Hi Please I want helpp

The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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Answer:

You can buy 8 pizzas

Step-by-step explanation:

$58 - $10 = $48

$48/$6 = 8

The given function is 6x-2f(x) = 2x-4, find the x- and y-intercepts, the domain, the vertical and horizontal asymptotes, and then sketch and label a complete graph of the function.

The given function is 6x - 2f(x) = 2x - 4.

The function can be rewritten as f(x) = 4x/3 + 2. Let's find the x and y-intercepts, domain, and asymptotes of this function.

X-Intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis.

If we set y = 0 in the equation f(x) = 4x/3 + 2, we get:0 = 4x/3 + 2 ⇒ 4x/3 = -2 ⇒ x = -3/2.

Domain: The domain of a function is the set of all real numbers for which the function is defined. In this case, since the function f(x) = 4x/3 + 2 is defined for all real numbers, the domain of the function is (-∞, ∞).Vertical Asymptote: The vertical asymptote of a function is a vertical line that the graph of the function approaches but never touches.

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If the height of a cylinder is doubled the surface area will not be doubled.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The surface area of a cylinder is expressed by;

A = 2πr(r+h)

Where r is the radius and h is the height.

This means that the surface area of a cylinder is affected both radius and height of the cylinder.

This means that if the height is doubled, the surface area will not be automatically doubled because radius has more effect than the height.

Therefore if height is doubled, the surface area is not necessarily doubled

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Answer:

It is the value of the coin when it was originally purchased. t=0  y=3

Step-by-step explanation:

The y intercept is the value when t=0

It is the value of the coin when it was originally purchased.  y=3

Since each side of the pen is being increased by 4 feet, the total increase in perimeter would be 4 feet multiplied by 4 sides, which equals 16 feet.

To determine how many feet of additional fence Craig should purchase, we need to calculate the increase in the perimeter of the enlarged pen. Therefore, Craig should purchase an additional 16 feet of fence to build his enlarged fence.

The original size of the pen is an 8 by 8 feet square, which means each side measures 8 feet. The perimeter of the original pen is calculated by adding up the lengths of all four sides, so 8 + 8 + 8 + 8 = 32 feet.

To enlarge the pen, Craig decides to increase each side by 4 feet. After the enlargement, each side of the pen would measure 8 + 4 = 12 feet. The perimeter of the enlarged pen is calculated in the same way, by adding up the lengths of all four sides: 12 + 12 + 12 + 12 = 48 feet.

To find the additional fence Craig needs to purchase, we subtract the original perimeter from the enlarged perimeter: 48 feet - 32 feet = 16 feet. Therefore, Craig should purchase an additional 16 feet of fence to build his enlarged fence.

This calculation is based on the assumption that the pen remains a square shape after enlargement. If the shape of the enlarged pen differs from a square, the calculation would vary.

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Answer:

c. (1,-1)

Step-by-step explanation:

5x + 2y = 3  4x – 8y = 12  Solve for (x, y)

4x-8y=12

+8y          +8y

4x=12+8y

Divide both sides by 4

4x/4=(12+8y)/4

x=3+2y

Then take x equation and input into 5x + 2y = 3

5(3+2y)+2y=3

15+10y+2y=3

Add 10y and 2y

15+12y=3

Subtract 15 on both sides

15-15+12y=3-15

12y=-12

Divide 12 both sides

12y÷12=-12÷12

Y = -1

Insert the Y equation into 4x – 8y = 12  

4x-8(-1)=12

4x+8=12

Subtract 8 on both sides

4x-8-8=12-8

4x=4

Divide 4 both sides

4x÷4=4÷4

X = 1

Answer: C. (1, -1)

Answer:

D

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Since angle 11 is next to angle 12, and they should add up to 180 degrees, which makes them supplementary angles.

Answer:

The person above me is right

Answer:

yes

Step-by-step explanation:

because you must find x in order to get y and y in order to get x

Answer:

21,704

Step-by-step explanation:

Find the volume of both the top of the silo (hemisphere) and the end bit of the silo (cylinder)

V = \(\frac{2}{3}\) \(\pi\)\(r^{3}\) is the formula for finding the volume of a hemisphere

V = \(\pi\)\(r^{2}\)h is the formula for finding the volume of a cylinder

Let's find the hemisphere first.

We're using 3.14 for pi, so the equation would look like this

V = \(\frac{2}{3}\) x 3.14 x \(12^{3}\)

V = \(\frac{2}{3}\) x 3.14 x 1728

V = 3617.28 \(ft^{3}\)

Now let's find the volume of the cylinder.

V = 3.14 x \(12^{2}\) x 40

V = 3.14 x 144 x 40

V = 18,086.4 \(ft^{3}\)

Last, you add both volumes together.

3617.28 + 18,086.4 = 21,703.68

Round it to make it 21,704.

The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 .

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

Radius(r) = 12 ft.

Then, the volume of a hemisphere is,

V = 2/3πr³

V = 2/3 x 3.14 x 12³

V = 10851.84 feet³

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder is,

V = πr²h

V = 3.14 x 12² x 40

V = 18095.57

So, the total volume is

V = 10851.84 + 18095.57

V = 28947.41

Then, total volume = total number of cubic feet of grain

Hence, the required answer is, 28947.41 .

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:3/9

Step-by-step explanation:

Answer:6 trays

Step-by-step explanation:

36 people two cupcakes each means 36x2=72

on tray holds 12 cupcakes 72/12=6 trays

Answer:

5

Step-by-step explanation:

x−y=−11, so x = y - 11

y+7=−2x, y + 7 = -2(y - 11)

y + 7 = -2y + 22

3y + 7 = 22

3y = 15

y = 5

Answer:

7 < 8.5 < 9

Step-by-step explanation:

Well < and > mean greater and less than so put it from the smallest to the largest

Answer:

The recipe will make 7.2 quarts of punch.

Step-by-step explanation:

A punch recipe calls for 3 liters of ginger ale and 1.5 liters of tropical fruit juice.

Then the recipe will make 4.5 liters of punch, obtained by the sum of ginger ale and tropical fruit juice.

The ration is the comparison of two quantities and is measured from the division of two values, then: \(\frac{a}{b}\).

The proportion is the equality between two or more ratios. That is, \(\frac{a}{b}=\frac{c}{d}\) equals a proportion.

In this case, being 1 L= 1.6 quarts, you have:

\(\frac{1.6 quarts}{1 L}=\frac{x}{4.5 L}\)

Solving:

\(x=4.5 L*\frac{1.6 quarts}{1 L}\)

x= 7.2 quarts

So, the recipe will make 7.2 quarts of punch.

x^2=-4

x^1=0.778

Step-by-step explanation:

3. Simplify square root Simplify  by finding its prime factors:The prime factorization of  is Write the prime factors:Group the prime factors into pairs and rewrite them in exponent form:Use the rule  to simplify further.

Answer:

turn the fraction into a decimal because it asks for the answer in 2 decimal places

Answer:

a= (bx -b -2c)/ 5x

Step-by-step explanation:

(5a-b)x +b +2c = 0

To find a in terms of c, will isolated a on one side of the equation

5ax -bx +b +2c = 0 , we distribute x in parenthesis

5ax = bx -b -2c , move the terms that do not have a on the other side of the equation with changed sign

a = (bx -b -2c)/ 5x , divide both sides by 5x

Answer: d = 4

Step-by-step explanation:

-24 + 12d = 2(d - 3) + 22

Multiple the 2 with whats in the parentheses

-24 + 12d = 2d - 6 + 22

Subtract both sides by 2d ( 12d - 2d )(2d - 2d is cancelled out)

-24 + 10d = -6 + 46

Add 24 to both side ( 22 + 24 )( -24 + 24 is cancelled out)

10d = -6 + 46

10d = 40 (Add -6 + 46 to get 40)

Divide both sides by 10

b = 4

Andrea's distance from the base of the cliff is given as follows:

233 feet.

The three trigonometric ratios are defined as follows:

For this problem, we have a right triangle in which:

Hence the distance is obtained as follows:

tan(42º) = 209.75/d

d = 209.75/tan(42º)

d = 233 feet.

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The real part of the particular solution to the differential equation is Re(y(t)) = (5 / 106) cos(3t).

We can start by assuming that the particular solution to the differential equation is of the form y = A e^(3it), where A is a complex constant that we need to determine.

We first take the first and second derivatives of y with respect to time:

dy/dt = 3i A e^(3it)

d^2y/dt^2 = -9 A e^(3it)

Substituting these into the differential equation, we get

-27i^2 A e^(3it) + 15i A e^(3it) + 7A e^(3it) = e^(3it)

Simplifying, we get

(-27 + 15i)A e^(3it) + 7A e^(3it) = e^(3it)

Factorizing, we get

(-27 + 15i + 7)A e^(3it) = e^(3it)

Solving for A, we get

A = 1 / (5 - 9i)

To find the real part of y, we can use Euler's formula

e^(3it) = cos(3t) + i sin(3t)

Substituting for A, we get

y = A e^(3it)

y = (1 / (5 - 9i)) (cos(3t) + i sin(3t)) e^(3it)

y = (1 / (5 - 9i)) [(cos(3t) + i sin(3t)) (cos(3t) + i sin(3t))] e^(3it)

y = (1 / (5 - 9i)) [(cos^2(3t) - sin^2(3t)) + 2i sin(3t) cos(3t)] e^(3it)

Taking the real part, we get

Re(y) = (1 / (5 - 9i)) (cos^2(3t) - sin^2(3t))

Re(y) = (1 / (5 - 9i)) (cos(6t))

Re(y) = (5 / 106) cos(3t)

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The given question is incomplete, the complete question is:

Find the real part of the particular solution Find the real part of the particular solution to the differential equation dạy 3 d^2y/dt^2 +5dy/dt + 7y =e^(3it) in the form y=Bcos(3t) + C sin(3t) where B, C are real fractions. = Re(y(t)) = ?

After considering the given data we conclude that the solution on the interval [0, 0.2] is 1.2620

To use the Euler Method to approximate the solution on the interval [0, 0.2] with step size h = 0.1 to four decimal places, we can apply the following steps:
Describe the differential equation and initial condition: \(y' = f(x, y) = 2x + y\), y(0) = 1.
Elaborating the step size h = 0.1 and the number of steps \(n = (0.2 - 0) / h = 2.\)
Initialize the variables: \(x_{0} = 0, y_{0} = 1.\)
For i = 0 to n-1, do the following:
a. Placing the slope at (xi, yi) using f(x, y) = 2x + y: \(k_{1} = f(xi, yi) = 2xi + yi\).
b. Placing the slope at \((xi + h, yi + hk_{1} )\) using \(f(x, y) = 2x + y: k_{2} = f(xi + h, yi + hk_{1} ) = 2(xi + h) + (yi + hk_{1} ).\)
c. Placing the next value of y using the  Euler Method formula: \(yi+1 = yi + h/2(k_{1} + k_{2} ).\)
d. Placing the next value of x: \(xi+1 = xi + h.\)
Rounding the final value of y to four decimal places.
Applying the above steps, we get:
\(x_{0} = 0, y_{0} = 1\)
n = 2
h = 0.1
For i = 0:
\(k1 = f(x_{0} , y_{0} ) = 2(0) + 1 = 1\)
\(k_{2} = f(x_{0} + h, y_{0} + hk_{1} ) = 2(0.1) + (1 + 0.1(1)) = 1.3\)
\(y_{1} = y_{0} + h/2(k_{1} + k_{2} ) = 1 + 0.1/2(1 + 1.3) = 1.115\)
For i = 1:
\(k_{1} = f(x_{1} , y_{1} ) = 2(0.1) + 1.115 = 1.33\)
\(k_{2} = f(x_{1} + h, y_{1} + hk_{1} ) = 2(0.2) + (1.115 + 0.1(1.33)) = 1.7965\)
\(y_{2} = y_{1} + h/2(k_{1} + k_{2}) = 1.115 + 0.1/2(1.33 + 1.7965) = 1.262\)
Hence, the approximate solution of the differential equation \(y' = 2x + y\)on the interval [0, 0.2] with step size h = 0.1 applying  Euler Method is y(0.2) ≈ 1.2620 (rounded to four decimal places).
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Answer:

See below

Step-by-step explanation:

If you consider an open circle, it would exclude the value with which we have circled when writing the inequality. Hence the only possible signs with in such an example can be a greater than sign ( > ) or less than sign ( < );

Let us take a look at an example to help. We are given a graph with an open circle on the number say 3. An arrow extends to the right of this number 3;

\(Inequality Sign - <,\\Inequality - x > 3,\\\)

Hope this helps!

Answer: y-3=3(x+6)

Step-by-step explanation:

(-6,3)      m=3

A line in the point-slope form is expressed as:

  \(y-y_1=m(x-x_1)\\\\x_1=-6\ \ \ \ y_1=3\ \ \ \ m=3\)    

Hence,

y-3=3(x-(-6))

y-3=3(x+6)                      

Answer:

C

Step-by-step explanation:

3³ = 27

(3x²)³ = 27x⁶

(y³)³ = y⁹

(z³)³ = z⁹

ans = (27x⁶y⁹)/z⁹, which is answer C

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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Answer:

Factors and multiples are different things. But they both involve multiplication: Factors are what we can multiply to get the number Multiples are what we get after multiplying the number by an integer

Step-by-step explanation:

By proving the explanation, It is established that a positive integer is expressible as the difference between two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ.

To prove that a positive integer is expressible as the difference of two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ, we will demonstrate two separate cases:

Case 1: If a positive integer is expressible as the difference between two squares of integers, then it is not of form 4n+2.

Assume there exists a positive integer, k, that can be expressed as the difference of two squares of integers, i.e., k = m² - n², where m and n are integers.

We can rewrite the expression as k = (m - n)(m + n).

Now, consider the parity of the terms (m - n) and (m + n).

If both (m - n) and (m + n) are even, then k would be divisible by 4, as it would have a factor of 2 from each term.

In this case, k cannot be of the form 4n+2.

If both (m - n) and (m + n) are odd, then their sum (m - n) + (m + n) would be even. In this case, k cannot be of the form 4n+2.

If one of (m - n) or (m + n) is odd and the other is even, their sum (m - n) + (m + n) would be odd. In this case, k cannot be of the form 4n+2.

Thus, in all cases, if k is expressible as the difference between two squares of integers, it cannot be of form 4n+2.

Case 2: If a positive integer is not of the form 4n+2, then it is expressible as the difference of two squares of integers.

Assume a positive integer, k is not of form 4n+2, where n ∈ ℤ.

Consider the two cases of k being odd or k being even:

If k is odd, we can represent k as k = (k+1)/2 - (k-1)/2.

Both (k+1)/2 and (k-1)/2 are integers, so k can be expressed as the difference between two squares of integers.

If k is even, we can represent k as k = (k/2)²- (k/2 - 1)².

Both (k/2)² and (k/2 - 1)² are squares of integers, so k can be expressed as the difference between two squares of integers.

Therefore, if a positive integer is not of form 4n+2, it is expressible as the difference of two squares of integers.

By proving the above explanation, It is established that a positive integer is expressible as the difference between two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ.

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