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2 years ago

What is the measure of Y

Mathematics

1 answer:

vova2212 [387]2 years ago

3 0

Answer:

Step-by-step explanation:

60 + 58 + y = 180

118 + y = 180

y = 180 - 118

y = 62

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A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

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

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

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

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

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

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

3 years ago

the cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of

ch4aika [34]

Answer:

equation: y=15x+95

it would cost $1250

5 0

3 years ago

Read 2 more answers

5(12-4)=5(12)-5(4) what is this property

kherson [118]

Answer:

distributive property

Step-by-step explanation:

The distributive property is described as

a(b + c) = ab + ac

5(12 - 4) = 5(12) - 5(4) ← is obtained using the distributive property

6 0

2 years ago

Find two consecutive odd integers if twice the larger, increased by the smaller equals 37,

Alexxx [7]

Answer:

11 and 13

Step-by-step explanation:

the first (smaller) odd integer can be called x

the second (larger) odd integer can be called x+2

2(x+2)+x = 37

[simplify . . .]

2x+4+x = 37

3x+4 = 37

[subtract 4 from each side]

3x = 33

[divide each side by 3; find smaller odd integer]

x = 11

[add 2 to find larger odd integer]

x+2 = 13

6 0

3 years ago

Im dumb and need help

ladessa [460]

Answer:

i thought this was a meme bro

Step-by-step explanation:

4 0

2 years ago

What is the measure of Y ​

What is the measure of Y