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Sonbull [250]
3 years ago
13

Write the expression. A number b squared

Mathematics
1 answer:
IgorC [24]3 years ago
8 0

B with a little 2 above it

2

b

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A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into the tank at 6 gallons per min
balandron [24]

Answer:

1.857 minutes

Step-by-step explanation:

From the given information:

Consider the amount of salt present in the tank as x(t) at a given time (t); &

The volume of the solution = V(t)

At t = 0 i.e. (at initial conditions)  x(0) = 30; and V(0) = 50

However, the overall increase taken place for 1 gallon per minute is:

V(t) = 50 + t

The amount of salt x(t) at any given point for time (t) is;

\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}

After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:

\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}

Taking the integral of what we have above, we get:

In x(t) = - 5 In(t + 50) + In (C)

In x(t) = In (t+ 50)⁻⁵ + In (C)

In x(t) = In C ( t + 50)⁻⁵

x(t) = C(t + 50)⁻⁵      (General solution)

To estimate the required solution; we apply the initial conditions x(0) = 30;

Thus;

x(0) = C(50)⁻⁵ = 30

⇒ C = 30 × 50⁵

Hence; x(t) =  30 × 50⁵ × (t + 50)⁻⁵

The above expression can be re-written as:

x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25

i.e.

\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}

\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}

\dfrac{50}{t+50}= 0.964192504

{50}= 0.964192504(t+50)

50 = 0.964192504t + 48.2096252

50 - 48.2096252 = 0.964192504t

1.7903748 =  0.964192504t

t = 1.7903748 / 0.964192504

t ≅ 1.857 minutes

We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.

7 0
2 years ago
What is the algebraic expression for the following word phrase: the sum of 5 and 2x?
Naya [18.7K]
<span>the sum of 5 and 2x :  5 + 2x 

You can't add this because they are not like terms
</span>
6 0
3 years ago
I need to know how I got number 27 because I can’t remember what I did
krok68 [10]
B=75, not 27
Sorry, I had to use a napkin because I was too lazy to get a paper....let me know if u need me to explain anything

4 0
3 years ago
Mark for review (Will be highlighted on the review page) 1. Solve this equation: 80 = 3y + 2y + 4 + 1.
saul85 [17]
First combine the like terms 3y + 2y to get 5y. Then combine 4 + 1 to get 5. Your equation will now be 80 = 5y + 5. To solve for y, 5 needs to be subtracted from both sides of the equation leaving 75 = 5y. Final step to solving for y, 5 needs to be divided from each side of the equation leaving the final answer of
15 = y.
7 0
3 years ago
Find the value of x.<br><br> help
Komok [63]

Answer:

X=62

Step-by-step explanation:

X=62 because the side where x is and where the other degree is, they are congruent. And since you have to add 12 it would have to be 62 to be equal to 74.

7 0
3 years ago
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