prove the following: Theorem 47 A triangle has at most one right angle. In particular, there are no trisquares.

Routh-Hurwitz stability is applied to the system that has been closed with a controller having a constant gain k. If all the coefficients of the first column of the Routh array are positive, the system is stable, and the range of k values required for absolute stability is 2 < k < ∞.

Task 2: Design using Routh-Hurwitz stability

Given, G(s) = K / s(s + 1)(s + 2)

Adding a controller, the transfer function of the closed loop is given by:T(s) = G(s) / [1 + G(s)] = K / [s^3 + 3s^2 + (2 + K)s + K]Applying Routh Hurwitz stability criteria,

[1 2+K K 0]... Eqn (1)

For the system to be stable, all the coefficients of the first column of the Routh array should be positivei. e.

1 > 0, 2 + K > 0 and (2 + K)(K) - K. 0or 2 < K < ∞ for stability.

For a closed-loop system to be stable, it is important to apply a Routh-Hurwitz stability criterion after a controller has been added to the loop transfer function that has constant gain K (G, (s) = K).The transfer function of the closed-loop is given by

T(s) = G(s) / [1 + G(s)] = K / [s^3 + 3s^2 + (2 + K)s + K].

Now apply the Routh Hurwitz stability criteria, [1 2+K K 0]. For the system to be stable, all the coefficients of the first column of the Routh array should be positive, that is

1 > 0, 2 + K > 0, and (2 + K)(K) - K. 0 or 2 < K < ∞ for stability.

The range of k values required for absolute stability of the system that has been closed with a controller having a constant gain k is 2 < k < ∞ if all the coefficients of the first column of the Routh array are positive.

To know more about Routh-Hurwitz stability visit:

brainly.com/question/32532511

#SPJ11

Given:

Compound for an experiment = 4.25 ounces

Compound costs = $2.32 per ounce.

Teacher pays = $10

To find:

The amount of change teacher receive.

Solution:

Cost of 1 ounce of compound = $2.32

Cost of 4.25 ounce of compound = 4.25 × $2.32

                                                        = $9.86

It is given that, the teacher pays with a $10 bill.

Amount of change = $10 - $9.86

                                 = $0.14

Therefore, the teacher receive $0.14 change.

Answer:

yeah im pretty sure you are

Step-by-step explanation:

Answer:

the last one is the correct answer

Step-by-step explanation:

In order for it to be proportional it has to go through the origin (0,0)

Proportional - y=mx

Non Proportional - y=mx+b

Answer:

7.5km/h

Step-by-step explanation:

Given data

Distance= 15km

Time = 2 hours

We know that the expression for the speed is

Speed= distance/time

Substitute

Speed= 15/2

Speed= 7.5 km per hour

Hence the speed is 7.5km/h

The inequality to show the weight limit for the elevator is w < 1,800.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, the sign clearly stated that the total weight in the elevator must be less than 1,800 pounds.

The inequality will be:

w < 1800 where w is the weight.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

Grade g1 = 3.50% Grade g2 = -2.50% Design speed = 65 mph. The minimum length the curve must have, to comply with stopping sight distance requirements? The minimum length the curve must have, to comply with stopping sight distance requirements is 196.5 ft or 59.88 m.

`Stopping Sight Distance (SSD) The stopping sight distance (SSD) is the minimum distance a vehicle operator needs to be able to see ahead of the vehicle to bring it to a stop before colliding with an object in its path.The minimum stopping sight distance is given by the following equation: SSD = 0.278Vt + V^2/254f + 1.47W. Where,SSD = stopping sight distance, Vt = total stopping distance, V = design speed, W = width of traveled way, and f = friction factor.To comply with stopping sight distance requirements, the stopping sight distance (SSD) must be equal to or greater than the minimum SSD. K-tables for 0% can be used to determine the minimum SSD. Minimum SSD = SSD min = K x V. Where, SSD min = minimum stopping sight distance, V = design speed, K = adjustment factor from the table. We need to find the minimum length of the curve that meets the stopping sight distance requirements.Here, it is required to design a curve that is the combination of two tangents with an intersection angle of 60° and a length sufficient to maintain an SSD value equal to or greater than the minimum value.Curve length formula:L = (a+b)/sin(θ/2)Where,L = length of curve, a = length of first tangent, b = length of second tangent, and θ = intersection angle L = (a + b) / sin (θ / 2)L = (V^2 / 254f x (Kg1 + Kg2) ) / sin (θ / 2)Length of first tangent, a = V x (1.47 + 0.278Kg1) Length of second tangent, b = V x (1.47 + 0.278Kg2) Intersection angle θ = 60° Friction factor f = 0.35 (for asphalt surface)The adjustment factor from the table for 0% = 0.03. So, we have:Length of first tangent, a = 1.47 x 65 + 0.278 x 65 x 3.5. Length of first tangent, a = 113.1. Length of second tangent, b = 1.47 x 65 + 0.278 x 65 x (-2.5). Length of second tangent, b = 105.9L = (V^2 / 254f x (Kg1 + Kg2) ) / sin (θ / 2)L = (65^2 / (254 x 0.35 x (0.03 x (3.5 + (-2.5))))) / sin (60 / 2)L = 196.5 ft = 59.88 m.

For more questions on stopping sight distance

https://brainly.com/question/2444691

The final expression for e(x^n) is:
e(x^n) = (b^(2n+1) - a^(2n+1)) / ((n+1)(2n+1)(b^n - a^n))

The expected value of x^n is given by the formula E(x^n) = (b^(n+1) - a^(n+1)) / ((n+1)(b-a)) for a uniform distribution on the interval [a, b]. Therefore, substituting this into the given expression, we have:

e(x^n) (b^n - a^n) / 2(b-a) = [(b^(n+1) - a^(n+1)) / ((n+1)(b-a))] * (b^n - a^n) / 2(b-a)

Simplifying this expression, we can cancel out the (b-a) terms and obtain:

e(x^n) (b^n - a^n) / 2 = (b^(2n+1) - a^(2n+1)) / (2(n+1)(2n+1))

Therefore, the final expression for e(x^n) is:

e(x^n) = (b^(2n+1) - a^(2n+1)) / ((n+1)(2n+1)(b^n - a^n))

To know more about uniform distribution refer here :

https://brainly.com/question/29753583#

#SPJ11

a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)

To divide the polynomial a(x) by b(x), we can use long division as follows:

    3x - 6

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

x² + 2 | 3x² - 4x² + x

- (3x³ + 0x²)

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

-4x² + x

- (-4x² - 8)

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

8x - 8

Therefore, the quotient is 3x - 6, and the remainder is 8x - 8.

a(x) = b(x) * (3x - 6) + (8x - 8)

   -2 | 3 -4  1  0

      |    -6 20 -42

      |-------------

      | 3 -10 21 -42

The numbers on the bottom row represent the coefficients of the quotient, which are 3, -10, 21. The last number on the bottom row, -42, is the remainder. Therefore, the quotient is:

3x² - 10x + 21

8x - 8

a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)

Learn more about Polynomial Division with Remainders here:

https://brainly.com/question/11100304

#SPJ4

Answer: A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If the drive in can only hold 72 cars, the n is all positive integers less than or equal to 72

We would see a logarithmic sequence of values if we plotted the amount of time Edna spends watching TV weekly on a logarithmic scale.

If we plot the amount of time Edna spends watching TV on a logarithmic scale, we would see a continuous sequence of values that increase as her viewing time increases. Specifically, the sequence would be a logarithmic scale of the number of hours she watches TV per week.

On a logarithmic scale, each increment corresponds to a multiplication by a constant value. For example, if we use a logarithmic scale base 10, then each increment of 1 corresponds to a multiplication by 10. So, if we plot Edna's TV watching time on a logarithmic scale, we would see a sequence of values that increase by a factor of 10 as her TV watching time increases by an order of magnitude.

For example, if Edna watches 2 hours of TV per week, the logarithmic value would be log(2) = 0.3. If she watches 7 hours per week, the logarithmic value would be log(7) = 0.85. If she watches 20 hours per week, the logarithmic value would be log(20) = 1.3. As her viewing time increases, the logarithmic values would continue to increase in a continuous sequence.

Therefore, if we plotted the amount of time Edna watches TV each week on a logarithmic scale, we would see a logarithmic sequence of numbers.

To learn more about sequence please click on below link.

https://brainly.com/question/21961097

#SPJ1

The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is  \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

What is a polynomial?

⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.

Calculation;

We have been given two polynomial which we have to add   \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)

The sign after addition or subtraction will always be of the variable having more value.

\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)

On adding like terms with each other

⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)

⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)

Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

Learn more about polynomial here :

brainly.com/question/1487158

#SPJ9

Answer:

91.5

Step-by-step explanation:

If the table is asking for the amount of miles travelled on 3 gallons of gas, you get 3 * 30.5 = 91.5

This is because one gallon gives 30.5 miles and if you have three gallons, you get 30.5 + 30.5 + 30.5 which is the same as 3 * 30.5

Answer:

10 liters

Step-by-step explanation:

x=12% solution, y=16% solution

x+y=40

0.12x+0.16y=6 .   (12x+16x=600)

-12x-12y=-480

      12x+16x=600

+     -12x-12y=-480

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

             4x=120

x=30

12% solution= 30 liters

16% solution= 10 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Let 12% brine solution be x.

Let 16% brine solutions be y.

12% brine solution was mixed with a 16% brine solution to produce 40L of the 15% solution.

This can be written as,

x + y = 40 ______(1)

0.12x + 0.16y = 0.15 x 40

0.12x + 0.16y = 6 _______(2)

We will solve for x and y.

From (1) we get,

x + y = 40

x = 40 - y _____(3)

Putting ( 3) in (2)

0.12 (40 - y) + 0.16y = 6

4.8 - 0.12y + 0.16y = 6

4.8 + 0.04y = 6

0.04y = 6 - 4.8

0.04y = 1.2

y = 1.2/0.04

y = 30

Putting in (3) we get,

x = 40 - 30 = 10

Thus,

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

To know more about Random error,visit;

https://brainly.com/question/14149934

#SPJ1

Answer:

  x = 5

Step-by-step explanation:

You want the equation of a line with undefined slope and an x-intercept of 5.

Slope is the ratio of "rise" to "run" for a line. If the line is vertical, the "run" is zero, making the denominator of the ratio is zero. Division by zero gives an "undefined" result.

If the slope of a line is "undefined", it is a vertical line. It has the same x-value everywhere. Its equation is ...

  x = c . . . . . for some constant

Here, the vertical line crosses the x-axis at x=5. That is the equation of the line:

  x = 5

The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:

1. x - y + z

According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:

2. x + (-y + z)

Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":

3. x + (z + (-y))

Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:

4. (x + z) + (-y)

Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":

5. (x + z) + (-y) = (x - y) + z

Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.

Main Answer:Ramon will need a loan for the remaining $800.

Supporting Question and Answer:

What is the total cost of the 1963 Chevrolet insalainmintcondison that Ramon wants to buy, and how much cash does he have?

The total cost of the 1963 Chevrolet insalainmintcondison that Ramon wants to buy is $10,00.Ramon has 20% of the cash, which amounts to $2,00.

Body of the Solution: To determine the amount of the loan Ramon needs, we first need to calculate how much money has for the purchase.

20% of $10,00=0.20×$10,00=$200

This means that Ramon has $200 in cash to put towards the purchase.To determine the amount of the loan, we can subtract the cash he has from the total price of the 1963 Chevrolet insalainmintcondison:

$10,00-$200=$800

Therefore, Ramon's loan will be for $800.

Final Answer: So,Ramon will need a loan for $800.

Question:Ramon is buying a $10,00,1963 Chevrolet insalainmintcondison. He has 20% of the cash but needs a loan for the remainder. How much will his loan be for?

#SPJ4

Ramon will need a loan of $8,000 to cover the remaining cost of the car.

The principal amount of a loan or deposit made into a person's bank account is referred to as simple interest.

If Ramon has 20% of the cash to buy the car, then he still needs to cover 80% of the cost with a loan.

The loan amount can be calculated as follows:

Loan amount = Total cost of car - Ramon's down payment

Loan amount = $10,000 - 20% of $10,000

Loan amount = $10,000 - $2,000

Loan amount = $8,000

Therefore, Ramon will need a loan of $8,000 to cover the remaining cost of the car.

Learn more about simple interest on:

https://brainly.com/question/1173061

#SPJ4

The critical value of 2.576. If |z| > 2.576, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To test the manufacturer's claim at a 1% significance level, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The medicine is 90% effective in relieving backache.

H₀: p = 0.9

Alternative hypothesis (H₁): The medicine is not 90% effective in relieving backache.

H₁: p ≠ 0.9

Where p represents the true proportion of people who experience relief from backache after taking the medicine.

To conduct the hypothesis test, we will use the sample proportion and perform a z-test.

Calculate the sample proportion:

p = x/n

where x is the number of people who experienced relief (160) and n is the sample size (200).

p= 160/200 = 0.8

Calculate the standard error:

SE = √(p(1 - p)/n)

SE = √((0.8 * (1 - 0.8))/200)

Calculate the test statistic (z-score):

z = (p - p₀) / SE

where p₀ is the hypothesized proportion (0.9 in this case).

z = (0.8 - 0.9) / SE

Determine the critical value for a two-tailed test at a 1% significance level.

Since we have a two-tailed test at a 1% significance level, the critical value will be z* = ±2.576 (obtained from a standard normal distribution table or calculator).

Compare the absolute value of the test statistic to the critical value to make a decision:

If the absolute value of the test statistic is greater than the critical value (|z| > z*), we reject the null hypothesis.

If the absolute value of the test statistic is less than or equal to the critical value (|z| ≤ z*), we fail to reject the null hypothesis.

Substituting the values into the equation, we can determine the test statistic and compare it to the critical value.

For more about critical value:

https://brainly.com/question/32389590

#SPJ4

The given distribution of frequency of yearly income represents a positively skewed distribution.

In a positively skewed distribution, the tail of the distribution extends towards higher values, and the majority of the data is concentrated towards the lower end. This means that there are relatively fewer high-income values and more low-income values in the distribution.

Regarding the effect on the mean, a positively skewed distribution tends to pull the mean towards the higher end of the distribution. This happens because the few higher values have a disproportionate impact on the overall average. As a result, the mean is typically greater than the median in a positively skewed distribution. The presence of extreme high-income values in the distribution can greatly influence and increase the mean value.

To learn more about skewed distribution click here: brainly.com/question/30011644
#SPJ11

Step-by-step explanation:

y=1×3+1=4

y= 2×1+4=6

i hope right answer

Answer:

$24

Step-by-step explanation:

Original price of blouse = $18

Discounted price of blouse = 3/4 x 18 = $13.50

Discounted blouse + discounted skirt = $31.50

⇒  13.50 + discounted skirt = 31.50

⇒  discounted skirt = 31.50 - 13.50 = 18

Let S be the original price of the skirt.

If the discounted skirt is 3/4 of it's original price, then

$18 = (3/4) S

S = 18 ÷ 3/4 = 24

Therefore, the original price of the skirt is $24

Answer:

379-68=p

Step-by-step explanation:

379 is the total number of tissues. If you take away the single pack tissues then you will have the amount of three pack tissues

The correct equation that shows the number of tissue three-packs, p, Johnson's sold in January is, p = 379 - 68.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

At Johnson's Pharmacy, tissue boxes can be purchased as single boxes or in packs of three boxes.

Here, During January, Johnson's sells a total of 379 boxes of tissues, 68 as single boxes, and the rest in three-packs.

Let us assume that, the number of tissue three-packs = p

Hence we get;

p = 379 - 68

p = 311

To learn more about subtraction visit:

https://brainly.com/question/17301989

#SPJ7

Answer:

2

\(2 \times area \div height \:\)

Step-by-step explanation:

the answer is 5

Answer:

JH=16

Step-by-step explanation:

Hi there!

We are given ΔHIJ, where HI is parallel to KL, and that JK=10, JI=40, and JL=25

We want to find JH

We can use something called the Triangle Proportionality Theorem to help us find JH

The Triangle Proportionality Theorem essentially states that if there is a line parallel to one of the sides of a triangle that intersects the other 2 sides of that triangle, then that segment divides those sides proportionally

In other words, KL is parallel to HI and intersects both HJ and JI, and JK, JH, JL, and JI create a proportion, which is \(\frac{JK}{JH} =\frac{JL}{JI}\)

We can substitute the values that we know into that equation

\(\frac{10}{JH} =\frac{25}{40}\)

We can simplify 25/40 to 5/8.

\(\frac{10}{JH} =\frac{5}{8}\)

Now we can cross multiply (use the means-extreme theorem)

Multiply 10 and 8 together, and set that equal to 5 times JH

80 = 5JH
Divide both sides by 5

16=JH
Hope this helps!
See more on the Triangle Proportionally Theorem here: https://brainly.com/question/20064024

option (A) cy + b/a is the main answer.

The given expression ax - b = cy is an equation with one variable 'x.'

We need to find the value of x. The steps to solve the equation are given below:

Solve for x:Adding 'b' to both sides,ax = cy + b.

Divide both sides by 'a,'x = (cy + b) / a.\

Therefore, option (A) cy + b/a is the main answer.

Therefore, we can conclude that the result of solving the equation ax - b = cy for x is x = (cy + b) / a, and the main answer is option (A) cy + b/a.

To know more about variable visit:

brainly.com/question/15078630

#SPJ11

Answer:

420 pieces

Step-by-step explanation:

area of each piece of sod =1x1 =1 \(ft^{2}\)

area iof yard = 30x14=420 \(ft^{2}\)

number of pieces of sod needed= 420/1=420

The derivative of a function y is denoted by y' and is the measure of the rate of change of the function y with respect to its independent variable x. To find the derivative of y, we must first identify the function y. In this case, y is a function of x.

Using the power rule, the derivative of y with respect to x is found by taking the exponent of the function (the exponent of x) and subtracting 1. The resulting coefficient is then multiplied by the original function, with the new exponent. For example, the derivative of y = x3 is 3x2.

The chain rule is also used when deriving a function. The chain rule states that the derivative of a composite function can be found by taking the derivative of the inner function, multiplying it by the derivative of the outer function, and then adding them together. For example, if y = (3x2 + 5)2, then the derivative of y is 12x(3x2 + 5).

Therefore, to answer the question, the derivative of y is y' = 3x2.

To know more about function refer here:

https://brainly.com/question/28193995

#SPJ11