**Suppose the unit step response of a feedback control system is given as \( y(t)=\left(0.8-e^{-t}(0.8 \cos (t)-3 \sin (t))\right) u(t) \). Answer the following five questions(Q1-Q6). Q1. The first ov

Answer:

351/1000

Step-by-step explanation:

Answer:

351/1000

Step-by-step explanation:

Step 1:

0.351 ÷ 1000

Answer:

351/1000

Hope This Helps :)

The double integral for calculating the flux of a vector field F through an open-ended circular cylinder of radius r and height h, with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis, is given by the expression ∫∫(F · n) r dr dθ, where n is the outward unit normal to the cylindrical surface S and the integration is over the cylindrical surface S.

Let F be the vector field and let S be the open-ended circular cylinder of radius r and height h, with its base on the xy-plane and centered about the positive z-axis. We want to calculate the flux of F through S, oriented away from the z-axis.

To set up the double integral for calculating the flux, we use the divergence theorem:

flux = ∫∫(F · n) dS = ∭(div F) dV

where n is the outward unit normal to the surface S, dS is the surface area element, dV is the volume element, and div F is the divergence of F.

Since S is a cylindrical surface, we can use cylindrical coordinates (r, θ, z) to parameterize the surface and the volume enclosed by S. Specifically, we have:

r ≤ r

0 ≤ θ ≤ 2π

0 ≤ z ≤ h

Then, the double integral for calculating the flux is:

flux = ∫∫(F · n) dS = ∬(F · n) r dr dθ

where n = (cos θ, sin θ, 0) is the outward unit normal to the cylindrical surface S.

Note that we do not need to integrate over the z-variable, since the cylindrical surface is orthogonal to the z-axis, and the divergence of F may not depend on z.

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The missing angle in the triangle is as follows:

m∠ABC = 54 degrees

When lines segment intersect, angle relationships are formed such as vertically opposite angles,  adjacent angles etc.

Therefore, let's find m∠ABC.

Hence,

9x - 9 + 3x + 9 = 180 (sum of angles on a straight line)

12x  = 180

divide both sides of the equation by 12

x = 180 / 12

x = 15

Therefore,

m∠ABC = 3x + 9(Vertically opposite angles)

m∠ABC = 3(15) + 9

m∠ABC = 45 + 9

m∠ABC = 54 degrees

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The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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The upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control is 1.008.

For a process with a normal distribution, the mean of the sample means is equal to the population mean and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size. In this case, the mean of the output is 1.0 liter and the standard deviation is 0.01 liter, so the standard deviation of the sample means is 0.01 / √25 = 0.002.

To construct a control chart for the sample means, we need to determine the upper and lower control limits such that the process is in control when the sample means fall within these limits. Assuming the process is in control, we want to find the upper limit such that roughly 97% of the sample means fall below this limit.

Using the standard normal distribution, the Z-score corresponding to the 97th percentile is approximately 1.88.

Therefore, the upper control limit is 1.0 + 1.88(0.002) = 1.008. Any sample mean above this limit should be investigated for potential process issues.

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When an auditor has performed a test of details during an audit and established that the sample results prove that the recorded account balance was materially misstated while in reality, it was not materially misstated, it illustrates sampling risk.

What is sampling risk?

Sampling risk refers to the likelihood of selecting sample data that are not indicative of the actual data population. It's a danger that arises because the auditor only audits a small portion of the population, which may or may not be representative of the whole population.

To summarize, the scenario presented in the problem statement is an instance of sampling risk.

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The curve is given by \(x = y^2,\)so we can express the integral as:

\(∫c x^3 y^4 dx = ∫c (y^2)^3 y^4 dx = ∫c y^10 dx\)

To find the limits of integration, we need to determine the values of y for the endpoints of the curve. At the starting point (0, 0), we have y = 0, and at the endpoint (4, 2), we have y = 2^(1/2). Therefore, the integral becomes:

\(∫c x^3 y^4 dx = ∫0^(2^(1/2)) y^10 dx = [1/11 y^11]_0^(2^(1/2)) =\)\(2^(11/2) / 11\)

Therefore, the value of the integral is \(2^(11/2) / 11\)

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Answer:

465.75

Step-by-step explanation:

If you do the math and divide 31,671 by 68, your answer should be:

465.75

Hope this helps :)

Answer:

51

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

because you basically divided by two on

Answer:

1/4 is the answer mark me brainliest

Answer:

if he can work 15 hours and must make at least 160 dollars, he'll need to work 8 hours lifeguarding and 7 hours washing cars

Step-by-step explanation:

13 x 8 = 104

8 x 7 =56

when added we get 160, and the hours are exactly 15

x + y ≤ 15

13x + 8y = 160

Answer:

Box 1: 38

Box 2: 72

Box 3: 110

Step-by-step explanation:

Add both numbers in each row up

The last box is 110 because it is the total number of students asked.

Answer:

b=− 3/4 =−1.333

b= 2/3=1.500

explanation

middle term, which is   -1 .  

     -72    +    1    =    -71

     -36    +    2    =    -34

     -24    +    3    =    -21

     -18    +    4    =    -14

     -12    +    6    =    -6

     -9    +    8    =    -1    That's it

Two real solutions:

b =(1+√289)/12=(1+17)/12= 1.500

or:

b =(1-√289)/12=(1-17)/12= -1.333

Daniella's graph is the first from the left and Kayla's is the other. Kayla's walk can be represented as ; d = 2t

Given that after 3 seconds:

This shows that the speed at which Daniela walked is faster than that of Kayla. Hence, the line with the steepest slope represents Daniela's movement.

Hence, Daniela's graph is the first from the left while Kayla's is the other.

2.)

Kayla's walk can be expressed mathematically as :

d = 6 feets ; t = 3 seconds

Walking speed = distance/ time

Walking speed = 6/3 = 2 ft/sec

Hence, Kayla's walk ;

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Answer:

IV QUADRANT

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Calculate the slopes between pairs of the 3 points using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)

m = \(\frac{9-3}{-3-(-9)}\) = \(\frac{6}{-3+9}\) = \(\frac{6}{6}\) = 1

Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)

m = \(\frac{9-1}{-3-5}\) = \(\frac{8}{-8}\) = - 1

If lines are perpendicular then the product of their slopes = - 1 , then

1 × - 1 = -1

Thus there is a right angle between the 2 lines

Then triangle is right- angled

We can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

To determine how many guests can be expected to receive free admission, we need to use the given information about the ratio of guests with coupons to guests without coupons. We can do this by setting up a proportion and solving for the unknown variable.

Let x be the number of guests we can expect to receive free admission.
1/50 = x/1500

Cross-multiplying gives us:
50x = 1500

Dividing both sides by 50 gives us:
x = 30

Therefore, we can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

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Answer: 3 centimeters equals 12 meters

Hope this helps!

Answer:

Three centimeters represent 12 meters.

Step-by-step explanation:

Answer:

9h=42-24 so it is 2 hours

Step-by-step explanation:

9h for 9 problems per hour. Also 42-24 because she had that much left to do.

Answer:

D

Step-by-step explanation:

What you need to apply there is basically 3D Pythagoras which goes like r=

\( \sqrt{23 { }^{2} + 10 { }^{2} + 15 {}^{2} } \)

then punching on the calculator, the answer will be 29. 22 in

Answer:

D 29.2 I am pretty sure that is the right one so if it not sorry

Answer:

C) 32 * 2**1/2

Step-by-step explanation:

For rectangle P = L + W = 24 but L = 2W so

2W + W = 24

3W = 24

W = 8 and L = 2W = 16

A = L * W = 16 * 8 = 128

SO for the square with the same area

A = L * L = 128

L**2 = 128

L = 8 * 2**1/2

P = 4L = 32 * 2**1/2

Answer:

Step-by-step explanation:

SecA - TanA

= 1/CosA - SinA/CosA

= 1 - SinA/CosA

We know that Sin2A = 2SinACosA  and Cos2A = Cos²A - Sin²A

Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2

       CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2

Now substituting the values back,

=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

// we know that Sin²θ + Cos²θ = 1

=> Sin²(A/2) + Cos²A/2 -  2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)

//We know that numerator is of form a² + b² - 2ab which is (a - b)².

//Similarly denominator is of form a² - b² which is (a - b)(a + b)

=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)]² /  [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]

=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]

= R.H.S

Hence proved.

Using the Laplace transforms the solution is y(t) = (15÷16)cos(4t) + (5÷16)tsin(4t) - (1÷32)sin(4t), where y(0) = 3 and y'(0) = 2.

To solve the given initial-value problem using Laplace transforms, we first take the Laplace transform of both sides of the differential equation:

L{y''(t)} + 16L{y(t)} = L{cos(4t)}

Using the property L{f'(t)} = sL{f(s)} - f(0), where f(0) is the initial value of f(t), and the fact that y(0) = 3 and y'(0) = 2, we have:

s² Y(s) - s y(0) - y'(0) + 16 Y(s) = L{cos(4t)}

Substituting y(0) = 3 and y'(0) = 2, and using the Laplace transform of cos(4t) from the table in Appendix III (L{cos(4t)} = s ÷ (s² + 16)), we obtain:

s² Y(s) - 3s - 2 + 16 Y(s) = s ÷ (s² + 16)

Simplifying and solving for Y(s), we get:

Y(s) = (s + 4)÷(s² + 16)²

Now we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t). We can use partial fraction decomposition and the Laplace transform table to obtain:

Y(s) = (s + 4)÷(s² + 16)² = A÷(s² + 16) + B÷(s² + 16)²

Multiplying both sides by (s² + 16)² and equating the numerators, we get:

s + 4 = A(s² + 16) + B

Setting s = 0, we get:

4 = 16A + B

Setting s = 4i, we get:

4i + 4 = -16B÷(16i)²

B = i÷8

Substituting B into the equation 4 = 16A + B, we get:

A = 15÷16

Therefore, we have:

Y(s) = 15÷(16(s² + 16)) + i÷(8(s² + 16)²)

Using the Laplace transform table, we can find the inverse Laplace transform of each term. The solution is:

y(t) = (15÷16)cos(4t) + (5÷16)tsin(4t) - (1÷32)sin(4t)

Therefore, the solution to the given initial-value problem is y(t) = (15÷16)cos(4t) + (5÷16)tsin(4t) - (1÷32)sin(4t), where y(0) = 3 and y'(0) = 2.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

The matrix A of T is:

A = [[5, 3], [-5, 1]]

We know that a linear transformation is completely determined by its action on the basis vectors. In this case, we are given the images of the standard basis vectors [1, 0] and [0, 1].

The matrix A of the linear transformation T is given by:

A = [T([1, 0]), T([0, 1])]

So we just need to compute T([1, 0]) and T([0, 1]).

Using the linearity of T, we have:

T([1, 0]) = T(1*[1, 0] + 0*[0, 1]) = 1T([1, 0]) + 0T([0, 1])

= [5, -5]

and

T([0, 1]) = T(0*[1, 0] + 1*[0, 1]) = 0T([1, 0]) + 1T([0, 1])

= [3, 1]

Therefore, the matrix A of T is:

A = [[5, 3], [-5, 1]]

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The solutions using laws of exponents are:

a) \((4x)^{\frac{3}{2} }\)= \(8 \sqrt[]{x^{3} }\)

b) \(x^{\frac{-2}{3}}\)\(= \sqrt[3]{x^{2} }\)

d) \(\frac{\sqrt[3]{x} }{\sqrt{x} }\)\(=\)  \(\sqrt[3]{x^{2} }\)

e) \(\frac{\sqrt{x} * x^{2} }{{x^{\frac{5}{2} } } }\)= 1

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

a) \((4x)^{\frac{3}{2} }\)

Using laws of exponents, the bracket is simplified to get:

\(4^{\frac{3}{2}} * x^{\frac{3}{2}}\)

= \(8 \sqrt[]{x^{3} }\)

b) The expression we want to solve is given as:

\(x^{\frac{-2}{3}}\)

This simplifies to get:

\(\sqrt[3]{x^{2} }\)

d) The expression we want to solve is given as:

\(\frac{\sqrt[3]{x} }{\sqrt{x} }\)

This simplifies to get:

\(x^{\frac{-2}{3}}\) = \(\sqrt[3]{x^{2} }\)

e) The expression we want to solve is given as:

\(\frac{\sqrt{x} * x^{2} }{{x^{\frac{5}{2} } } }\)

This simplifies to get:

\(\frac{{x^{\frac{5}{2} } } }{{x^{\frac{5}{2} } } }\)

= 1

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Answer:

little falls has more

Step-by-step explanation:

show your work: little falls total rainfall is 1 6/8 and riverside is 1 5/8

use that to explain :) your welcome

Answer:

  Riverside had the greatest rainfall total

Step-by-step explanation:

The total amount of rain in a city will be the sum of products of rain amount and days that got that amount. The city with the largest sum got the most rain. The difference in rainfall can be found by subtracting the lesser amount from the greater.

__

Total rainfall in Riverside was ...

  (1/8)×1 +(2/8)×3 +(3/8)×3 +(4/8)×1 +(5/8)×1

  = (1 +6 +9 +4 +5)/8 = 25/8 = 3 1/8 . . . . inches

__

Total rainfall in Little Falls was ...

  (1/8)×1 +(3/8)×1 +(4/8)×1 +(6/8)×2

  = (1 +3 +4 +12)/8 = 20/8 = 2 1/2 . . . . inches

__

Riverside had more rainfall, because 3 1/8 is more than 2 1/2.

__

You can "cancel" dots that are in the same place on each plot. Doing so leaves Riverside with 3 dots at 2/8, 2 dots at 3/8, and 1 dot at 5/8. The remaining dots on the Little Falls plot are the 2 dots at 6/8.

The 3 dots at 2/8 add up to 6/8, as do the 2 dots at 3/8 on the Riverside plot. These two 6/8 values cancel the two 6/8 dots on the Little Falls plot. That leaves one uncancelled dot at 5/8 on the Riverside plot, indicating more rain fell at Riverside.

Answer:

288 inches

Step-by-step explanation:

Just do 24 x 12 you will get the answer since 1ft=12 inches!

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Answer:

∠ SRT = 55°

Step-by-step explanation:

angles on the circle ( inscribed angles ) from the same chord are equal.

∠ SRT and ∠ SVT are inscribed angles from the same chord ST , then

∠ SRT = ∠ SVT = 55°

The charges by both streaming services are illustrations of linear functions

Service 1 charges more for 8 extra channels, than service 2

Let x represents the number of extra channels, and y represents the cost.

For service 1, we have:

$20 service fee plus $8 for each extra channel

So, the linear equation that represents this service is:

\(y = 20 + 8x\)

For service 2, we have:

$45 service fee plus $3 for each extra channel

So, the linear equation that represents this service is:

\(y = 45 + 3x\)

For extra 8 channels, the total charges of service 1 is:

\(y = 20+ 8 \times 8\)

\(y = 84\)

For extra 8 channels, the total charges of service 2 is:

\(y = 45 + 3 \times 8\)

\(y = 69\)

By comparison, 84 > 69

Hence, service 1 charges more for 8 extra channels, than service 2

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