Plz I need help on this question

Answer:

a. dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. y = 20000/(200 + t)

Step-by-step explanation:

a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.

Let y be the mass of salt.

The net flow into the tank dy/dt = mass flow in - mass flow out

Since only water flows into the tank, the mass flow in = 0 g/min

Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by  2t. So, the volume of the tank in time, t is V = 200 + 2t.

So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).

Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out =  y/(200 + 2t) × 2 = 2y/(200 + 2t)

The net flow into the tank dy/dt = mass flow in - mass flow out

dy/dt = 0 - 2y/(200 + 2t)

dy/dt = - 2y/(200 + 2t)

Since the initial mass of salt in the tank is 100 g, y(0) = 100 g

So, the initial value problem IVP is

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.

Solving the IVP, we have

dy/dt = - 2y/(200 + 2t)  where y(0) = 100 g

Separating the variables, we have

dy/y = - 2dt/(200 + 2t)

Integrating both sides, we have

∫dy/y = - ∫2dt/(200 + 2t)

㏑y = - ㏑(200 + t) + ㏑C

㏑y + ㏑(200 + t) = ㏑C

㏑[y(200 + t)] = ㏑C

y(200 + t)] = C

y = C/(200 + t) since y(0) = 100, we have

100 = C/(200 + 0)

100 = C/200

C = 100 × 200

C = 20000

So, y = C/(200 + t)

y = 20000/(200 + t)

Answer:

HJ = 52

JK = 79

Step-by-step explanation:

Hello, I want to assume you are trying to determine either HJ or JK. Below is an illustration of how to determine either HJ or JK.

From the question given above, the following data were obtained:

HJ = 5x – 3

JK = 8x – 9

KH = 131

If we draw a straight line, we'll observe the following:

H_______J_______K

KH = HJ + JK

Next, we shall determine the value of x.

HJ = 5x – 3

JK = 8x – 9

KH = 131

KH = HJ + JK

131 = (5x – 3) + (8x – 9)

131 = 5x – 3 + 8x – 9

Collect like terms

131 + 3 + 9 = 5x + 8x

143 = 13x

Divide both side by 13

x = 143 / 13

x = 11

Finally, we shall determine HJ and JK. This can be obtained as follow:

For HJ:

HJ = 5x – 3

x = 11

HJ = 5(11) – 3

HJ = 55 – 3

HJ = 52

For JK:

JK = 8x – 9

x = 11

JK = 8x – 9

JK = 8(11) – 9

JK = 88 – 9

JK = 79

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

Answer:

(0,1) and (3,4)

Step-by-step explanation:

It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4

put them in the equation and you'll see the the values satisfies the equation

Answered by GAUTHMATH

Answer:

jhshejwjabsgsgshshsnsjs

Answer:

Step-by-step explanation:

Put the equation into center-radius form.

x² + y² + 8x - 12y + 24 = 0

x² + y² + 8x - 12y = -24

(x²+8x) + (y²-12y) = -24

(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24

(x+4)² + (y-6)² = 28

Center: (-4,6)

radius: √28

Answer:

0>

Step-by-step explanation:

===========================================

Explanation:

There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.

Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.

-------------------

There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.

Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35

This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).

-------------------

We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35

9514 1404 393

Answer:

Step-by-step explanation:

A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).

(a) the x-values at which f has a local minimum are -1 and 3.

(b) the local minimum values of f are -2 and -1 at those x-values.

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer: The altitude is 90.

Step-by-step explanation: the formula to calculate a trapezoid: A = (.5)(B+b)h.

plug the values in.

8100 = (.5)(180)h

8100 = 90h

h = 8100/90

h = 90

Answer: P(a) + P(b) - P(a and b)

Step-by-step explanation:

Use set diagrams to show answer.

Answer:

0.68

Step-by-step explanation:

correct on edge

Answer:

39-13=26

Step-by-step explanation:

plus(minus)=minus

Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

Answer:

Option C, F(x) = (x+2)/(x+1)

Answered by GAUTHMATH

Answer:

In 24 years.

Step-by-step explanation:

Let the sum of money be 100 which amounts to 200 ( doubles itself ) in 6 years time. Interest on 100rs. Is 100. Putting the following in simple interest formula. You get :

[tex]100=\dfrac{100\times R\times 6}{100}\\\\R=\dfrac{100}{6}[/tex]

Now when 100 will become 5 times i.e 500 the interest will be 400rs.

Putting in simple interest formula:

[tex]400=\dfrac{\dfrac{100\times 100}{6T}}{100}\\\\T=\dfrac{2400}{100}\\\\=24\ yrs[/tex]

So, in 24 years, it will become 5 times.

where's the diagram?

Answer:

A. y + 1 = -5(x - 2)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Slope m = -5

Point (2, -1)

Step 2: Find Equation

Answer:

A.

Step-by-step explanation:

the equation of the parabola shown in the graph is y=x²-5, then the inequality is y≥x²-5 (inside the parabola).

Answer:

7/20 mile farther

Step-by-step explanation:

Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:

3/4 - 2/5 = ?

Here the LCD is 20.  Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.

Then 3/4  - 2/5 = 15/20 - 8/20, or 7/20.

You still have 7/20 mile to walk to get home.

Answer:

Step-by-step explanation:

Answer:

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with an average of three errors per page

This means that [tex]\mu = 3[/tex]

What is the probability that a randomly selected page does not need to be retyped?

Probability of at most 3 errors, so:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]

0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.

Answer:

56+35=180 then solve it thanks

Answer:

Step-by-step explanation:

we have a two right triangle, with one side 115

lets say that the other side of the big right triangle is y

-in the big triangle find the third angle

180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180

tan 55 = opp. /adj= y / 115

y = 115 * tan 55

-in the small right triangle

tan 56 = opp./ adj. = 115 / y-x

y-x = 115/ tan 56 , subtract y from both sides

- x=  -y +( 115/tan 56), multiply by -1 both sides

x= y -(115/tan56), substitute y for 115 * tan 55

x= (115*tan 55)- (115/tan56)

x≅86.6685

Answer:

Obtuse Scalene Triangle

Step-by-step explanation:

Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from angle I, we know the opposite side and the hypotenuse. Therefore, we should use sine.

sin(I) = [tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex]

To solve, you can use your calculator and the inverse sine function (sin^-1).

I = sin^-1([tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex])

I = 61 degrees

Hope this helps!

The function f has a an exponent which is the variable ( the letter x) therefore it is an exponential function.

The base is the number being raised by the exponent ( -1/4)

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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10% of 360 is 18 more than 5% of 360.

The percentage is defined as ratio expressed as a fraction of 100.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given data as :

10% of 360

5% of 360

Firstly, we have to determine 10% of 360,

⇒ 10% of 360

⇒ (10/100)360

⇒ (0.10)360

So, 10% of 360 is 36.

⇒ 5% of 360

⇒ (5/100)360

⇒ (0.05)360

So, 5% of 360 is 18.

Since 10% of 360 is more than 5% of 360

So, substract 18 from 36, and

⇒ 36 - 18

⇒ 18

Hence, 10% of 360 is 18 more than 5% of 360.

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Answer:

Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.