After t hours of work. Astrid has completed S(t)=0.3t2+0.2t tasks per hour. Find Astrid's average rate of completion per hour during the first 5 hours of her shift. Round your answer to one decimal place as needed.

Answers

Answer 1

Astrid's average rate of completion per hour during the first 5 hours of her shift is 1.6, rounded off to one decimal place. This is due to the total number of tasks completed during the first 5 hours/total number of hours = 7.75/5.

Given, After t hours of work. Astrid has completed S(t)=0.3t2+0.2t tasks per hour We need to find the average rate of completion per hour during the first 5 hours of her shift. To find the average rate of completion per hour during the first 5 hours of her shift, we need to find the number of tasks completed in the first 5 hours of her shift

.So, put t = 5 in S(t)

S(t) = 0.3t² + 0.2t

S(5) = 0.3(5)² + 0.2(5)

S(5) = 7.75

Tasks completed in the first 5 hours of her shift = S(5) = 7.75Average rate of completion per hour during the first 5 hours of her shift=Total number of tasks completed during the first 5 hours/total number of hours=7.75/5= 1.55 (approx)

Therefore, Astrid's average rate of completion per hour during the first 5 hours of her shift is 1.6 (approx).Note: We have rounded off the answer to one decimal place.

To know more about average Visit:

https://brainly.com/question/24057012

#SPJ11


Related Questions

Let y= x+ln(x). Knowing that y(1)=1, use linear approximation to approximate the value of y(0.9)

Answers

To approximate the value of y(0.9), we can use linear approximation, also known as the tangent line approximation.

The linear approximation involves finding the equation of the tangent line to the curve at a given point and using it to estimate the function value at a nearby point.

Given that y = x + ln(x), we want to approximate the value of y(0.9). First, we find the derivative of y with respect to x, which is 1 + 1/x. Then we evaluate the derivative at x = 1, which gives us a slope of 2.

Next, we determine the equation of the tangent line at x = 1. Since the function passes through the point (1, 1), the equation of the tangent line is y = 2(x - 1) + 1.

Finally, we can use this linear equation to approximate the value of y(0.9). Substituting x = 0.9 into the equation, we get y(0.9) ≈ 2(0.9 - 1) + 1 = 0.8.

Therefore, using linear approximation, the approximate value of y(0.9) is 0.8.

To know more about linear approximation click here: brainly.com/question/1621850

#SPJ11

The first five terms of the recursive sequence
a₁ = 4,a_n+1= -a_n
are
• 4,-4, 4, -4, 4
• 4, -16, 64, -256, 1024
• -4, 4, -4, 4, -4
• 4, 0, -4,-8, -12

Answers

The first five terms of the recursive sequence a₁ = 4, a_{n+1} = -a_n are:4, -4, 4, -4, 4.

To find the second term, we need to use the recursive formula a_{n+1} = -a_n. Since the first term is given as a₁ = 4, the second term is:

a₂ = -a₁ = -4

Using this value of a₂, we can find a₃:

a₃ = -a₂ = -(-4) = 4

Now we can use a₃ to find a₄:

a₄ = -a₃ = -4

Finally, using a₄, we can find a₅:

a₅ = -a₄ = -(-4) = 4

Therefore, the first five terms of the sequence are 4, -4, 4, -4, 4.

To learn more about arithmetic sequence, refer to the link-

brainly.com/question/6561461

#SPJ11

Consider the one-country model of technology and growth. Suppose that L=1,μ=5, and γA​=0.5. Further, assume the initial value of A is also 1 . (a) Calculate both the level of output per worker and the growth rate of output per worker. (b) Now suppose that YA​ is raised to 0.75. What would be the new levels of output per worker and the new growth of output per worker? (c) How many years will it take before output per worker returns to the level it would have reached if ψA​ had remained constant?

Answers

When YA is raised to 0.75, the level of output per worker remains 1, but the growth rate decreases to approximately 0.464.

To calculate the level of output per worker and the growth rate of output per worker in the one-country model of technology and growth, we'll use the following equations:

Output per worker (y) = A^(1/(1-μ))

Growth rate of output per worker (g) = γA^(1/(1-μ))

Given the values L=1, μ=5, γ=0.5, and initial value of A=1, let's calculate the initial level of output per worker and growth rate:

(y_initial) = A^(1/(1-μ)) = 1^(1/(1-5)) = 1

(g_initial) = γA^(1/(1-μ)) = 0.5 * 1^(1/(1-5)) = 0.5

(a) The initial level of output per worker is 1, and the initial growth rate of output per worker is 0.5.

Now, let's consider the case where YA is raised to 0.75:

(y_new) = A^(1/(1-μ)) = 1^(1/(1-5)) = 1

(g_new) = γA^(1/(1-μ)) = 0.5 * 0.75^(1/(1-5)) ≈ 0.464

(b) The new level of output per worker remains 1, but the new growth rate of output per worker decreases to approximately 0.464.

To determine the number of years it will take for output per worker to return to its initial level, we need to find the time it takes for A to reach its initial value of 1. Since the growth rate of output per worker is given by g = γA^(1/(1-μ)), we can rearrange the equation as follows:

A = (g/γ)^(1-μ)

To find the time it takes for A to reach 1, we need to solve for t in the equation:

1 = (g/γ)^(1-μ)t

(c) The number of years it will take for output per worker to return to its

initial level depends on the values of g, γ, and μ. By solving the equation above for t, we can determine the time it takes for output per worker to return to its initial level.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

Let f(x)=4x2−3x−7. The secant line through (2,f(2)) and (2+h,f(2+h)) has slope 4h+13. Use this formula to compute the slope of the given lines.
Find the slope of the secant line through (2,f(2)) and (3,f(3)). (Give your answer as a whole or exact number.)

Answers

The slope of the secant line through the points (2, f(2)) and (3, f(3)) is 17.

Given the function f(x) = 4[tex]x^{2}[/tex] - 3x - 7, we are asked to find the slope of the secant line passing through the points (2, f(2)) and (3, f(3)). To find the slope using the formula provided, we need to substitute the values into the formula 4h + 13, where h represents the difference in x-coordinates between the two points.

In this case, the x-coordinates are 2 and 3, so the difference h is equal to 3 - 2 = 1. Plugging this value into the formula, we get 4(1) + 13 = 17. Therefore, the slope of the secant line passing through the points (2, f(2)) and (3, f(3)) is 17.

The formula for the slope of a secant line, 4h + 13, represents the difference in the function values divided by the difference in the x-coordinates. By substituting the appropriate values, we can calculate the slope. In this case, we consider the points (2, f(2)) and (3, f(3)), where the x-coordinates differ by 1. Plugging this value into the formula yields 4(1) + 13 = 17, which gives us the slope of the secant line. Therefore, the slope of the secant line through the given points is 17.

Learn more about slope here:

https://brainly.com/question/30162654

#SPJ11

Find the particular solution to this equation:
\( x[n]=2: \) \( \quad y[n]-(9 / 16) y[n-2]=x[n-1] \)

Answers

The particular solution to the difference equation y[n] - (9/16) y[n-2] = x[n-1] with x[n] = 2 is y[n] = 2 - (3/4)^n. The first step to solving the difference equation is to find the homogeneous solution. The homogeneous solution is the solution to the equation y[n] - (9/16) y[n-2] = 0.

This equation can be solved using the Z-transform, and the solution is y[n] = C1 (3/4)^n + C2 (-3/4)^n, where C1 and C2 are constants. The particular solution to the equation is the solution that satisfies the initial condition x[n] = 2. The particular solution can be found using the method of undetermined coefficients. In this case, the particular solution is y[n] = 2 - (3/4)^n.

The method of undetermined coefficients is a method for finding the particular solution to a differential equation. In this case, the method of undetermined coefficients involves assuming that the particular solution is of the form y[n] = an + b. The coefficients a and b are then determined by substituting the assumed solution into the difference equation.

To learn more about Z-transform click here : brainly.com/question/32622869

#SPJ11

Find dy/dy for
e^cos y = x^6 arctan y
NOTE: Differentiate both sides of the equation with respect to
x, and then solve for dy/dx
Do not substitute for y after solving for dy/dx

Answers

Therefore, the expression for dy/dx is [tex](6x^5 * arctan(y)) / (-sin(y) * e^cos(y) - x^6 * (1/(1+y^2))).[/tex]

To find dy/dx for the equation[tex]e^cos(y) = x^6 * arctan(y[/tex]), we need to differentiate both sides of the equation with respect to x and solve for dy/dx.

Differentiating [tex]e^cos(y) = x^6 * arctan(y[/tex]) with respect to x using the chain rule, we get:

[tex]-d(sin(y)) * dy/dx * e^cos(y) = 6x^5 * arctan(y) + x^6 * d(arctan(y))/dy * dy/dx[/tex]

Simplifying the equation, we have:

[tex]-dy/dx * sin(y) * e^cos(y) = 6x^5 * arctan(y) + x^6 * (1/(1+y^2)) * dy/dx[/tex]

Now, let's solve for dy/dx:

[tex]-dy/dx * sin(y) * e^cos(y) - x^6 * (1/(1+y^2)) * dy/dx = 6x^5 * arctan(y)[/tex]

Factoring out dy/dx:

[tex]dy/dx * (-sin(y) * e^cos(y) - x^6 * (1/(1+y^2)))) = 6x^5 * arctan(y)[/tex]

Dividing both sides by (-sin(y) * e^cos(y) - x^6 * (1/(1+y^2)):

[tex]dy/dx = (6x^5 * arctan(y)) / (-sin(y) * e^cos(y) - x^6 * (1/(1+y^2)))[/tex]

To know more about expression,

https://brainly.com/question/32716956

#SPJ11

You and your coworker together make $16 per hour. You know your coworker earns 10 percent more than you do. Your hourly wage is $ ___. After taking Math 1010 your hourly wage is raised to $12. This is a raise of ___ %. After returning to work you can't help mentioning casually to your coworker that now you make ___ % more than he does. He responds wistfully that this is as it should be since now you can figure problems like the ones on this assignment!

Answers

After taking Math 1010, their hourly wage increases to $12, which is a raise of 20%. They now make 20% more than their coworker. the person's new wage is $12 and the coworker's wage is $11, the person now makes ($12 - $11) / $11 * 100 ≈ 9.09% more than the coworker.the raise is 57.4%.

The hourly wage of the person is $10, while their coworker earns 10% more, making it $11 per hour.
Let's denote the person's hourly wage as x. According to the given information, the coworker earns 10% more than the person. This means the coworker's hourly wage is x + 0.10x = 1.10x.
Together, they make $16 per hour, so their combined wages are x + 1.10x = 2.10x. Since this equals $16, we can solve for x: 2.10x = $16, which gives x = $7.62.
After taking Math 1010, the person's hourly wage increases to $12. The raise amount can be calculated as the difference between the new wage and the previous wage, which is $12 - $7.62 = $4.38. To calculate the raise percentage, we divide the raise amount by the previous wage and multiply by 100: (4.38 / 7.62) * 100 ≈ 57.4%. Therefore, the raise is approximately 57.4%.
Since the person's new wage is $12 and the coworker's wage is $11, the person now makes ($12 - $11) / $11 * 100 ≈ 9.09% more than the coworker.

Learn more about hourly wage here
https://brainly.com/question/1582269



#SPJ11

Form 1: \( 2 e^{-i / 1}+1 e^{-1 / n}+3 \) Form 2: \( \operatorname{Cte}^{-1 / n}+3 e^{-1 / \pi}+3 \) Form 3: \( 3 e^{-1 / t} \) con \( (\omega f)+e^{-1 / 7} \sin (\omega t)+3 \) exponential time const

Answers

The three forms given represent exponential time constants and a rational frequency.The rational frequency term in these forms represents the frequency of the oscillation. For example, in Form 3, the rational frequency term is ωf, which means that the frequency of the oscillation is ω times the frequency of the input signal f.

Form 1: 2e ^−i/1 +1e ^−1/n +3 is a sum of two exponential terms, one with a time constant of 1 and one with a time constant of n. The time constant of an exponential term is the rate at which the term decays over time.

Form 2: Cte ^−1/n +3e ^−1/π +3 is a sum of three exponential terms, one with a time constant of n, one with a time constant of π, and a constant term.

Form 3: 3e ^−1/t con (ωf)+e ^−1/7 sin(ωt)+3 is a sum of an exponential term with a time constant of t, a sinusoidal term with frequency ω, and a constant term. The frequency of a sinusoidal term is the rate at which the term oscillates over time.

To learn more about exponential terms click here : brainly.com/question/30240961

#SPJ11

Simplify (g(b)-g(a))/(b-a) for the function g(x) = 1/5x

Answers

The value of the expression (g(b)-g(a))/(b-a) when fucntion g(x) = 1/5x is

-1/(5ab).

The given function is,

g(x) = 1/5x,

Evaluate g(b) and g(a) as follows:

g(b) = 1/(5b)

g(a) = 1/(5a)

Substituting these values into the expression (g(b)-g(a))/(b-a), we get:

(g(b)-g(a))/(b-a) = ((1/(5b)) - (1/(5a))/(b-a)

Simplifying this expression,

Factor out 1/5 from the numerator:

((1/5 b) - (1/5 a))/(b-a) = (1/5) (1/b-1/a)/(b-a)

                                 = (1/5)(a-b)/(ab(b-a))

                                 = -(1/5)(b-a)/(ab(b-a))

                                 =  -1/(5ab)

Hence the value of the given expression is,

(g(b)-g(a))/(b-a) = -1/(5ab)

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ4

"A clothing manufacturer has determined that the cost of producing T-shirts is $2 per T-shirt plus $4480 per month in fixed costs. The clothing manufacturer sells each T-shirt for $30
Find the break-even point."

Answers

The break-even point is 160 T-shirts.

Break-even point is a critical metric used to determine how many goods or services a business must sell to cover its expenses.

It is calculated by dividing the total fixed costs by the contribution margin, which is the difference between the selling price and the variable cost per unit.

Here's how to calculate the break-even point in this problem:

Variable cost per unit = Cost of producing one T-shirt = $2Selling price per unit = $30

Contribution margin = Selling price per unit - Variable cost per unit= $30 - $2 = $28Fixed costs = $4480

Break-even point = Fixed costs / Contribution margin= $4480 / $28= 160

Therefore, the break-even point is 160 T-shirts.

To know more about break-even point visit:

brainly.com/question/2673777

#SPJ11

3. Consider the causal discrete system defined by the following differences equation: y(n)=5x(n)-2x(n-1)-x(n-2)-y(n-1) Assuming that the system is sleeping, determine the system response, with n up to 5, at the input x(n)= 28(n)+8(n-1)-8(n-3) (2 v.) Write the frequency response of the system, H(z). (1 v.) In the z plane, represent zeros, poles and the region of convergence (ROC). (1 v.) a) b) c)

Answers

The system response, y(n), for the given input x(n) up to n = 5 is as follows: y(0) = 5x(0) - 2x(-1) - x(-2) - y(-1),    y(1) = 5x(1) - 2x(0) - x(-1) - y(0),   y(2) = 5x(2) - 2x(1) - x(0) - y(1),      y(3) = 5x(3) - 2x(2) - x(1) - y(2),                  y(4) = 5x(4) - 2x(3)-x(2) - y(3),     y(5) = 5x(5) - 2x(4) - x(3) - y(4).

To calculate y(n), we substitute the given values of x(n) and solve the equations iteratively. The initial conditions y(-1) and y(0) need to be known to calculate subsequent values of y(n). Without knowing these initial conditions, we cannot determine the exact values of y(n) for n up to 5.

The frequency response of the system, H(z), can be obtained by taking the Z-transform of the given difference equation. However, since the equation provided is a time-domain difference equation, we cannot directly determine the frequency response without taking the Z-transform.

To represent the zeros, poles, and the region of convergence (ROC) in the z-plane, we need the Z-transform of the given difference equation. Without the Z-transform, it is not possible to determine the locations of zeros and poles, nor the ROC of the system.

Learn more about difference equation here: brainly.com/question/14950581

#SPJ11

A population of crabs is growing according to the logistic growth equation, with r=1.1 and carrying capacity of 500crabs. At which population size will the population grow the fastest? In a year tracking a population of widowbirds, you recorded that 150 individuals were born, 75 birds died. If λ=2, how many birds were there when you started tracking the population?

Answers

The population will grow the fastest at half of the carrying capacity, which is 250 crabs.

In the logistic growth equation, the population growth rate is highest when the population is at half of the carrying capacity. This is because, at this point, there is a balance between birth rates and death rates, maximizing the net population growth.

For the given logistic growth equation with a carrying capacity of 500 crabs, the population will grow the fastest at half of the carrying capacity, which is 250 crabs.

Regarding the second question, to determine the initial population size of widowbirds when tracking started, we can use the equation λ = (births - deaths) / initial population.

Given that 150 individuals were born and 75 birds died during the tracking period, and λ is equal to 2, we can solve the equation for the initial population.

2 = (150 - 75) / initial population

Multiplying both sides by the initial population:

2 * initial population = 150 - 75

2 * initial population = 75

Dividing both sides by 2:

initial population = 75 / 2

initial population = 37.5

Since population size cannot be a decimal, we round down to the nearest whole number.

Therefore, when tracking the population of widowbirds, the initial population size would be approximately 37 birds.

Learn more about population here

https://brainly.com/question/30396931

#SPJ11

Find the derivative of the function.
f(x) = (5x3 + 4x)(x − 3)(x + 1)

Answers

The derivative of the function f(x) = (5x^3 + 4x)(x - 3)(x + 1) can be found using the product rule and the chain rule.

f'(x) = (15x^2 + 4)(x - 3)(x + 1) + (5x^3 + 4x)[1 + (x - 3) + (x + 1)]

First, let's apply the product rule to differentiate the function f(x) = (5x^3 + 4x)(x - 3)(x + 1). The product rule states that the derivative of the product of two functions u(x) and v(x) is given by u'(x)v(x) + u(x)v'(x).

Let u(x) = 5x^3 + 4x and v(x) = (x - 3)(x + 1).

Applying the product rule, we have:

f'(x) = u'(x)v(x) + u(x)v'(x)

To find u'(x), we differentiate u(x) = 5x^3 + 4x with respect to x:

u'(x) = 15x^2 + 4

To find v'(x), we differentiate v(x) = (x - 3)(x + 1) with respect to x:

v'(x) = (1)(x + 1) + (x - 3)(1)

     = x + 1 + x - 3

     = 2x - 2

Now, we substitute the values into the product rule formula:

f'(x) = (15x^2 + 4)(x - 3)(x + 1) + (5x^3 + 4x)(2x - 2)

Simplifying further, we get:

f'(x) = (15x^2 + 4)(x - 3)(x + 1) + (5x^3 + 4x)(2x - 2)

Therefore, f'(x) = (15x^2 + 4)(x - 3)(x + 1) + (5x^3 + 4x)(2x - 2).

Learn more about derivative  here:

https://brainly.com/question/29144258

#SPJ11

A golf ball is driven so that its height in feet
after t seconds is s (t) = -16t- + 48t + 20 . Find the maximum
height of the golf ball. O 56 feet O 20 feet O 1.5 feet O -88 feet

Answers

The maximum height of the golf ball is 56 feet, as determined by the equation s(t) = -16t^2 + 48t + 20.



To find the maximum height of the golf ball, we can determine the vertex of the parabolic function representing its height.

The function s(t) = -16t^2 + 48t + 20 is a downward-opening parabola since the coefficient of t^2 is negative.

The vertex of the parabola can be found using the formula t = -b / (2a),

where a and b are the coefficients of the quadratic equation. In this case, a = -16 and b = 48.

Calculating t = -48 / (2*(-16)) gives t = 1.5 seconds.

Substituting this value into the equation s(t) gives s(1.5) = -16(1.5)^2 + 48(1.5) + 20 = 56 feet.

Therefore, the maximum height of the golf ball is 56 feet.

learn more about equation click here:

brainly.com/question/649785

#SPJ11

There are 7 2500K LED luminaires and 5 4500K LED luminaires (ALL DIFFERENT). The assembly of 7 luminaires will be carried out. How many is feasible if you must have 4 DIFFERENT 2500K. and 3 DIFFERENT 4500K.

Answers

The number of feasible combinations can be calculated by selecting 4 different luminaires from the available 2500K LED luminaires (7 options) and selecting 3 different luminaires from the available 4500K LED luminaires (5 options).

To calculate the number of feasible combinations, we use the concept of combinations. The number of ways to select k items from a set of n items without regard to the order is given by the binomial coefficient, denoted as "n choose k" or written as C(n, k).

For the 2500K LED luminaires, we have 7 options available, and we need to select 4 different luminaires. Therefore, the number of ways to select 4 different 2500K LED luminaires is C(7, 4).

Similarly, for the 4500K LED luminaires, we have 5 options available, and we need to select 3 different luminaires. Therefore, the number of ways to select 3 different 4500K LED luminaires is C(5, 3).

To find the total number of feasible combinations, we multiply the number of combinations for each type of luminaire: C(7, 4) * C(5, 3).

Calculating this expression, we get the total number of feasible combinations of luminaires that satisfy the given conditions.

Learn more about feasible here:

https://brainly.com/question/29314086

#SPJ11

The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem.

y = c_1+c_2 cos(x) + c_3 sin(x), (−[infinity],[infinity]);
y′′′+y′ = 0, y(π) = 0, y′(π) = 6, y′′(π) = −1
y = ____

Answers

A member of the family that satisfies the initial-value problem is y = -6 + (-7)sin(x) + (-6)cos(x).

The general solution to the differential equation y′′′+y′=0 is given by y=c₁+c₂cos(x)+c₃sin(x). To find a specific solution, we apply the initial conditions y(π)=0, y′(π)=6, and y′′(π)=−1.

The general solution to the given differential equation is y=c₁+c₂cos(x)+c₃sin(x), where c₁, c₂, and c₃ are constants to be determined. To find a member of this family that satisfies the initial conditions, we substitute the values of π into the equation.

First, we apply the condition y(π)=0:

0 = c₁ + c₂cos(π) + c₃sin(π)

0 = c₁ - c₂ + 0

c₁ = c₂

Next, we apply the condition y′(π)=6:

6 = -c₂sin(π) + c₃cos(π)

6 = -c₂ + 0

c₂ = -6

Finally, we apply the condition y′′(π)=−1:

-1 = -c₂cos(π) - c₃sin(π)

-1 = 6 + 0

c₃ = -1 - 6

c₃ = -7

Therefore, a member of the family that satisfies the initial-value problem is y = -6 + (-7)sin(x) + (-6)cos(x).

For more information on family visit: brainly.com/question/16930980

#SPJ11

An LII system has an impulse response: \( \backslash\left(h(t)=e^{\wedge}\{\cdot(t-1)\} u(t-3) \cup\right. \) This system is: Select one: Not causal but stable Causal and stable Not causal and not sta

Answers

The correct answer is: Causal and stable. To analyze the causality and stability of the LTI (Linear Time-Invariant) system with impulse response [tex]\(h(t) = e^{-(t-1)}u(t-3)\)[/tex].

\(u(t)\) is the unit step function, which is 1 for [tex]\(t \geq 0\)[/tex] and 0 for [tex]\(t < 0\)[/tex].

1. Causality: A system is causal if the output at any given time depends only on past and present inputs, not on future inputs. In other words, the impulse response must be zero for \(t < 0\) since the system cannot "see" future inputs.

From the given impulse response, we see that \(h(t) = 0\) for \(t < 1\) (due to \(e^{-(t-1)}\)) and for \(t < 3\) (due to \(u(t-3)\)). This means that the system is causal.

2. Stability: A system is stable if its output remains bounded for all bounded inputs. In simpler terms, if the system does not exhibit unbounded growth when presented with finite inputs.

For stability, we need to check if the impulse response \(h(t)\) is absolutely integrable, which means that the integral of \(|h(t)|\) over the entire time axis should be finite.

Let's compute the integral of \(|h(t)|\) over the entire time axis:

[tex]\(\int_{-\infty}^{\infty} |h(t)| dt = \int_{-\infty}^{1} |e^{-(t-1)}u(t-3)| dt + \int_{1}^{\infty} |e^{-(t-1)}u(t-3)| dt\)[/tex]

Since \(u(t-3) = 0\) for \(t < 3\), the first integral becomes:

[tex]\(\int_{-\infty}^{1} |e^{-(t-1)}u(t-3)| dt = \int_{-\infty}^{1} |0| dt = 0\)[/tex]

For \(t \geq 1\), \(u(t-3) = 1\), so the second integral becomes:[tex]\(\int_{1}^{\infty} |e^{-(t-1)}u(t-3)| dt = \int_{1}^{\infty} |e^{-(t-1)}| dt\)[/tex]

Now, \(e^{-(t-1)}\) is a decaying exponential function for \(t \geq 1\), which means it converges to 0 as \(t\) approaches infinity. Therefore, the integral above is finite.

Since the integral of \(|h(t)|\) over the entire time axis is finite, the system is stable. So, the correct answer is: Causal and stable.

To learn more about Linear Time-Invariant: brainly.com/question/33513987

#SPJ11

Find the sum of the infinite geometric series below. k=1∑[infinity]​ 16(21​)k

Answers

The sum of the infinite geometric series can be found using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. In this case, the first term 'a' is 16 and the common ratio 'r' is 1/21. Substituting these values into the formula, we have:

S = 16 / (1 - 1/21)

To simplify the expression, we need to find a common denominator:

S = 16 / (21/21 - 1/21)

  = 16 / (20/21)

  = 16 * (21/20)

  = 336/20

  = 16.8

Therefore, the sum of the infinite geometric series 16(1/21)^k is equal to 16.8.

In more detail, we can observe that the given series is a geometric series with a common ratio of 1/21. This means that each term is obtained by multiplying the previous term by 1/21. The first term of the series is 16.

To find the sum of an infinite geometric series, we can use the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Substituting the given values into the formula, we get:

S = 16 / (1 - 1/21)

To simplify the expression, we need to find a common denominator for the denominator:

S = 16 / (21/21 - 1/21)

  = 16 / (20/21)

Now, to divide by a fraction, we can multiply by its reciprocal:

S = 16 * (21/20)

  = 336/20

  = 16.8

Hence, the sum of the infinite geometric series 16(1/21)^k is equal to 16.8.

Learn more about series here:

brainly.com/question/12707471

#SPJ11

Maris purchased a building for £10 m on 1 January 2020 and rented it out to an unassociated company. At 31 December 2020 it is estimated that the building could be sold for £10.8 m, with selling costs of £200,000. If Maris uses the fair value model, which of these statements concerning the fair value exercise for the year ended 31 December 2020 is true?
a. Gain of £600,000 to Statement of Profit or loss
b. Gain of £600,000 to Revaluation surplus and OCl
c. Gain of £800,000 to Statement of Profit or loss
d. Gain of £800,000 to Revaluation surplus and OCl

Answers

The correct answer is: c. Gain of £800,000 to Statement of Profit or loss.

Since Maris uses the fair value model, the gain from the increase in the fair value of the building is recognized in the Statement of Profit or Loss. In this case, the building's fair value increased from £10 million to £10.8 million, resulting in a gain of £800,000. Therefore, the gain of £800,000 should be recognized in the Statement of Profit or Loss.According to the fair value model, any gain or loss resulting from the change in fair value of the asset should be recognized in the financial statements. In this case, the increase in the fair value of the building is considered a gain.

Since the gain of £800,000 (the difference between the fair value of £10.8 million and the original purchase price of £10 million) is a result of the change in the asset's fair value, it should be recognized in the Statement of Profit or Loss. This gain represents the increase in the value of the building during the year.

Learn more about probability here:

https://brainly.com/question/31740607

#SPJ11

write the following expression as a function of an acute angle. cos (125°) -cos55° cos35° cos55°

Answers

The expression cos (125°) - cos 55° cos 35° cos 55° can be written as cos (55°) + cos (55°) cos (35°) cos (55°).

cos (125°) can be rewritten as cos (180° - 125°). Similarly, cos (35°) can be rewritten as cos (180° - 35°). Therefore, the expression can be written as:

cos (180° - 125°) - cos (55°) cos (180° - 35°) cos (55°)

Simplifying further, we have:

cos (55°) - cos (55°) cos (145°) cos (55°)

Since 145° is the supplement of 35°, we can rewrite it as:

cos (55°) - cos (55°) cos (180° - 35°) cos (55°)

Now, cos (180° - 35°) is equal to -cos (35°). Therefore, the expression becomes:

cos (55°) + cos (55°) cos (35°) cos (55°)

Hence, the expression as a function of an acute angle is:

cos (55°) + cos (55°) cos (35°) cos (55°)

To know more about expression,

https://brainly.com/question/29082858

#SPJ11

Use the Laplace transform to solve the given system of differential equations.
dx/dt = 3y+e ^t
dy/dt =12x-t
x(0)=1 , y(0)=1
x(t)= ______
y(t)= ______

Answers

Applying the inverse Laplace transform, we get:

[tex]y(t) = 4sin3t + 4cos3t + (1/3)(1 + 3t + 3e^-3t)[/tex]

Now, substituting the value of L(x) from equation (5) into equation (3), we get: [tex]x(t) = [3L(y) - e/s] / s2[/tex]

Applying the Laplace transform to the first equation (1), we get:[tex]sL(x) - x(0) = 3L(y) / s - e/s[/tex]

where x(0) = 1

and y(0) = 1.

Substituting the initial condition in the above equation, we get:[tex]sL(x) - 1 = 3L(y) / s - e/s ....[/tex] (3)

Similarly, applying the Laplace transform to the second equation (2),

we get: [tex]sL(y) - y(0) = 12L(x) / s2 + 1 - 1/s[/tex]

where[tex]x(0) = 1 and y(0) = 1[/tex].

Substituting the initial condition in the above equation,

Substituting the value of L(x) from equation (5) into equation (6),

we get: [tex]12(3s/[(s2+1)(s2+3)] - 12e/s(s2+1)(s2+3)) = sL(y) - 1 + 12/s2+1[/tex]

We get:[tex]L(y) = s(576s2 + 1728)/(s4 + 6s2 + 9) + (s2 + 1)/[s(s2+3)(s2+1)][/tex]

Applying the inverse Laplace transform, we get:

[tex]y(t) = 4sin3t + 4cos3t + (1/3)(1 + 3t + 3e^-3t)[/tex]

Now, substituting the value of L(x) from equation (5) into equation (3), we get: [tex]x(t) = [3L(y) - e/s] / s2[/tex]

To know more about differential visit:

https://brainly.com/question/31383100

#SPJ11

Use the intermediate Value theorem to guarantee that F(C)=11 on the given interval F(X) = x^2 + x - 1 Interval [0,5) F(C)=11

Answers

Since the function F(x) = x^2 + x - 1 is continuous on the interval [0, 5), and

F(0) < 11 < F(5), the Intermediate Value Theorem guarantees the existence of at least one value C in the interval (0, 5) such that

F(C) = 11.

To use the Intermediate Value Theorem to guarantee that F(C) = 11 on the interval [0, 5), we need to show that there exists a value C in the interval [0, 5) such that

F(C) = 11.

First, let's calculate the values of F(x) for the endpoints of the interval:

F(0) = (0)^2 + (0) - 1

= -1,

F(5) = (5)^2 + (5) - 1

= 29.

Since F(0) = -1 and

F(5) = 29, we have

F(0) < 11 and F(5) > 11.

Now, since the function F(x) = x^2 + x - 1 is continuous on the interval [0, 5), and F(0) < 11 < F(5),

the Intermediate Value Theorem guarantees the existence of at least one value C in the interval (0, 5) such that F(C) = 11.

To know more about interval visit

https://brainly.com/question/29179332

#SPJ11

I need the answer please

Answers

The magnitude of the resultant force is approximately 57.60 pounds, and the direction is approximately -85.24 degrees (measured counterclockwise from the positive x-axis).

To find the magnitude and direction of the resultant force when the three force vectors are added together, we can use vector addition.

Convert the angles to radians.

Angle of wolf 1 = 45 degrees = π/4 radians

Angle of wolf 2 = 90 degrees = π/2 radians

Angle of wolf 3 = 230 degrees = (230/180)π radians

Resolve the forces into horizontal and vertical components.

Horizontal component of wolf 1 = 150 * cos(π/4) ≈ 106.07 pounds

Vertical component of wolf 1 = 150 * sin(π/4) ≈ 106.07 pounds

Horizontal component of wolf 2 = 200 * cos(π/2) = 0 pounds

Vertical component of wolf 2 = 200 * sin(π/2) = 200 pounds

Horizontal component of wolf 3 = 300 * cos((230/180)π) ≈ -112.36 pounds

Vertical component of wolf 3 = 300 * sin((230/180)π) ≈ -248.69 pounds

Sum the horizontal and vertical components of the forces.

Horizontal component of resultant force = 106.07 + 0 - 112.36 ≈ -6.29 pounds

Vertical component of resultant force = 106.07 + 200 - 248.69 ≈ 57.38 pounds

Find the magnitude of the resultant force using the Pythagorean theorem.

Magnitude of resultant force = √((-6.29)^2 + (57.38)^2) ≈ 57.60 pounds

Find the direction of the resultant force using the inverse tangent function.

Direction of resultant force = atan(57.38 / -6.29) ≈ -85.24 degrees

Therefore, the magnitude of the resultant force is approximately 57.60 pounds, and the direction is approximately -85.24 degrees (measured counterclockwise from the positive x-axis).

for such more question on magnitude

https://brainly.com/question/17157624

#SPJ8

If the point (1, 4) is on the graph of an equation, which statement must be
true?
OA. The values x = 1 and y = 4 make the equation true.
B. The values x = 1 and y = 4 are the only values that make the
equation true.
C. The values x = 4 and y= 1 make the equation true.
D. There are solutions to the equation for the values x = 1 and x = 4.

Answers

The statement that must be true is (a) the values x = 1 and y = 4 make the equation true.

How to determine the statement that must be true?

From the question, we have the following parameters that can be used in our computation:

The point (1, 4) is on the graph of an equation

This means that

x = 1 and y = 4

The above does not represent the only value that make the equation true.

However, the point can make the equation true

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

The marginal cost of a product is given by 204+76/√x dollars per unit, where x is the number of units produced. The current level of production is 151 units weekly. If the level of production is increased to 271 units weekly, find the increase in the total costs. Round your answer to the nearest cent.

Answers

The increase in total costs, when the level of production is increased from 151 units to 271 units weekly, is approximately $24,677.10.

To find the increase in total costs, we need to calculate the total cost at the current level of production and the total cost at the increased level of production, and then subtract the former from the latter.

First, let's calculate the total cost at the current level of production, which is 151 units per week. We can find the total cost by integrating the marginal cost function over the range from 0 to 151 units:

Total Cost = ∫(204 + 76/√x) dx from 0 to 151

Integrating the function gives us:

Total Cost = 204x + 152(2√x) evaluated from 0 to 151

Total Cost at 151 units = (204 * 151) + 152(2√151)

Now, let's calculate the total cost at the increased level of production, which is 271 units per week:

Total Cost = ∫(204 + 76/√x) dx from 0 to 271

Integrating the function gives us:

Total Cost = 204x + 152(2√x) evaluated from 0 to 271

Total Cost at 271 units = (204 * 271) + 152(2√271)

Finally, we can calculate the increase in total costs by subtracting the total cost at the current level from the total cost at the increased level:

Increase in Total Costs = Total Cost at 271 units - Total Cost at 151 units

Performing the calculations, we have:

Total Cost at 271 units = (204 * 271) + 152(2√271) = 55384 + 844.39 ≈ 56228.39 dollars

Total Cost at 151 units = (204 * 151) + 152(2√151) = 30904 + 647.29 ≈ 31551.29 dollars

Increase in Total Costs = 56228.39 - 31551.29 ≈ 24677.10 dollars

For more such questions on total costs

https://brainly.com/question/5168855

#SPJ4

A mineral deposit along a strip of length 6 cm has density s(x)=0.02x(6−x)g/cm for 0≤x≤6.
M=

Answers

To find the mass (M) of a mineral deposit along a strip of length 6 cm, with density s(x) = 0.02x(6-x) g/cm for 0 ≤ x ≤ 6, we can integrate the density function over the interval [0, 6].  the mass of the mineral deposit along the 6 cm strip, with the given density function, is 0.72 g.

The density of the mineral deposit is given by the function s(x) = 0.02x(6-x) g/cm, where x represents the position along the strip of length 6 cm. The function describes how the density of the mineral deposit changes as we move along the strip.

To find the total mass (M) of the mineral deposit, we integrate the density function s(x) over the interval [0, 6]. The integral represents the accumulation of the density function over the entire length of the strip.

Using the given density function, the integral for the mass is:

M = ∫[0, 6] 0.02x(6-x) dx

Evaluating the integral:

M = 0.02 ∫[0, 6] (6x - x^2) dx

M = 0.02 [(3x^2 - (x^3)/3)] |[0, 6]

M = 0.02 [(3(6^2) - (6^3)/3) - (3(0^2) - (0^3)/3)]

M = 0.02 [(3(36) - (216)/3) - (0 - 0)]

M = 0.02 [(108 - 72) - 0]

M = 0.02 (36)

M = 0.72 g

Therefore, the mass of the mineral deposit along the 6 cm strip, with the given density function, is 0.72 g.

Learn more about integrate here:

https://brainly.com/question/31744185

#SPJ11

The information shown below gives the equation of a hyperbola and how many units up or down and to the right or left the hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes. y2−x2=1, right 1 , down 1 Write an equation for the new hyperbola in standard form. =1 Find the center of the new hyperbola. (Type an ordered pair.) The foci of the new hyperbola are (Type ordered pairs. Use a comma to separate answers as needed. Type an exact answer for each coordinate, using radicals as needed.) What are the vertices? (Type ordered pairs. Use a comma to separate answers as needed. Type an exact answer for each coordinate, using radicals as needed.) What are the equations of the hyperbola's asymptotes? A. y+1=±(x−1) B. x+1=±(y−1) C. x−1=±(y+1) D. y−1=±(x+1)

Answers

The equations of the hyperbola's asymptotes are:y + 1 = +/- (x - 1). The correct option is A.

The information given is:

y² - x² = 1

We can start with the initial standard equation of the hyperbola with center at (0, 0)

y² / a² - x² / b² = 1

We can also note that in the equation given that y² is positive, therefore a² is 1 and b² is -1.

We can substitute these values and the shifts given into the initial equation and get:

y² / 1 - x² / -1 = 1

So, the new equation of the hyperbola in standard form is:

y² - x² = -1

To find the center, we can note that the center shifted 1 unit to the right and 1 unit down from the origin.

Therefore, the new center is (1, -1).Next, we can use the formula to find the distance from the center to each focus:

c = sqrt(a² + b²)

= sqrt(1 - 1)

= 0

The distance from the center to each vertex is a = 1.

Now, we can find the foci, since we know that the foci lie along the axis of the hyperbola and are a distance c from the center. The distance from the center to each focus is 0, so the foci are at (1, -1) and (1, -1).

The vertices lie on the same axis as the foci and are a distance a from the center.

The vertices are at (1, 0) and (1, -2).

Finally, the equations of the asymptotes are:

y + 1 = +/- x - 1Or, written in slope-intercept form:

y = +/- x - 2

The center is (1, -1)

The foci are at (1, 0) and (1, -2)

The vertices are at (1, -1) and (1, -3)

The correct option is A.

Know more about the hyperbola's asymptotes

https://brainly.com/question/29192802

#SPJ11

Shane's retirement fund has an accumulated amount of $45,000. If it has been earning interest at 2.19% compounded monthly for the past 24 years, calculate the size of the equal payments that he deposited at the beginning of every 3 months.
Round to the nearest cent

Answers

The equal payments that Shane deposited at the beginning of every 3 months can be calculated to be approximately $218.47.

To find the size of the equal payments that Shane deposited, we can use the formula for the accumulated amount of a series of equal payments with compound interest. The formula is:

A = P * (1 + r/n)^(nt) / ((1 + r/n)^(nt) - 1),

where A is the accumulated amount, P is the payment amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we are given A = $45,000, r = 2.19% (or 0.0219 as a decimal), n = 12 (since interest is compounded monthly), and t = 24 years.

We need to solve the formula for P. Rearranging the formula, we have:

P = A * ((1 + r/n)^(nt) - 1) / ((1 + r/n)^(nt)).

Substituting the given values, we can calculate P to be approximately $218.47. Therefore, Shane deposited approximately $218.47 at the beginning of every 3 months.

Learn more about compound interest here: brainly.com/question/29639856

#SPJ11

a. Find the linear approximation for the following function at the given point.
b. Use part (a) to estimate the given function value.
f(x,y)= -4x^2 +y^2 ; (2,-2); estimate f(2.1, -2.02)
a. L(x,y) = ______
b. L(2.1, -2.02) = _________ (Type an integer or a decimal.)

Answers

a.  to find the linear approximation for the given function f(x, y) = -4x² + y²; (2, -2) is given by L(x, y)

= f(2, -2) + fx(2, -2)(x - 2) + fy(2, -2)(y + 2). The linear approximation equation is denoted by L(x, y) which is the tangent plane to the surface of the function f(x, y) at (2, -2).L(x, y)

= f(2, -2) + fx(2, -2)(x - 2) + fy(2, -2)(y + 2)

= [-4(2)² + (-2)²] + [-16x] (x - 2) + [4y] (y + 2)

=-16(x - 2) + 8(y + 2) - 12The equation of the tangent plane is L(x, y)

= -16(x - 2) + 8(y + 2) - 12b.

to estimate the given function value using the linear approximation from part a is L(2.1, -2.02) = -16(2.1 - 2) + 8(-2.02 + 2) - 12.L(2.1, -2.02)

= -0.16.The estimate of the given function value is -0.16. Hence, the correct option is (a) L(x,y)

= [-4(2)² + (-2)²] + [-16x] (x - 2) + [4y] (y + 2)

= -16(x - 2) + 8(y + 2) - 12; (b) L(2.1, -2.02)

= -16(2.1 - 2) + 8(-2.02 + 2) - 12

= -0.16.

To know more about function, visit:

https://brainly.com/question/30721594

#SPJ11

The following decimal X and Y values are to be added using 4-bit registers. Determine the Carry and oVerflow values, i.e., the C and V flags. Hint: use the 2 's complement to represent the negative values. - X=2,Y=3 - X=2,Y=7 - X=4,Y=−5 - X=−5,Y=−7 - X=2,Y=−1

Answers

To determine the Carry (C) and Overflow (V) flags when adding the given decimal values using 4-bit registers, we need to convert the values to 4-bit binary representation and perform the addition. Here's the calculation for each case:

X = 2, Y = 3

Binary representation:

X = 0010

Y = 0011

Performing the addition:

0010 +

0011

0101

C (Carry) = 0

V (Overflow) = 0

X = 2, Y = 7

Binary representation:

X = 0010

Y = 0111

Performing the addition:

0010 +

0111

10001

Since we are using 4-bit registers, the result overflows the available bits.

C (Carry) = 1

V (Overflow) = 1

X = 4, Y = -5

Binary representation:

X = 0100

Y = 1011 (2's complement of -5)

Performing the addition:

0100 +

1011

1111

C (Carry) = 0

V (Overflow) = 0

X = -5, Y = -7

Binary representation:

X = 1011 (2's complement of -5)

Y = 1001 (2's complement of -7)

Performing the addition:

1011 +

1001

11000

Since we are using 4-bit registers, the result overflows the available bits.

C (Carry) = 1

V (Overflow) = 1

X = 2, Y = -1

Binary representation:

X = 0010

Y = 1111 (2's complement of -1)

Performing the addition:

0010 +

1111

10001

Since we are using 4-bit registers, the result overflows the available bits.

C (Carry) = 1

V (Overflow) = 1

Note: The Carry (C) flag indicates whether there is a carry-out from the most significant bit during addition. The Overflow (V) flag indicates whether the result of an operation exceeds the range that can be represented with the available number of bits.

To know more about binary representation, visit:

https://brainly.com/question/31150048

#SPJ11

Other Questions
(b) Fault Tree Analysis (FTA) employs logical operators, most notably the OR and AND gates. When an electric car is unable to start, create three (3) layers of FTA conditions (engine not running). (7 it is a discreate time signal processing lesson'stopic and question please solve with hand not solve with code orprogram please solve woth hand ,very urgent4. Consider the discrete time signal x [n] = 0.5cos (2fn) + sin(2fn), n=1,...,8. What is the DFT of x[n] if f=1/4 and f=3/8? Plot the magnitude and phase. Write a program that prompts the user to inputtwo integers. Using any loop, output the multiples of 7 and 11between the two integers Design using D flip flops A sequential detector thatdetects the code 1011 11. Who benefits from inflation?a. No one. Inflation decreases everyone's buying power.b. Creditors at the expense of debtors.c. Debtors at the expense of creditors. How are triangleABC and triangle ADE related? How do you know pls explain. how to find confidence interval on ti 84 without standard deviation IP RANGE TO Calculate the subnetworkin such a way so that there is minimum waste of the IP addresses.Create a table and show all the IP subnets with network address,subnet An air conditioner can be modeled as a cloced system in which refrigerant circulates "in a circle." In mast autamobiles, the refrigerant is called R-1343. The following steps occur in the refrigeration cycle as shown and described below: a. Refrigerant vapor (gas) is compressed from a low pressure (about 30 psig-pounds per square inch gauge-where zero represents atmospheric pressurel to a high pressure \it depends on a number of factors, such as how hot it is on a particular day and how much air is flowing across the condenser that is mounted in the frant of the car, but is diten about 225 psigi. This raises the temperature of the refrigersnt vapor. Typically, mechanical energy fram the engine is used to rotate the compressar pulley. The pulley has an electrically operated clutch to cannect and disconnect the pulley with the compressor shaft. The clutch allows the compresser to be turned on and off as needed. b. Refrigcrant vapor [gas) at high pressure passes through the condenser where heat is removed 50 that the temperature drops and the refrigerant condenses into a liquid (still at high pressure|. An electriazlly or mechanically driven (condenser\} fan \{or the movement of the wahicle) maves air across the conderser to coal the refrigerant. c. Refrigerant next passes through the expansion valwe thigh pressure, "225psig to law pressure, -30 psigl. As the refrigerant passes through an arifice, it becomes an atomized spray of liguid droplets. Because the pressure drops, the temperature of the refrigerant is also reduced \{to about 35 F. A probe measuring the temperature of the eraporator provides a signal to control the site of the orifice in the expancion vahe to regulate the flow of the refrigerant. d. Refrigerant passes through the evaporator (usually located inside the passenger compartment of the vehicle) where it evaporates (wums from atomized droplets to a gas). As it does so, the refrigerant absorbs hest from the passenger compartment and occupants [you []. An clectrically driven tan (evaporator blower) is used to fiow air from the passenger compartment, across the evaporator, and back into the passenger compartment. Do the following: - Draw your own system diskram for this air conditioner. - Drare a system boundary that separates your system from its erwironment. - Indicate quantities that cross your system boundary. Three types of quantities can cross system boundaries: Mass, Energy, and signals ftypically an effort vsriable with an ins gnificant quantity of a flow wariablel. 1. Massesi air 2. Energetic quantities: Combination of effort and flow variables, meaning power. They can be in forms such as linear mecharical, rotary mecharical, electrical, hydraulic, and pneumatic). They wil have both an effort and a flow variable. Examples might be the power to run the compressor and the power to run the fans. 3. Signals. These generally have nedie ble amounts of power and energy, so usualy the effort variable (a voltage that represents some measured cuantity is a significant quantity, while flow variable is essentially zero. Examples incluce the sigral from the themastat to tum the compressar on or off, the signal to tum a fan on or off, and the temperature probe controlling the orifice need e position. (7 pts) System components HA2042 just ans b.marks) (a) Explain how erroneous journal vouchers may lead to litigation and significant financial losses for a firm. (5 marks) ANSWER a): (b) Controls are only as good as the predetermined standard o 1. What happens to firms that routinely overpay forassets?2. Why do firms choose one form of deal paymentover another? Write a Python class that represents a cylinder:You will need to import the math package, like this: import mathCylinder needs an __init__ method that takes a parameter for the radius of the base, and can take a second parameter for the height. If it does not receive a parameter for height, it sets the height of the Cylinder to 1.Set the instance variables using try.. except so that if radius and height can not both be cast to floats, an exception is raised, to be handled in the calling code.An exception is also raised if the radius or height is less than 0. Give both of these exceptions appropriate error messages (like "radius may not be less than 0").If the parameters are correct, __init__ also sets an instance variable for volume to 3.14159 * math.pow(self._radius, 2) * self._heightCylinder also needs an appropriate __eq__ method. For the purpose of this question, two cylinders are equal if their volumes are within .001 (don't worry about the units; they might be CC or cubic inches) of each other. Use this code at the top of the method to return false if other is null:if other == None:return FalseCylinder also needs an appropriate __str__ method.Unlike in the RightTriangle exercise, for this one you do not need to write __add__ or __sub__ methods.Write driver code thatcreates a Cylinder using only one parameter, using a loop that continues until the user provides a valid parameter, using try..except to print the messages from any exceptionstakes user input for a second cylinder using two parameters, using a loop that continues until the user provides two valid parameterschecks whether the first Cylinder is equal to itselfchecks whether the first Cylinder is equal to the second one #4 Crash-Test A car (m-2500 kg; v=140 km/h) hits a wall (m infinite, v-0). The car becomes deformed and the crush zone (0.5 m) is compressed. Calculate the corresponding acceleration (assuming a constant value). Within which time interval does that compression happen? Try to find out, how fast each part of the airbag system therefore has to operate Answer all of the questions below. . Q.1.1 Distinguish between brief use case description and fully developed use case (4) description Please use your own words. Q.1.2 (13) Identify four use cases that has Commissioner as an Actor and use your own words to construct a brief use case description for each use case you have identified. Q.1.3 (13) Choose one of the Use Cases you have identified in Q.1.2 above and create a fully developed use case description. You do not have to include Flow of Activities and Exception Conditions. Please put your answer in a tabular form. g) A wire has a diameter of 5 mm, original length is 20m. Applying a force of 40 N causes the wire to extend by 0.5 mm. Calculate the following: i) The tensile stress. ii) The tensile strain. iii) Young's Modulus. The enzymes involved in the pyruvate dehydrogenase complex are:A. physically separated form each otherB. Crosslinked to each other by lipoid acid linkersC. covalently conned to coenzyme AD. Associated with each other in an ordered and complex array The arch of a bridge, which forms an arc of a circle, is modelled on a grid. The supports are located at \( (-15,0) \) and \( (15,0) \), and the highest part of the arch is located at \( (0,9) \). Wha All of the following brought Hitler support in Germany excepthis promise to uphold the Versailles Treaty in spite of its unpopularity. the borrowing' component in a financial plan relates to the logical first step of the market screening process is based on