Find the transfer function from a reference input θr to the Hapkit output θ for the closed-loop system when the Hapkit (the plant) is placed in a unity gain negative feedback with a PID controller. How many poles does the closed loop system have?

By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.

In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:

Since PQ ǁ RS, PT = 16

PT/RP = QT/SQ

16/4 = 20/SQ

Cross-multiplying, we have:

16SQ = 20 × 4

SQ = 80/16

SQ = 5 cm.

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Complete Question:

In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?

The length of the hypotenuse of the isosceles triangle is 7.1 units.

We can use the distance formula to find the length of ST (base) and TU(perpendicular). Further, using these lengths, we can find the hypotenuse of the isosceles triangle.

The distance formula is given as follows,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Here, d is the distance between the two points (x₁, y₁) and (x₂, y₂)

As shown in the drawn isosceles triangle STU,

The length of the base ST is given as,

ST = √(x₂ - x₁)² + (y₂ - y₁)²

Here,

x₁ = 1 and y₁ = 1

x₂ = 6 and y₂ = 1

∴ ST = √(6-1)² + (1-1)²

ST = √5²

ST = 5 units

Similarly, for TU as the other leg passes through the point(6,2) and is of length 5 units ( STU being isosceles triangle), we have,

x₁ = 6 and y₁ = 1

x₂ = 6 and y₂ = 6

Also, TU = 5 units

Now, using Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

(SU)² = (ST)² + (TU)²

(SU)² = (5)² + (5)²

(SU)² = 50

SU = √50

SU = 7.071 units

SU ≈ 7.1 units (after rounding of to the nearest tenth)

hence, the hypotenuse of the isosceles triangle is of 7.1 units.

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Answer:

- 4/7 , -1/9, 7/4

Step-by-step explanation:

You know that 7/4 is the largest number because it is the only positive number.  To compare the two negative numbers you need common denominators.  The common denominator would be 133 (19 x 7).  Now make equivalent fractions.-4/7 = x/133  133 divided by 7 is 19.  Multiple the -4 by 19 to get -76/133.  Next, make an equivalent fraction for -1/19.  The new denominator will be 133.  If I divide 133 by 19, I will get 7, so I multiple -1x7 and get -7 and the new fraction -7/133.

I have two fractions to compare -7/133 and -76/133.  -76/133 if farthest from 0 so it has the least value.

Answer:

26

Step-by-step explanation:

You want to know the value of x that makes y=1000. You can plug the equation in to your calculator or desmos. Look at the table for when y=1000. X is 26.

To check, plug in 26 for x. 26^2 + 20(26) - 196 = 1000.

Answer: 26 sales

Step-by-step explanation:

Using the laws of indices , 4⁵ ÷ 4² can rewritten as 4³.

Given the expression; 4⁵ ÷ 4²

To perform the division operation, we use one of the laws of indices;

[tex]n^a/n^b = n^{a-b}[/tex]

Given that;

Now, we apply the laws of indices ;

4⁵ ÷ 4² = 4⁵⁻² = 4³

Therefore, using the laws of indices, 4⁵ ÷ 4² can rewritten as 4³.

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The statement (inequality) which best describes all possible values of m is: -12 < m < 4.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

The table indicates two local extremes or potential turning points at x = 1 and x = -1. Thus, the value of m can't exceed f(-3) = -12.

In conclusion, the statement (inequality) which best describes all possible values of m is: -12 < m < 4.

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Answer:

Math = 97

English = 66

Step-by-step explanation:

Let the score of the Math test be x, and the score of the English text be y

Then we have the two equations

[tex]x+y = 163\\x-y = 31[/tex]

To solve for x and y there are multiple ways, one of the easy ways is just to add the two equations together because that would cancel out the y:

[tex]x + x + y -y = 163 +31\\2x = 194\\x = 97\\[/tex]

Then using the  x, we can find y by doing

[tex]x+y = 163\\97 + y = 163\\(97 + y) - 97 = (163) - 97\\y = 66[/tex]

Therefore, we have a math score of 97, and an English score of 66.

The equation will be like this,

6.89 + t = 8.00

t = 8 - 6.89

t = 1.11

tips = $1.11

6.89 + t = 8.00

To sum up the total amount of cash and coins you have, first, sort each invoice and coin by denomination. Create a separate stack for each denomination and count how many denominations or coins you have.

For each denomination of banknotes and coins, multiply the number you have by the denomination. For example, if you have 4 out of $ 10, multiply by 4x10 to get $ 40. If you have three $ 5 bills, multiply by 3x5 to get $ 15.

Sum the totals to calculate the total amount.

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I'm guessing the equation should read something like

[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]

or possibly with minus signs in place of +.

Multiply both sides by [tex]\frac1{x^2}[/tex] to get

[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]

Now substitute

[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]

to transform the equation to

[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]

which simplifies to

[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]

The ODE is now separable.

[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]

Integrate both sides. On the left, substitute

[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]

[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]

[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]

[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex].

[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]

[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]

[tex]w^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]v[/tex].

[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]

Put this back in terms of [tex]y[/tex].

[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]

Solve for [tex]y[/tex].

[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]

[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]

[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]

[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]

Using the t-distribution, it is found that there is not enough evidence that the diet is helping people lose weight.

At the null hypothesis, it is tested if the mean hasn't decreased, that is:

[tex]H_0: \mu_B \leq \mu_A[/tex]

[tex]H_0: \mu_B - \mu_A \leq 0[qtex]

At the alternative hypothesis, it is tested if the mean has decreased, that is:

[tex]H_1: \mu_B - \mu_A > 0[qtex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are:

The test statistic is:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{9.88 - 0}{11.66}[/tex]

t = 0.85.

Considering a right-tailed test with 9 + 9 - 2 = 16 df, with a standard significance level of 0.05, the critical value is t = 1.7459. Since t = 0.85 < 0.85, there is not enough evidence that the diet is helping people lose weight.

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Answer:

A

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then

[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8

Answer:

A

Step-by-step explanation:

loga(b)=x

a^x=b

since the answer to log2(8)=3

a^3=8

b=8

a=2

so 2^3=8

I hope this helped!

Answer:

[tex]y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]

Step-by-step explanation:

To make y subject of formular, we place y in terms of other variables.

[tex] A = \pi \: x {}^{2} - \pi \: y {}^{2} \\ making \: y \: subject \\ A + \pi \: y {}^{2} = \pi \: x {}^{2} \\ \pi \: y {}^{2} = \pi \: x {}^{2} - A \\ Dividing \: bothsides \: by \: \pi \\ y {}^{2} = \frac{\pi \: x { - A}^{} }{\pi} \\ Squarerooting \: bothsides \\ y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]

Answer:

20

Steps-by-step explanation:

sorry mistake

Answer:

12

Explanation: I just counted them! :) and there was 6 in the middle and on the outside so 6 + 6 = 12! :)

The transformation for circle 1 exists (x+9), (y+5) and the scale factor of circle 1 exists 2.

Scale exists described as the ratio of the length of any object on a model to the actual length of the exact object in the entire world.

The function transformation rules: f(x)+b changes the function b units upward. f(x)−b shifts the function b units downward. f(x + b) shifts the function b units to the left.

Circle 1

center: (−4, −2)

Radius: 3 centimeters

Circle 2

center: (5, 3)

Radius: 6 centimeters

Transformations can be used to circle 1 to verify that the circles exist similar.

As circle 2 and circle 1 do not contain the exact coordinates

So, circle 1 has to utilize transformation rules.

The difference between the coordinates of circle 2 and circle 1 exists

[tex]$x_2 - x_1 = 5 - (-4 ) = 9[/tex]

[tex]y_2 - y_1 = 3 - (-2) = 5[/tex]

Therefore, transformation for circle 1: (x+9), (y + 5)

The scale factor between circle 2 and circle 1 exists

The radius of Circle 2 = 2 [tex]*[/tex] radius of circle 1

Therefore, the scale factor of circle 1 = 2

Therefore, the transformation for circle 1 exists (x+9), (y+5), and the scale factor of circle 1 exists 2.

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Answer:

A:(1/3x)+(x-2/4x^2+9)

Step-by-step explanation:

Edg2022

Answer:

α = αG − αZL

thos is the equation for the absoulute angle of attack

Given that (p - 1/p) = 4, the value of p² + 1/p² is 18. Detail below

(p - 1/p) = 4

Square both sides

(p - 1/p)² = (4)²

(p - 1/p)² = 16 ....(1)

Recall

(a - b)² = a² + b² - 2ab

Thus,

(p - 1/p)² = p² + 1/p² - (2 × p × 1/p)

(p - 1/p)² = p² + 1/p² - 2

From equation (1) above,

(p - 1/p)² = 16

Therefore,

p² + 1/p² - 2 = 16

Rearrange

p² + 1/p² = 16 + 2

p² + 1/p² = 18

Thus, the value of p² + 1/p² is 18

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The illustration to determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence is given below.

Congruence of triangles means that two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In this case, these triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

To illustrate the question, this will be:

Step 1: Draw  a line segment AB

Step 2:Draw an acute angle (let's say 45° ) at A  as AX

Step 3: From B draw an altitude on AX     BY ⊥ AX

Step 4  Using suitable compass width and taking  Y as center cut AX  on both sides  at C and D

Now BC = BD   as  BY is perpendicular bisector

Now compare ΔABC and ΔABD. Using suitable compass width and taking B as center cut AX at 2 points C & D  directly  so BC = BD.

This can illustrate that SSA is not a valid  means for establishing triangle congruence.

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Answer:

Below is an example to show whether side-side-angle (SSA) is a legitimate method for proving triangle congruence. How should the information be illustrated? Triangle congruence refers to the property that two triangles are congruent if their three corresponding sides and their three corresponding angles are both equal in size. In this instance, the triangles can be moved around, rotated, flipped, and turned to have a same appearance. They are in alignment with one another when moved. This can serve as an example of why SSA cannot be used to prove triangle congruence.

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

Opposite angles of a rhombus are congruent, so

[tex]5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18[/tex]

The distance between the helicopter and the first home is 369. 87 m

The distance between the helicopter and the first home can be found using sine law,

Hence,

180 - 72 - 49 = 59 degrees.

Therefore,

420 / sin 59 = A / sin 49°

where

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

Therefore, the distance between the helicopter and the first home is 369. 87 m

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The expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

The given parameters are:

Initial value, a = 33741  

Rate, r = 2.8%

The cost of tuition each year since 2015 is represented as

B(x) = a * (1 + r)^x

This gives

B(x) = 33741 * (1 + 2.8%)^x

Evaluate

b(x) = 33741 * (1.028)^x

Hence, the expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

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Complete question

A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.

Find the expression that completes the function b(x)​

The equation of the parallel line is  2y-x=-7

A parallel line will have the same slope, but different intercept. Let's assume C in the intercept of this parallel line. Therefore, equation of the parallel would be,

2y-x=C, coefficients of x and y remain the same, since parallel lines.

This line passes through (3, -2). Therefore, substituting those values, we will get value of C.

2.(-2) -3=C

C=(-7)

The equation of the parallel line is therefore 2y-x=-7

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By critically observing and comparing the functions for the given graphs, we can logically deduce that the widest graph is: "Function 1: y = 0.25x²."

In Geometry, a graph which has the smallest positive coefficient of x² in absolute value is generally considered as the widest graph while the graph with the largest positive coefficient of x² in absolute value is the narrowest graph.

By critically observing and comparing the functions for the given graphs, we can logically deduce that "Function 1: y = 0.25x²" is the widest.

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Complete Question:

Compare the graphs of the functions listed below.

Function 1: y = 0.25x²

Function 2: y = 4x²

Function 3: y = -½x²

Function 4: y = -16x²

The graph of ______ is the widest?

No this does not indicate that the population proportion of women athletes who graduate from the university is now less than 67%.

Given long term graduation rate of 67%, sample size of 36  and the women athletes graduated is 23.

We have to find whether  the given information shows  that the population proportion is less than 67%.

First we have to create hypothesis for this :

[tex]H_{0}[/tex]:P=0.67

[tex]H_{1}[/tex]:P<0.67

Under null hypothesis the test statistic is

z=p bar-p/[tex]\sqrt{p(1-p)/n}[/tex]

where p bar=23/36

=0.638

z=(0.638-0.67)/[tex]\sqrt{0.67(1-0.67)/36[/tex]

=-0.032/[tex]\sqrt{0.67*0.33/36}[/tex]

=-0.032/[tex]\sqrt{0.0064}[/tex]

=-0.032/0.078

=-0.41

Now we have to find the left tailed critical at 0.01 significance level using z table.

z=-2.33

Since the z value does not fall in the critical region,therefore we fail to reject the null hypothesis. So we can conclude that there is not sufficient evidence to say that the population proportion of women athletes who graduate from the university is now less than 67%.

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Question is incomplete as it should specify the signficance level of 0.01 to be used.

v = 1.21 m/s is the answer

Kinetic energy of object = 25 J

Mass of object = 34 kg

The formula for the kinetic energy of an object is given by

K.E. = 1/2 m v2.

25 =  1/2 *34* v2.

v2= 25/17

v2 = 1.47

v = 1.21 m/s

In physics, the kinetic energy of an object is the energy that the object has due to its motion. This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, it retains this kinetic energy unless the velocity changes

Everything that moves at home is an example of kinetic energy. This could be a cue ball rolling on a pool table, a fan that circulates air on warm days, or a glass that shatters on the floor after falling off the counter. Electrical equipment that is turned on uses kinetic energy, much like people move around the house.

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Answer:

$127.50

Step-by-step explanation:

The average profit is found by adding up the profits from both scenarios.

39(4.5) + 1(-48)

= $127.50

Brainliest, please :)

The option which makes more sense for Jake to choose is option (1) He can accept the tie, and the game is over.

The complete question is added as an attachment

From the complete question, the probability in part D is

Probability = 33.5%

The options to choose one from are:

The calculated probability is less than 0.5.

This means that Jake is more likely to lose than win

So, the best option for Jake is option (A) walk away

Hence, the option which makes more sense for Jake to choose is option (1) He can accept the tie, and the game is over.

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Answer:

L (1, - 7 )

Step-by-step explanation:

give endpoints (x₁, y₁ ( and (x₂, y₂ )  then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = K (9, - 7 ) and (x₂, y₂ ) = L (x, y )

use the midpoint formula and equate to corresponding coordinates of M

[tex]\frac{9+x}{2}[/tex] = 5 ( multiply both sides by 2 to clear the fraction )

9 + x = 10 ( subtract 9 from both sides )

x = 1

and

[tex]\frac{-7+y}{2}[/tex] = - 7 ( multiply both sides by 2 )

- 7 + y = - 14 ( add 7 to both sides )

y = - 7

Then L  = (1, - 7 )

Two possibilities  --- see below

Step-by-step explanation:

So it could be GREATER than 46

  .85 x = 46    x = 54.11 cm^3

Or it could be  smaller than 46

  46= (1.15)  x      x = 40 cm^3