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2 years ago

What's an equivalent equation for -5(3-2x)

Mathematics

1 answer:

kobusy [5.1K]2 years ago

7 0

Answer:

-15 + 10x

10x - 15

(either one works)

Step-by-step explanation:

You mean you just want me to expand it?

Ok.

Multiply -5 by 3 and -2x.

(-5)(3) = -15

(-5)(-2x) = +10x

Add those together:

-15 + 10x

10x - 15

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100pts: Is 999962000357 a prime number? If it is not, then give its prime factorization.

Serhud [2]

Answer:

No, it is NOT a prime number.

Step-by-step explanation:

To find out if a number is a prime number, you can divide it by two. If it is a whole number, it isn't prime. It would be a mixed number/fraction if so.

All prime numbers are whole numbers but the result of the division shouldn't be when you divide the number you want to find out. If it is a fraction/mixed number, your unknown number is most likely a prime number. (my explanation was confusing)

6 0

3 years ago

Read 2 more answers

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}}$