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1 year ago

Question Solve the equation. 0.6=0.2a

Mathematics

2 answers:

Delvig [45]1 year ago

7 0

Answer:

A = 3

Step-by-step explanation:

0.6=0.2a

Divide both sides by 0.2.

0.2

0.6

Expand

0.2

0.6

by multiplying both numerator and the denominator by 10.

Divide 6 by 2 to get 3.

3=a

vazorg [7]1 year ago

7 0

ANSWER: When simplified, <u><em>a=3</em></u>

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-2 < 3x+4 < 31 find x

Eva8 [605]

First rewrite into 2 inequalities,

$-2\lt3x+4$

$3x+4\lt31$

Solve each of the inequalities,

$-2\lt3x+4\implies3x\gt-6\implies x\gt-2$

$3x+4\lt31\implies 3x\lt27\implies x\lt9$

So our x is between -2 and 9 which can be written as,

$-2\lt x\lt9$

or as an interval,

$x\in(-2,9)$

Hope this helps :)

8 0

2 years ago

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

2 years ago

When a number is subtracted from x the result is 6. What is that number?

just olya [345]

I think the answer is 2/3

3 0

2 years ago

Emma jogs 2 miles along the beach in

Juli2301 [7.4K]

Answer:

<h3><u>3 times the time --> 3 times the distance</u></h3>

Step-by-step explanation:

Emma jogs 2 miles along the beach in 1/3 of an hour. If she travels at a constant rate, how far will she jog in an hour?

6 0

2 years ago

Read 2 more answers

2(7x-9)=5(x+3)<br> Solve for x

Nadya [2.5K]

Answer:

x = 3.67

Step-by-step explanation:

Simplify both expressions

14x - 18 = 5x + 15

Subtract the bigger (n)x by the smaller

14x - 5x = 9x

Plus the smallest by itself, giving you:

9x - 18 = 15

+18 +18

9x = 33

Simplify ( divided by 3 )

3x = 11

x = 3.67

7 0

2 years ago