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3 years ago

Help me asap please!

Mathematics

1 answer:

sveta [45]3 years ago

4 0

Answer:

Earths moon:

Scientific: 7.35x10^22

Standard:73500000000000000000000

for the rest im only going to give you the scientific method

Mercury: 3.205x10^23

Venus 4.867x10^24

Jupiter 1.898x10^27

Saturn 5.683x10^26

Uranus 8.681x10^25

Neptune 1.024x10^26

Phobos 10.6x10^15

Ariel 1.27x10^21

Titan 1.3452x10^23

I hope this helps

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Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

aliya0001 [1]

Answer:

$A=1500-1450e^{-\dfrac{t}{250}}$

Step-by-step explanation:

The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.

Volume = 500 gallons

Initial Amount of Salt, A(0)=50 pounds

Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min

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

$=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}$

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

Concentration c(t) of the salt in the tank at time t

Concentration, $C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}$

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

$=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}$

Now, the rate of change of the amount of salt in the tank

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

$\dfrac{dA}{dt}=6-\dfrac{A}{250}$

We solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}$

Recall that when t=0, A(t)=50 (our initial condition)

$50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}$

4 0

4 years ago

What is the sum of 15 and it's additive inverse

Inga [223]

<span>The opposite of a number. For example, the additive inverse of 12 is –12. The additive inverse of –3 is 3. Formally, the additive inverse of x is –x. Note: The sum of a number and its additive inverse is 0. Hope i helped :)</span>

3 0

4 years ago

Read 2 more answers

2/3x - 1/2y = 3

nevsk [136]

2/3x - 1/2y = 3 |multiply both sides by 6

4x - 3y = 18

1/2x + y = 5 |multiply both sides by 2

x + 2y = 10

Answer: 4x - 3y and x + 2y = 10.

7 0

3 years ago

A large envelope is 0.085 cm thick. How thick would a stack of 100 of these envelopes be? Explain your reasoning.

Pavlova-9 [17]

Answer:

8.5 cm

Step-by-step explanation:

I think because wouldn't you take the 0.085 · 100

(get mad if I'm wrong i might be)

3 0

3 years ago

Create a list of steps, in order, that will solve the following equation 2(x+2)^2-5=93

solong [7]

Answer:

x = (-7,7)

Step-by-step explanation:

1.add 5 on both side

2.divide each side of the equation by 2

3.take the square root of each side of the equation to solve for x

7 0

3 years ago