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Evgen [1.6K]
3 years ago
9

:

Mathematics
2 answers:
Vesna [10]3 years ago
8 0

Answer:is yes

Step-by-step explanation:

no

iren [92.7K]3 years ago
8 0

Answer:

A= 8.182

B= 8

Step-by-step explanation:

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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
HELP FAST 100 POINTS: The manager of a basketball arena randomly selected 150 fans and asked if they were pleased with the new s
V125BC [204]

Answer:

6400 fans will be pleased.

Step-by-step explanation:

Out of 150 fans, 120 were pleased. Assuming the same ratio, out of 8000 fans, 8000x120/150 = 6400 will be pleased.


8 0
3 years ago
Read 2 more answers
Solve 2x2 + 8x + 10 = 0. using this model to he<br> X =<br> -b+ ✓ 62 - 4ac<br> 2a
Lesechka [4]

Answer:

x can have two complex solutions, which are:

-2 + i

-2 - i

Step-by-step explanation:

2x² + 8x + 10 = 0

4x² + 16x + 20 = 0

4x² + 16x + 16 = -4

(2x + 4)² = -4

2x + 4 = √-4

2x =  -4 ± i√4

2x = -4  ± 2i

x = -2 ± i

So x is equal to -2 + i and -2 - i.

8 0
3 years ago
Describe the process of writing the equation of a line
lara [203]
If you are writing in slope-intercept form:

You first find the slope.

Put the slope in the equation.

Substitute any point into the equation and find the y-intercept. 
7 0
3 years ago
Helppp me i neeed help
dexar [7]

Total no. of buttons = 300 + 700 + 1000

+ 500 = 2500

Possibility for a person to pick a pink button = 300/2500 = (3/25)%

Amount of pink buttons she can expect her friends to pick = 50(3/25) = 6

She can expect to make 6 pink barrettes.

6 0
3 years ago
Read 2 more answers
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