2 = 3/1

b = 3√2 . . . . . multiply by √2

8 0

2 years ago

Evaluate. 54 Btw its worth 30 points

mina [271]

Answer:

what do you mean evaluate

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A group of 5 men and 5 women are applying for a job at a local company. Each of the 10 job candidates has the same chance of rec

Zielflug [23.3K]

Answer: 1/4

Explanation: Because there is a 1/2 chance that a female will get the first job, and a half chance that a lady will get a second job. So (1/2)*(1/2)=(1/4)

7 0

3 years ago

Solve the following equation by factoring: x^2+ x– 42 = 0

Anastaziya [24]

Answer:

x=6,x=-7

Step-by-step explanation:

x^2+x-42=0

x^2-6x+7x-42=0

x(x-6)7(x-6)=0

(x-6)(x+7)=0

3 0

2 years ago