consider the following system. Dx/dt = 6x +13y Dy/dt = −2x + 8y find the eigenvalues of the coefficient matrix a(t). (enter your answers as a comma-separated list.)

Answers

Answer 1

The eigenvalues of the Coefficient matrix A(t) are 7 + 3i√2 and 7 - 3i√2.

The matrix A: A = |  6   13  |
     | -2    8   |
Next, we compute the determinant of (A - λI), where λ is an eigenvalue and I is the identity matrix:
det(A - λI) = |  6-λ  13  |
                   | -2     8-λ |
det(A - λI) = (6 - λ)(8 - λ) - (-2 * 13)
Now, solve the characteristic equation for λ:
(6 - λ)(8 - λ) + 26 = 0
λ^2 - 14λ + 48 + 26 = 0
λ^2 - 14λ + 74 = 0
To find the eigenvalues, solve this quadratic equation. In this case, the equation does not have real roots, so the eigenvalues are complex:
λ = (14 ± √(-112)) / 2
λ1 = 7 + 3i√2
λ2 = 7 - 3i√2
Therefore, the eigenvalues of the coefficient matrix A(t) are 7 + 3i√2 and 7 - 3i√2.

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Answer 2

To find the eigenvalues of the coefficient matrix A(t) for the given system, first write down the matrix:

A(t) = |  6  13 |
       | -2   8 |

Next, we need to find the determinant of (A(t) - λI), where λ represents the eigenvalues and I is the identity matrix:

A(t) - λI = | 6 - λ  13   |
            | -2    8 - λ |

Now, calculate the determinant:

(6 - λ)(8 - λ) - (-2)(13) = 0

Expand and simplify:

48 - 14λ + λ^2 - 26 = λ^2 - 14λ + 22 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

λ = (14 ± √(14^2 - 4(22)))/2 = (14 ± √(144))/2 = (14 ± 12)/2

The eigenvalues are:
λ1 = (14 + 12)/2 = 13
λ2 = (14 - 12)/2 = 1

So, the eigenvalues of the coefficient matrix A(t) are 13 and 1.

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Related Questions

True or false? if i were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit.

Answers

Answer: True

Explanation:

g wastewater is to be treated with aerated lagoons. You are considering two different design options: A) A single lagoon with a surface area of 180 m2 B) Two lagoons in series with surface areas of 90 m2 each. All ponds have a depth of 2 m. The flow rate of wastewater is 5000 L/day. The waste contains 600 mg/L of organic material that is readily biodegradable with a first-order rate constant of 0.35 day-1. What final effluent concentration of organic material would you expect for each design

Answers

The answer is 3 because I just took the test!

A cantilever beam has a length L and is loaded by a triangularly distributed load of maximum intensity q0 at B. (Solve this problem by integration the differential equations of the deflection curve. The beam has constant flexural rigidity E I.)

Answers

The Deflection due to Triangular load is 11q₀L⁴/120EI

What is deflection due to triangular load?

The deflection due to the triangular load is usually given as:

σ₁ = 11q₀L⁴/120EI

Deflection due to reaction (R[tex]_{b}[/tex])(σ₂) =

R[tex]_{b}[/tex]L³/3EI

⇒ σ₁ = σ₂⇒ 11q₀L⁴/120EI

= R[tex]_{b}[/tex]L/3EI= R[tex]_{b}[/tex]

= 11q₀L/40

What is the significance of deflection in a beam?

In terms of structural engineering, a beam or node moving from its initial location is referred to as deflection.

It occurs as a result of the loads and forces that are placed on the body.

Deflection, also known as displacement, can result from the weight of the body structure itself or from externally applied stresses.

What is the relevance of deflection due to triangular load?

A structure's deflection must be taken into account during design, and the consequences of not doing so can be disastrous.

Deflections may be caused by various loads. These include, among others,

ground pressureearthquakeswind loadsshear loadspoint loadsevenly distributed loads and uniformly distributed loads.

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A flexible hydraulic hose identified as mil-h-8788 will have a stripe running the length of the hose. This stripe?

Answers

Answer: This a system of equations question. What you will do is make an equation comparing the two lengths then make another one as the sum of the lengths.  H1 will stand for hose 1 and H2 will stand for hose 2.

so our first equation is H1=4*(H2)-20. We know this because H1 is 20 less than 4 times H2.

After landing equipment, a hydraulic flexible hose has been removing the everlasting form of a hose because of stress is called a save you high strain from extruding the seal among the transferring and desk-bound parts.

What are Hydraulics?

Hydraulics is a mechanical characteristic that operates via the pressure of liquid pressure. In hydraulics-based totally structures, mechanical motion is produced with the aid of contained, pumped liquid, normally via hydraulic cylinders transferring pistons.

Hydraulic structures paintings through using pressurized fluid to energy an engine. these hydraulic presses position pressure on a small amount of fluid for you to generate a massive amount of power. Hydraulic structures are capable of shifting heavier loads in addition to offering greater force than mechanical, electrical, or pneumatic systems. The fluid energy gadget approach can without difficulty address a huge weight variety without having to use gears, pulleys, or heavy leavers.

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what is the basic concept of the finite element method.​

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Answer:

The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements.

When converting liquid level units to sensor output signal units, you should first convert the liquid level units to _____ units

Answers

The answer is 2 because I just took the test!

When converting liquid-level units to sensor output signal units, you should first convert the liquid-level units to engineering units.

The engineering units are the actual physical measurements of the liquid level, such as meters, feet, inches, or any other relevant unit of length or depth.

Once the liquid level is expressed in engineering units, you can then proceed with the conversion to the sensor output signal units, which typically involves scaling the engineering units to match the range and sensitivity of the sensor's output.

This ensures that the sensor provides an accurate and meaningful representation of the liquid level, making it easier to interpret and use the data for various applications.

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What dimensions are used when measuring the area of a building

Answers

Answer:According to NEC 220.12,

“the floor area shall be calculated from outside dimensions of the buildings, dwelling unit, or other area involved.

The area should not include open porches, garages or unused or unfinished spaces not adaptable for future use”.

pa brainliest plss..thankss

Explanati

Area deals with two dimensions, or two directional measurements (length × width), so our answer will be meters squared or m 2 . Area deals with two dimensions, or two directional measurements (length × width), so our answer will be inches squared or in 2 .
Hope that helps:)

What advanced safety features are now standard on 2023 Z?

Answers

The advanced safety features that are now standard on 2023 Z are:

Pedestrian Detection and Automatic Emergency BrakingIntelligent Forward Collision Warning (IFCW).Blind Spot Alert.

What is 2023 Z?

The above is the short name or nickname for the All New 2023 Nissan Z coupe Sports car.

The care also features Advanced driver assist and safety technology which relieves the driver's everyday workload, allowing you to focus on what matters most.

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Structural Safety Assessment and Traffic Control Strategies of Widened Highway Bridges under Maintenance Works Requiring Partial Lane Closure

Answers

Structural Safety Assessment and Traffic Control Strategies of Widened Highway Bridges under Maintenance Works Requiring Partial Lane Closure journal is based on the  way and techniques that can be used in maintaining  the Safety on the road as well as the Assessment of Traffic Control.

What are the techniques in controlling the traffic?

There are Devices that are typically used in the traffic control, and this can  include speed bumps as well as the barricades to block streets.

Others techniques are:

turn prohibitions stop signs raised pavement markers.

Traffic restraint can also entails the includes programs  that can foster bicycle as well as the pedestrian travel.

The rapid structural safety assessment help in inspecting and evaluating the concrete structure as well in determining  the damaged structure if it is  unsafe for personnel within the building .

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Water enters a vertical jet with low velocity and a pressure of 350 kPa. What is the maximum height that the water can rise above the jet

Answers

The maximum height that the water can rise above the jet is: 35 meters.

Maximum height that the water can rise above the jet

Given:

P = 350 kPa = 350000 Pa

We would use pressure(p)  formula to determine the maximum height that the water can rises above the jet by solving for h (height).

Using this formula

Pressure(P) = P₀ + ρgh

Where;

P₀ represent Pressure at the fluid's surface

ρ represent Density of the fluid = 1000 kg/m³

g represent acceleration due to gravity = 10 m/s².

h represent height

Solving for h (height)

350000 = 0 + (1000 × 10 ×h)

350000 = 10000h

Divide both side by  10000h

h = 350000/10000

h = 35 meters

Therefore the maximum height that the water can rise above the jet is: 35 meters.

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If a dielectric material, such as teflon®, is placed between the plates of a parallel-plate capacitor without altering the structure of the capacitor, how is the capacitance affected?.

Answers

The capacitance is affected is that the capacitance increases because of the insertion of Teflon.

What is capacitance?

A capacitance is known to be a form of a device that is said to be used to save some measures of charges in any kind of an electrical circuit.

Note that the capacitor functions on the principle that the capacitance of a conductor is said to go up if an earthed conductor is  taken close to it.

Therefore, The capacitance is affected is that the capacitance increases because of the insertion of Teflon and so the teflon tends to widen the capacitance.

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Modern aircraft are designed in a way that, when all seats are occupied, the baggage compartment is full, and all fuel tanks are full, the aircraft is:

Answers

Modern aircraft are designed in a way that, when all seats are occupied and baggage is full, and all fuel tanks are full, the aircraft is overloaded.

What is aircraft storage?

Aircraft storage refers to all storage systems in an aircraft for human transportation and also to transport products among countries.

The aircraft storage system is well calculated to work is a maximum capacity in commercial fly lines.

In conclusion, modern aircraft are designed in a way that, when all seats are occupied and baggage is full, and all fuel tanks are full, the aircraft is overloaded.

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Technician A says that a voltage drop on the ground side of a bulb won’t affect its brightness because the electricity has already been used up. Technician B says that a voltage drop is one way to determine if there is unwanted resistance in a circuit. Who is correct?

Answers

Answer:

  Technician B

Explanation:

For a given circuit current, the voltage drop is an indication of the resistance in the circuit.

If the voltage drop on the ground side of a bulb is unexpectedly high, it means the circuit resistance is unexpectedly high. Technician B is correct.

Someone claims that the volume flow rate in a circular pipe with laminar flow can be determined by measuring the velocity at the centerline in the fully developed region, multiplying it by the cross-sectional area, and dividing the result by 2. Do you agree

Answers

The answer is 6 because I just took the test!

An isolation transformer whose main purpose is to reduce voltage spikes will have a turns ratio of?

Answers

Answer:

An isolation transformer whose main purpose is to reduce voltage spikes will have a turns ratio of 1 to 1.

This is due to the windings input and output having the same waveform and amplitude.

When a system is in deep vacuum;
a. never add refrigerant to the system.
b. never use a micron gauge.
c. never energize the compressor.
d. never energize system fans and blowers.

Answers

When a system is in a deep vacuum, never energize the compressor. The correct option is a.

What is a deep vacuum?

A deep vacuum is a system in which the boiling point of liquid lowers down and the temperature lowers for outgassing. They help in freeze drying, metallurgy, distillation, etc. It used 500 or less than 500 microns for deep vacuum.

Vacuum tubes, such as cathode ray tubes, and electron microscopes are made possible by the electronic resistivity of the vacuum. Torr is the unit used to measure vacuums.

Thus, the correct option is a. never energize the compressor.

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A______solid-state relay is an electronic device that performs the same function as an electromechanical relay.

Answers

Answer: Non-programmable

Explanation:

A non-programmable solid-state relay is an electronic device that performs the same function as an electromechanical relay.

What is a solid-state relay?

An SSR is an electrical switching device that turns on or off when an external voltage (AC or DC) is applied across its control terminals. They perform the same job as an electromechanical relay, but because they include no moving parts, they have a longer operational lifetime.

Solid-state relays are the semiconductor analogs of electromechanical relays and can thus control electrical loads. When energized, the solid-state relay is a fairly complex device with a simple purpose: to activate a single output load.

Therefore, a non-programmable solid-state relay is a type of electrical device that functions similarly to an electromechanical relay.

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Manual transmission has a driver-operated clutch and a movable gear selector. In manual transmission, the gears are engaged .....................

Answers

In the case above about manual transmission, the gears are engaged manually.

What is manual transmission?

The Definition of the term manual transmission is regarded as a kind of a system where there is the changing gears in a manual way.

Hence, In the case above about manual transmission, the gears are engaged manually is correct.

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Metal wireways are sheet metal troughs with _____________ for housing and protecting electrical conductors and cable.

Answers

Answer:

Metal wireways are sheet metal "U"s with removable housing for protecting electrical equipment, wires, and cables.

Explanation:

These are especially used to run wire in manufacturing environments.

To put out a class D metal fire, you must _______ the fire.

Answers

To put out a class D metal fire, you must smother the fire and eliminate the oxygen element in the fire.

What is a Class D fire?

A class D fire is a type of fire that cannot be extinguished by water. This is because adding water to it reacts with other elements in the fire intensifying the fire even more.

Smothering in this context involves adding a solution like carbon dioxide (CO2) into the fire, this results in a reduction of oxygen in the atmosphere surrounding the class D fire.

By so doing, smothering the fire eliminates the oxygen element in the fire, thereby extinguishing the fire.

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When you approach an uncontrolled intersection, you should treat it as though which sign is present?

Answers

Answer: A yield sign

Explanation:

Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt.% at a position of 4 mm into an iron-carbon alloy that initially contains 0.10 wt.% C. The surface concentration is to be maintained at 0.90 wt.% C, and the treatment is to be conducted at C. Use the diffusion data for -Fe in Table 5.2

Answers

Answer:

the carburizing time necessary to achieve a carbon concentration is 31.657 hours

Explanation:

Given the data in the question;

To determine the carburizing time necessary to achieve the given carbon concentration, we will be using the following equation:

(Cs - Cx) / (Cs - C0) = ERF( x / 2√Dt)

where Cs is Concentration of carbon at surface = 0.90

Cx is Concentration of carbon at distance x = 0.30 ; x in this case is 4 mm = ( 0.004 m )

C0 is Initial concentration of carbon = 0.10

ERF() = Error function at the given value

D = Diffusion of Carbon into steel

t = Time necessary to achieve given carbon concentration ,

so

(Cs - Cx) / (Cs - C0) = (0.9 - 0.3) / (0.9 - 0.1)

= 0.6 / 0.8

= 0.75

now, ERF(z) = 0.75; using ERF table, we can say;

Z ~ 0.81; which means ( x / 2√Dt) = 0.81

Now, Using the table of diffusion data

D = 5.35 × 10⁻¹¹ m²/sec at (1100°C) or 1373 K

now we calculate the carbonizing time by using the following equation;

z = (x/2√Dt)

t is carbonizing time

so we we substitute in our values

0.81 = ( 0.004 / 2 × √5.35 × 10⁻¹¹ × √t)

0.81 = 0.004 / 1.4628 × 10⁻⁵ × √t

0.81 × 1.4628 × 10⁻⁵ × √t = 0.004

1.184868 × 10⁻⁵ × √t = 0.004  

√t = 0.004 / 1.184868 × 10⁻⁵

√t = 337.5903

t = ( 337.5903)²  

t = 113967.21 seconds

we convert to hours

t = 113967.21 / 3600

t = 31.657 hours

Therefore, the carburizing time necessary to achieve a carbon concentration is 31.657 hours

When performing a vertical analysis which income statement item do you use to determine the cost contribution for each expense category? (What is the denominator?)

Review Later
Net income
Sales
Gross profit
Operating expenses

Answers

Sales represent the income statement item used in verticla analyses in order to determine the cost contribution for each expense category (Option C).

What is a vertical analysis?

In business, a vertical analysis represents a methodology used to examine financial statements that are ordered as specific points.

A vertical analysis analyzes numbers for only one period, conversely to the horizontal analyses that generally involve many different periods.

In conclusion, sales represent the income statement item used in verticla analyses in order to determine the cost contribution for each expense category (Option C).

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Vivian's Violins has sales of $326,000, contribution margin of $184,000 and fixed costs total $85,000. Vivian's Violins net operating income is Blank______. Multiple choice question. $241,000 $57,000 $99,000

Answers

Based on the calculations, Vivian's Violins net operating income is equal to: D. $99,000.

How to calculate net operating income?

Mathematically, the net operating income of an individual or business firm can be calculated by using this formula:

Net operating income = Contribution margin - Total fixed costs

Given the following data:

Sales = $326,000Contribution margin = $184,000Fixed costs total $85,000

Substituting the given parameters into the formula, we have;

Net operating income = $184,000 - $85,000

Net operating income = $99,000.

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Water enters a vertical jet with low velocity and a pressure of 350 kPa. What is the maximum height that the water can rise above the jet

Answers

The maximum height that the water can rise above the jet is; 35 m

How to find the height pressure of water?

The formula for pressure here is;

P = P₀ + ρgh

where;

P₀ is the pressure at the fluid's surface.

ρ is the density of the fluid. (density of water = 1000 kg/m³)

g is the acceleration due to gravity = 10 m/s².

h is height of rise of fluid

Now, the pressure at water surface is zero because the pressure the atmosphere exerts on the water is equal to the pressure the water exerts on the atmosphere. Thus, P₀ = 0 Pa

We are given P = 350 kPa = 350000 Pa. Thus;

350000 = 0 + (1000 * 10 * h)

350000 = 10000h

h = 350000/10000

h = 35 meters

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A line has a slope of 2/5 and contains the point (-10, -6). What is the y-intercept (b) of the line?

Answers

Answer:

y-intercept = -2

Explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this formula, "m" represents the slope and "b" represents the y-intercept. Remember how the Point (-10, -6) contains one "x" value and one "y" value. Using these values in addition to the slope, you can plug them into the equation to find the y-intercept.

x = -10 (from point)

y = -6 (from point)

m = 2/5

y = mx + b                                            <----- Slope-intercept form

y = (2/5) x + b                                       <----- Plug 2/5 into "m"

-6 = (2/5)(-10) + b                                  <----- Plug in "x" and "y" values from point

-6 = -4 + b                                             <----- Multiply 2/5 and -10

-2 = b                                                    <----- Add 4 to both sides

Therefore, the value of the y-intercept is b = -2. The complete equation of the line is:

y = (2/5)x - 2

Soru No 3
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Answers

D) Never in a million years

True or false? if i were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit.

Answers

if a person were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit and this is a true statement.

What is the role of a resistor in an AC circuit?

A resistor is known to be a form of a passive tool that does not create or consume power.

Note that it often changes electrical energy into heat and as such, if a person were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit and this is a true statement.

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Which is not one of the primary characteristic of unit testing:

Answers

Answer:

Unit testing is a software development process in which the smallest testable parts of an application, called units, are individually and independently scrutinized for proper operation. This testing methodology is done during the development process by the software developers and sometimes QA staff. The main objective of unit testing is to isolate written code to test and determine if it works as intended.

Unit testing is an important step in the development process, because if done correctly, it can help detect early flaws in code which may be more difficult to find in later testing stages.

Unit testing is a component of test-driven development (TDD), a pragmatic methodology that takes a meticulous approach to building a product by means of continual testing and revision. This testing method is also the first level of software testing, which is performed before other testing methods such as integration testing. Unit tests are typically isolated to ensure a unit does not rely on any external code or functions. Testing can be done manually but is often automated. It might be helpful

A handsfree device may be used if it can be activated or deactivate with a?

Answers

A handsfree device may be used if it can be activated or deactivate with a cellphone.

What is hands-free?

Handsfree is a device which when connected to a cell device can be used in listening to audio, video and messages.

A driver can also activate or deactivate with a swipe when connect to the vehicle audio device.

Therefore,

A handsfree device may be used if it can be activated or deactivate with a cellphone.

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how much work does a tugboat need to do in order to move a barge from rest to a velocity of 0.550 m/s? the mass of the barge is 879,000 kg. the mass of the tugboat is insignificant. Analysts reporting on companies will pay close attention to the disclosures regarding pension benefits. Key points include all of the following except: Multiple ChoiceA) to help analysts determine whether fund assets are large enough to satisfy currently anticipated pension benefit payouts, FASB ASC Topic 715 requires firms to provide a table that lists the dollar benefits expected to be paid in each of the ensuing five years and in the aggregate for the five years thereafter.B)while companies with overfunded plans can suspend funding for long periods and use the cash for other operating purposes, underfunded plans may reflect past and continuing cash flow difficulties.C) the common rule of thumb is that a 1% decrease in discount rate would increase PBO by 17.0% whereas a 1% increase would decrease it by 14.5%.D) because of high assumed discount rates, most pension plans have remained underfunded with funding ratios ranging between 69% and 86% since 2008. strike insurance is a form of labor racketeering in which the union threatens a walkout and the employer pays to assure a steady supply of labor.T/F create the following relationships using existing fields and enforcing referential integrity. do not cascade update or cascade delete. each room is of a single room type. the practice of a shaman creating art linked to ritual and to accomplish tasks, like ensuring a successful hunt, or bringing rain for crops is an example of _______________. 5. The interior angle of a polygon is 60 more than its exterior angle. Find the number of sides of the polygon 100 tickets are sold for $1 each there is $25 prizes and a $10 prize what is the expected value for a person that buys a ticket round to the nearest cent _____ is used by many organizations and subunits within organizations to help members identify with the culture and help preserve it. calculate the hydronium ion concentration of a solution in which the concentration of nah2po4 is 0.25m and the concentration of na2hpo4 is 0.45 m. the ka for h2po4- is 6.2*10-8 Ivy Corporation gave 74 people a bonus. If Ivy had given 3 more people bonuses, Ivy would have rewarded 13 of the workforce. How large is Ivys workforce? The energy of muscle contraction is derived from the following except: . O B.muscle glycogen O C. lactic acid D. Creatine phosphate 10.8. Using the data in Table 18.1, compute the resistance of an aluminum wire 5 mm in diameter and 5 m in length.(a) What would be the current flow if the potential drop across the ends of the wire is 0.04 V?(b) What is the current density?(c) What is the magnitude of the electric field across the ends of the wire? State the weighted Interval Scheduling problem precisely and completely. Describe the steps involved in the Dynamic Programming solution of the weighted Interval Scheduling problem as we did in class. For each step, you should include what is done in the step (how the step is to be performed and what is the result obtained and the complexity of execution of the step with a brief justification). No coding is necessary. Assume you are given n activities in any arbitrary order and each activity is specified with its start time, finish time, and weight (value). Be precise (not verbose) in your statements. zn(s) hgo(s) h2o zn(oh)2(s) hg(l) identify the oxidation and reduction. The nuclear mass of 48Ti is 47.9359 amu. Calculate the binding energy per nucleon for 48Ti in J/nucleon. Convert this from active to passive they are panting my office today in the case of a strength/power athlete such as a gymnast who is rotating between apparatuses, which energy system replenishes atp and cp levels during the recovery period? the concept of a human or moral right is central to the utilitarian ethical tradition. true or false? Which of the following is the correct IUPAC name for the tertbutyl substituent?a. (1,1-dimethylethyl)b. (1,1,1-trimethyl)c. (1-methyl-2-propyl)d. 2-methyl-2-propyl) a client is diagnosed with a spontaneous pneumothorax necessitating the insertion of a chest tube. what is the best explanation for the nurse to provide this client?