the model airplane is 30 feet above the ground.



Write an integer to represent the situation.

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

4 ft/min

Step-by-step explanation:

I'm sorry no one has helped you in 40 minutes, so let me.

Theres a fun trick when it comes to saying something 'per' something;

as you can look at the word per as a fancy word for divide.

So if I have Xylophones per Megaphone then I'm basically saying:

Xylophones divided by megaphones

So in this case its 10 feet per 2 1/2 minutes and we'd understand it as 10/2.5

Lets show this

10 ft per 2 1/2 minutes = 10/2.5 ft/min = 4 ft/min

Hope this helps :)

For the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, P equals atmospheric pressure (atm), V equals liters of volume (L), n equals the number of moles, R is the gas constant (0.0821 Latm/(molK)), and T equals Kelvins of temperature (K).

Take into account the following circumstances: a 3,500 mL tank containing 27 moles of argon gas was pressurized to 12 atm.

The ideal gas equation is,

PV=nRT

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, for the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

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The probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

The probability of rain on any given day is 0.66.

To find the probability that it will rain on exactly one of the seven days the Hiking Club is there, we can use the binomial probability formula.

The binomial probability formula is

\(P(x) = C(n, x) * p^x * (1-p)^{(n-x)}\),

where:

P(x) is the probability of exactly x successes,

C(n, x) is the combination formula, which calculates the number of ways to choose x successes from n trials,

p is the probability of success on a single trial, and

n is the total number of trials.

In this case, we want to find the probability of rain on exactly one day out of the seven days.

So, x = 1,

n = 7, and

p = 0.66.

Using the combination formula,

C(n, x) = n! / (x! * (n-x)!),

we can calculate

C(7, 1) = 7! / (1! * (7-1)!)

C(7, 1) = 7.

Plugging the values into the binomial probability formula, we get:

\(P(1) = C(7, 1) * 0.66^1 * (1-0.66)^{(7-1)}\)

\(= 7 * 0.66^1 * 0.34^6\)

Calculating this expression, we find that P(1) is approximately 0.293.

Therefore, the probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

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Answer:

36

Step-by-step explanation:

(2p-3r)^2

(2•6-3•2)^2

(12-6)^2

(6)^2

36

Adiosss

Answer

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Explanation

To solve this, we need to note that √(-1) = i

So, for this simplification

√(36 - 40) = √(-4) = √[(4)(-1)] = 2i

We can now fully simplify the expression given

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Hope this Helps!!!

Answer:

NO

Step-by-step explanation:

two sides must be of equal length for a triangle to be iscoceles

Answer:

Not isosceles

Step-by-step explanation:

The given, is a right triangle because AC is perpendicular to BC so x = 30

For the triangle to be isosceles |AC| must be equal to |BC|

x + 20 ➡ 30 + 30 = 50

2x - 20 ➡ 60 - 20 = 40 as we can see the length of sides aren't equal so the triangle is not isosceles.

Your graph should look like this :) !

Answer:

second one: EFG NML

THIRD: 82°

Answer: I'd say reflection

Answer:

It is a reflection

Step-by-step explanation:

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Answer:

-1 + \(\frac{x}{7}\)

Step-by-step explanation:

( 2/7x-6 ) - ( 1/7x - 5 )

First you should combine 2/7 and x, and 1/7 and x. You do this by "bringing the x up". This is how the expression looks now: (2x/7 - 6) - (x/7 - 5). Notice: when you have 1x you can just remove the 1 since it is implied. The next step is to apply the distributive property. The number we are distributing is -1 to (x/7 - 5). This is how the expression now looks like: (2x/7 - 6) - x/7 + 5. Notice: since 5 was already negative, when we multiplied it by a negative, it became positive. Now we can remove the parenthesis since they are no longer necessary: 2x/7 - 6 - x/7 + 5. The next step is to combine the fractions since they have the same denominator. This is how the expression will look like now: -6 + 5 + \(\frac{2x - x}{7}\). Now we should subtract x from 2x (remember x really just means 1x). This is what we have so far: -6 + 5 + x/7. Lastly, we should add 5 to -6. This is how the finished expression should look like: -1 + x/7.

Hope this was clear!

The x-intercept represents that after 10 in. of rain, there are mosquitoes in that area.

The function is quadratic. The standard form of the quadratic equation is;

f(x) = ax² + bx + c

Here (a, b, c) are the real numbers and (x) is the variable. For the first point (0,0). The equation becomes,

f(0) = a(0)² + b(0) + c

c = 0

For the second point (1,9). The equation becomes,

f(1) = a(1)² + b(1) + 0

9 = a + b   ----(1)

For the third point (3, 21). The equation becomes,

f(3) = a(3)² + b(3) + 0

21 = 9a + 3b   ----(2)

Solving eq 1 and eq 2 simultaneously gives;

a = -1 and b = 10

Thus, our quadratic equation is;

f(x) = -x² + 10x

At f(x) = 0, x = 10.

Thus, x-intercept is at x = 10

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Answer:

8

Step-by-step explanation:

8/3 * 3/1 = 24/3= 8

Answer: 35

Step-by-step explanation:

If there is 50 pieces of fruit in total then . . . find out how much the percentages are ( remember to do that SEPARATELY )

What is 20% of 50 ? 10 pieces

Equation :  20 ( percentage ) times 50 ( whole )

What is 10% of 50 ? 5 pieces

Equation :  10 ( percentage ) times 50 ( whole )

total of apples and grapes in the fruit bowl :  15

Finally do . . . 50 - 15 = 35 pieces

Answer:

$80 interest will be owed for 4 months

Step-by-step explanation:

P is the principal amount, $4000.00.

r is the interest rate, 8% per year, or in decimal form, 8/100=0.08.

t is the time involved, 3....month(s) time periods.

Since your interest rate is "per year" and you gave your time interval in "month(s)" we need to convert your time interval into "year" as well.

Do this by dividing your time, 3- month(s), by 12, since there's 12 months in 1 year.

So, t is 0.25....year time periods.

To find the simple interest, we multiply 4000 × 0.08 × 0.25 to get that

Answer:

t=2

Step-by-step explanation:

Answer:

t=2

Step-by-step explanation:

t=6-4

t=2

There are exactly φ(n) primitive nth roots of unity, where φ is the Euler totient function.

To show that this is a primitive nth root of unity, we need to show that it is not a power of any other nth root of unity. Let k be a positive integer such that

=> \((e^{2\pi ik/n})^n = 1.\)

Then, \(e^{2\pi ik} = 1\), so k must be an integer multiple of n. But if k = mn for some integer m, then

=> \((e^{2\pi ik/n}) = (e^{2\pi im})^{n/m} = 1^{n/m} = 1,\)

which contradicts our assumption that \(e^{2 \pi ik/n}\) is an nth root of unity. Therefore, e^(2πi/n) is a primitive nth root of unity.

For n = 1, there is only one root of unity, namely 1 itself. It is also a primitive root of unity, since it cannot be written as a power of any other root of unity.

For n = 2, there are two roots of unity, namely 1 and -1. Both of these are primitive roots of unity, since neither can be written as a power of the other.

For n = 3, there are three roots of unity, namely 1, \(e^{2 \pi i/3}\), and \(e^{-2 \pi i/3}\). The latter two are primitive roots of unity, since neither can be written as a power of the other or of 1.

For n = 4, there are four roots of unity, namely 1, i, -1, and -i. The primitive roots of unity are \(e^{ \pi i/2}\) and \(e^{ -\pi i/2}\), which cannot be written as powers of each other or of 1, i, or -1.

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As per unitary method, the height of the light pole is 3 feet.

The unitary method involves finding the value of one unit and then using it to find the value of another unit. In this problem, we can use the height of Jenny as one unit and her shadow length as another unit. Let's assume that Jenny's height is 1 unit and her shadow length is x units.

Now, we need to find the value of one unit in terms of the height of the light pole. To do this, we can use the fact that the lengths of the two shadows are proportional to the heights of the objects casting the shadows. That is, if the height of the light pole is h units, then we have:

Jenny's height / Jenny's shadow length = Light pole's height / Light pole's shadow length

Substituting the values, we get:

1 / x = h / y

where y is the length of the shadow of the light pole.

We can rearrange this equation to find the value of h in terms of x and y:

h = (x * y) / 1

Now, we can substitute the given values of x and y to find the height of the light pole. If Jenny's shadow is 10 feet long and the shadow of the light pole is 30 feet long, then we have:

h = (1 * 30) / 10 = 3 feet

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Answer:

The height above ground when the ride stops is 96 feet

Step-by-step explanation:

The given diameter of the carnival ride, d = 120 ft.

The height of the ride above the ground, h = 6 ft.

The angle through which the ride is rotated, θ = 240° counterclockwise

Therefore, we have;

The radius of the ride, r = d/2

∴ r = 120 ft./2 = 60 ft.

We note that at 180° rotation, the ride is at the highest point, \(h_{max}\) = 6 ft. + 120 ft. = 126 ft.

When the ride rotates a further 240° - 180° = 60° the height drops from the maximum point by y = 60 ft. × cos (60°) = 30 ft., such that the final height above ground is therefore;

h = 126 ft. - 30 ft. = 96 ft.

The height above ground when the ride stops, h = 96 ft.

21

\( \frac{1}{2} height \: of \: trapezium(a + b) = area \: of \: trapezium\)

half the height is 3

a=7

b=x

3(7+x)=84

21+3x=84

place the like terms on one side

84-21=3x

63=3x

x=21

Answer:

Step-by-step explanation:

\( \frac{2x - 4}{5} =4\)

First of all multiply through by 5 to eliminate the fraction

That's

\(5 \times \frac{2x - 4}{5} = 4 \times 5 \\ 2x - 4 = 20\)

Next using the addition property add 4 to both sides of the equation

We have

\(2x - 4 + 4 = 20 + 4 \\ 2x = 24\)

Divide both sides by 2

\( \frac{2x}{2} = \frac{24}{2} \)

We have the final answer as

Hope this helps you

x=12

I take a photo of the problem, I hope I helped you

when the account reaches 600, well, it had a Principal of $500, so to get there it'd need $100 more, so by the time the earned interest is 100, when is it?

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 100\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 100 = (500)(0.05)(t) \implies \cfrac{100}{(500)(0.05)}=t\implies 4=t\)

Answer:

b) Make b the subject of the formula a = 4 - 3b​

Step-by-step explanation:

I took the quiz

The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.

Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.

The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.

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The pictogram shows information about the houses in a street. the number of bedrooms each house have is 82 bedrooms

Using the pictogram the number of houses are listed

3-bedroom houses = 9 houses

4-bedroom houses = 10 houses

5-bedroom houses = 3 houses

Multiplying out to get the number of bedroom per house

9 * 3= 27 bedrooms

10 * 4= 40 bedrooms

3 * 5 = 15 bedrooms

Adding the bedrooms together

27 + 40 + 15

= 82 bedrooms

the house has 82 bedrooms

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Answer:

x=5

Step-by-step explanation:

Move the x's to one side, and the numbers to the other. So 2x+19=x+24, subtract the x on the left to the right side, and subtract 19 from the left to the right side. You are left with 2x-x=24-19. Reduce this. X=5

Answer: Solve for x by simplifying both sides of the equation, then isolating the variable:

x=5

Answer:

A = B (base) x H (height)

A = 55 x 55

A = 3025

To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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