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A miniature connector is shaped like this hexagonal prism. The prism has a base area of 8.15 cm².


What is the volume of the connector?


Enter your answer as a decimal in the box.

Transfer function of the system is:X(s)/Y(s) = 10/(s^2+1.6s+4)We need to find the following:

a) Y(t); b) Percent overshoot; c) Ultimate value of Y(t); d) Maximum value of Y(t) and e) Period of oscillation.

(a) Calculation of Y(t):The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)Now, applying the Laplace inverse on both sides,Y(s) = 10/(s^2+1.6s+4) × X(s)Taking the inverse Laplace of Y(s),y(t) = L^-1 {10/(s^2+1.6s+4) × X(s)}Using partial fraction decomposition to find the inverse Laplace of Y(s), we get:y(t) = 1.2508{ 2.22 e^(-0.8t) - 0.22 e^(-3.2t)}Therefore, the value of Y(t) is 1.2508{ 2.22 e^(-0.8t) - 0.22 e^(-3.2t)}.

(b) Calculation of percent overshoot:The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)The damping ratio (ζ) can be given asζ = 1/2 √(ζ²-4)ζ = 1/2 √(1.6²-4)ζ = 0.6For a second-order system with a damping ratio of 0.6, the percent overshoot is given as:%OS = e^(-ζπ/√(1-ζ²)) × 100%OS = e^(-0.6π/√(1-0.6²)) × 100OS = 26.12%Hence, the percent overshoot is 26.12%.

(c) Calculation of the ultimate value of Y(t):The transfer function of the system isX(s)/Y(s) = 10/(s^2+1.6s+4)For the ultimate value of Y(t), we take the limit of sY(s) as s tends to 0.The value of Y(s) is given as:Y(s) = 10/(s^2+1.6s+4) × X(s)On simplifying the above equation, we get:sY(s) + 1.6 Y(s) + 4 Y(s) = 10 X(s)Now, taking the limit of sY(s) as s approaches 0,sY(s) = lim s→0 sY(s) = 0Therefore, 1.6 Y(s) + 4 Y(s) = 10 X(s)Taking the limit of Y(s) as s approaches 0,0 = 10 X(0)Y(0) = 2.5Hence, the ultimate value of Y(t) is 2.5.

(d) Calculation of the maximum value of Y(t):The maximum value of Y(t) is given as:Ymax = 2.5 + (1+ζ²)^0.5 e^(-ζπ/√(1-ζ²)) / (ζ√(1-ζ²))The value of ζ is 0.6Hence, substituting the value of ζ in the above equation, we get:Ymax = 2.5 + (1+0.6²)^0.5 e^(-0.6π/√(1-0.6²)) / (0.6√(1-0.6²))Ymax = 3.129

(e) Calculation of the period of oscillation: The period of oscillation is given as:T = 2π / ωnWhere,ωn = √(1-ζ²) / (2ζ)Therefore,ωn = √(1-0.6²) / (2 × 0.6)ωn = 1.302Therefore,T = 2π / ωnT = 4.830sHence, the period of oscillation is 4.830s.

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Answer: if ur looking for an equation then y = -4 + 6

Step-by-step explanation:

Since the y intercept is 6 and it’s going 4 units down and 1 to the left

102 degrees

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees.

y = 360 - (120 + 85 + 53)

y = 360 - 258

y = 102 degrees

Answer:

-1/4

Step-by-step explanation:

Hello!

The rate of change is also known as the slope.

Standard equation of a line: y = mx + b

So, if we match the standard form to the given function:

-1/4 is m, or the rate of change.

Answer:

  x = 6

Step-by-step explanation:

You want the value of x in the geometry where an angle bisector has divided a triangle into sides 42 and (6x-1), and corresponding sides 78 and (10x+5).

The angle bisector divides the sides of the triangle proportionally:

  (6x -1)/42 = (10x +5)/78

  13(6x -1) = 7(10x +5) . . . . . . . . multiply by 546

  78x -13 = 70x +35 . . . . . . . simplify

  8x = 48 . . . . . . . . . . . . . . add 13-70x

  x = 6 . . . . . . . . . . . . . . divide by 8

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Answer:

It shifts 4 units to the right

Step-by-step explanation:

The -4 is inside the parentheses with x in it, which means it shifts the function horizontally. The - sign indicates the function is moving to the right.

hope this helps!

The angle of depression of the fish from the given height to the bottom of the lake is 60° .

The bird caught the fish at site A, flew it 100 yards to location B, and then dropped it off at location C. (which is horizontally 50 yards from A).

The right angled triangle BAC is equal to the length of the perpendicular and base .

The angle the bird creates with the water piques our interest (horizontal). This angle is BAC. We can claim to be knowledgeable about the "hypotenuse" and "adjacent" side of the right triangle to angle BAC. Since the cosine relationship between the hypotenuse and its neighbors exists, we can write:

cos BAC = 50/100

BAC = cos ⁻¹ 1/2

BAC = 60 °

Here, our goal is to determine the length (distance) of segment BC. We can say that BC is "opposite" to the angle BAC, which we discovered to be 60 degrees. The hypotenuse is known to be 100. So let's utilize sine since sine is the ratio of the hypotenuse's opposite.

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Answer:

C. Box c

Step-by-step explanation:

Took this assignment the other day

Hope this helped

Answer:

C

Step-by-step explanation:

box c

The question is incomplete, the complete question is:

Carmella works 37.5 h per week for Century Home selling electronics equipment. She earns a base salary of $12/h and receives a commission of 5¢ for every dollar of sales she makes. What is Carmella’s weekly base salary?

Answer: The base salary of Carmella is $450

Step-by-step explanation:

We are given:

Amount of hours worked by Carmella = 37.5 hours

Amount earned as a base salary = $12/hr

To calculate the base salary, we multiply the total amount of hours worked and the amount earned each hour for it.

\(\text{Base salary}=\$ 12/hr\times 37.5hr\\\\\text{Base salary}=\$ 450\)

Hence, the base salary of Carmella is $450

Answer:

O.4x 0.25

Step-by-step explanation:

It just is as a decimal

Answer:

11...................

Answer:

11

Step-by-step explanation:

the sqare root of something is a number x its self ex.

3x3=9 so the sqare root of 9 is 3

and 8x8=64 so the sqare root of 64 is 8

so the simplified equation is 8+3=11

The two non negative real numbers with a sum of 60 that have the largest possible​ product are 30 and 30.

What are non negative numbers?

Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.

An integer that is either positive or zero is considered a non-negative integer.

Let us assume the two non negative numbers are \(x\) and \(y\).

According to the question,

Sum of two non negative numbers = 60

⇒ \(x+y=60\)

⇒ \(y=60-x\)

Their product will be given as,

⇒ \(P=xy\)

⇒ \(P=x(60-x)\)

⇒ \(P=60x-x^2\)

For the product to be largest \(P'(x)=0\)

⇒ \(P'(x) = 60-2x\)

⇒ \(60-2x=0\)

⇒ \(2x=60\)

⇒ \(x=30\)

Now, for the value of \(y\)

⇒ \(y=60-x\)

⇒ \(y=60-30\)

⇒ \(y=30\)

Therefore, the two non negative numbers are 30, 30.

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Answer:

Round 1.9 to 2 cm and multiply by 18.

Step-by-step explanation:

Round 1.9 to 2 cm and multiply by 18. then you will get your answer

Answer: (3, 1)

Step-by-step explanation:

point D is at (0,3) if it is translated 3 units to the right and 2 units down that means the x value will be added by 3 and the y value will be subtracted by 2

0+3 = 3; 3-2 = 1

D' is at (3,1)

Answer:

Step-by-step explanation:

Wich equation has the solution x = 5?

6x-5=25

6x-3=63

6x-2=-28

6x+7=34​

6x-5=25

6x = 30

x = 30 : 6

Step-by-step explanation:

n = 10 False

n = 6 False

n = -10 True

N = -6 True

Answer:

n=10 false

N=6 false

N = - 10 true

N = - 6 true

Answer:

3 + 9 = 12 !

Step-by-step explanation:

Answer:

is it radius or diameter?

Answer:

37.68

Step-by-step explanation:

circumference is diameter, which in this case is 12,times pi which I always simplify to 3. 14

12 times 3. 14 is approximately 37cm so that is why I have given this answer

brainliest?

Option B) is correct.

Here, we are given –

Let's find it's radius first.

\(\qquad\)\( \sf \longrightarrow Radius = \dfrac{Diameter }{2} \)

\(\qquad\)\( \sf \longrightarrow Radius = \dfrac{12 }{2}\)

\(\qquad\)\( \sf \longrightarrow Radius = \cancel{\dfrac{12 }{2}}\)

\(\qquad\)\( \bf \longrightarrow Radius = 6 \: cm\)

We know that–

\(\qquad\)\( \pink{\bf \longrightarrow Circumference \: of \: circle = 2\pi r}\)

\(\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}\)

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

\(\qquad\)\( \sf \longrightarrow Circumference_{(Circle)} = 2 \pi r\)

\(\qquad\)\( \sf \longrightarrow Circumference_{(Circle)} = 2 \pi \times 6\)

\(\qquad\)\( \sf \longrightarrow Circumference_{(Circle)} =2 \times 3.14\times 6\)

\(\qquad\)\(\pink{ \bf \longrightarrow Circumference_{(Circle)} = 37.68 \: cm }\\\)

The determinant of the given matrix is 22.

To calculate the determinant of the matrix, we can use the Laplace expansion along the first row.

Using this method, we get:

det = 4 * det\[\begin{array}{ccc}3&4\\-1&1\end{array}\] - 2 * det\[\begin{array}{ccc}4&4\\-1&1\end{array}\] - 2 * det\[\begin{array}{ccc}4&3\\-1&1\end{array}\]

To calculate each of the 2x2 determinants, we can again use the

Laplace expansion

along the first row. This gives:

det\[\begin{array}{ccc}3&4\\-1&1\end{array}\] = 3 * 1 - 4 * (-1) = 7

det\[\begin{array}{ccc}4&4\\-1&1\end{array}\] = 4 * 1 - 4 * (-1) = 8

det\[\begin{array}{ccc}4&3\\-1&1\end{array}\] = 4 * 1 - 3 * (-1) = 7

Substituting these values back into the original formula for the determinant, we get:

det = 4 * 7 - 2 * 8 - 2 * 7 = 28 - 16 - 14 = -2

Therefore, the determinant of the given matrix is -2.

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Answer:

B- (-5, -6)

Step-by-step explanation:

By looking on the graph, if you were to reflect this point across the x-axis if will fall under point (-5, -6)

I hope this helps! If not I'm so sorry! Have a lovely day.

The square root √(7 · x - 4) = 2 has a solution for the variable x is 8 / 7.

In this problem, we find a square root whose solution for the variable x has to be found solely by algebra properties. First, write the radical equation:

√(7 · x - 4) = 2

Second, elevate to the square of the expression:

7 · x - 4 = 4

Third, clear the variable x by algebra properties:

7 · x = 8

x = 8 / 7

The solution to the square root is equal to 8 / 7.

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Answer:

use the formula to find area, then multiply by the leingth, so 18 in your case. Also, the formula for area is A=(pi)r squared

Step-by-step explanation:

hope this helps

Answer:

B. 3,052.08

Step-by-step explanation:

Radius:

r=d/2

r=18/2

r=9

Volume of Sphere:

V=(4/3)π\(r^{3}\)

V=(4/3)(3.14)\(9^{3}\)

V=(4/3)(3.14)729

V=(4/3)2289.06

V=3052.08

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Answer:

C. No solutions exist Because the situation describes two lines that have the same slope and different y-intercepts

Step-by-step explanation:

it is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope so there is no solution.

Answer:

Step-by-step explanation:

9994ddaefeaf

Answer:

A=1,2,3

B=x^2 is the answer