All digital systems that perform arithmetic operations must indicate _______ and ________ for numbers.
A. size, base
B. sign, magnitude
C. sign, base
D. magnitude, base

Answers

Answer 1

For numbers, any digital systems that perform arithmetic operations must display the "sign" and "magnitude."

A "digital system" is a collection of components that uses hardware, software, and networks. For instance, a computer has a central processing unit, a hard drive, a keyboard, a mouse, and a monitor, among other things. One system may be made up of a multitude of different pieces. There are just a few discrete values available for signals in digital systems. Analog systems take values from a continuous set, whereas Mixed Signal Systems use both Digital and Analog components. The digital and analog systems are commonly used to represent signals. The numerous digital systems that are all around us include computers, smartphones, scanners, cash registers, and digital ticket readers.

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Related Questions

Prove that in a 2’s complement number system addition overflows if and only if the carry from the sign position does not equal the carry into the sign position. Consider the three cases: adding two positive numbers, adding two negative numbers, and adding two numbers of opposite sign.

Answers

Consider the four sub-cases for each of those three cases two positives, two negatives, one of each . Show that some of those sub-cases are not possible in each case. Then examine each sub-case to see if it indicates overflow.

What is 2's complement system?

Two's complement is a mathematical operation that converts a positive binary number with equivalent value reversibly into a negative binary number with equivalent value.

it occurs using the binary digit with the greatest place value to indicate whether the binary number is positive or negative.

Consider each of those three cases' four sub-cases. There are two positives and two negatives, with one of each.

Demonstrate that some of the sub-cases are not feasible in each case. Then, for each sub-case, determine whether it indicates overflow.

Thus, by this it can be proved that in a 2’s complement number system addition overflows if and only if the carry from the sign position does not equal the carry into the sign position.

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A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [100] direction. If the critical resolved shear stress for this material is 1.98 MPa, calculate the magnitude of applied stress necessary to cause slip to occur on the (111) plane in the direction.

Answers

Answer:

the magnitude of the stress necessary to cause slip to occur on the (111) plane in the \([1 0 \overline 1]\) direction is 4.85 MPa

Explanation:

From the given information;

To determine the angle \(\phi\) between the direction [100] and [111]; we have:

\(\phi = cos ^{-1} [\dfrac{u_1u_2+v_1v_2+w_1w_2}{ \sqrt{(u_1^2+v_1^2+w_1^2) (u_2^2+v_2^2+w_2^2) }}}\)

where;

[u₁,v₁,w₁] and [u₂, v₂, w₂] are directional indices.

replacing 1 for u₁ , 0 for v₁ and 0 for w₁  ;

also replacing 1 for u₂, 1 for v₂ and  1 for w₂ ; we have :

\(\phi = cos ^{-1} [\dfrac{1*1+0*1+0*1}{ \sqrt{(1^2+0^2+0^2) (1^2+1^2+1^2) }}}\)

\(\phi = 54.7^0\)

To determine the angle \(\lambda\) for the slip direction \([1 0 \overline 1]\)

\(\lambda= cos ^{-1} [\dfrac{u_1u_2+v_1v_2+w_1w_2}{ \sqrt{(u_1^2+v_1^2+w_1^2) (u_2^2+v_2^2+w_2^2) }}}\)

replacing 1 for u₁ , 0 for v₁ and 0 for w₁  ;

also replacing 1 for u₂, 1 for v₂ and  -1 for w₂ ; we have :

\(\lambda = cos ^{-1} [\dfrac{1*1+0*0+(0*-1)}{ \sqrt{(1^2+0^2+0^2) (1^2+0^2+(-1^2)) }}}\)

\(\phi = cos ^{-1} [\dfrac{1}{\sqrt{2}}]\)

\(\lambda = 45^0\)

The yield strength  for the slip process \([1 0 \overline 1]\) can now be calculated as:

\(\sigma_x = \dfrac{t_{xr}}{cos \phi \ \ cos \lambda}\)

where

\(t_{xr}\) = 1.98 MPa

\(\sigma_x = \dfrac{1.98}{cos 54.7^0 \ \ cos 45}\)

\(\sigma_x = \dfrac{1.98}{0.5779 *0.7071}\)

\(\mathbf{\sigma _x = 4.85 \ MPa}\)

Hence, the magnitude of the stress necessary to cause slip to occur on the (111) plane in the \([1 0 \overline 1]\) direction is 4.85 MPa

How to write an essay of informative speaking

Answers

Answer:

Do not use I me my we. Less exclamation points, bigger words like "Pompous" Lots of uptight language, as if you are at an interview. structure should be precise and sharp, sharper than Angelina Jolie's cheekbones

Explanation:

An engineer is interested in the relative strength of machine parts made of two different metals. She measures the force required to break 200 parts made out of plastic, and 200 parts made out of aluminum. After conducting her measurements, she learned that a small number of the plastic parts may have had cracks in them before testing, which would have caused them to break at ridiculously low force levels. (There was no possibility of cracked aluminum parts.) Given the uncertainty about the number of cracked parts in her sample, what measure of central tendency would probably be the best to provide a fair comparison between the relative strengths of the two materials

Answers

Answer:

Median

Explanation:

Since the engineer is interested in the relative strength of machine parts made of two different metals. And after conducting her measurements, she learned that a small number of the plastic parts may have had cracks in them before testing, which would have caused them to break at ridiculously low force levels. Whereas, there was no possibility of cracked aluminum parts.

This small crack in the plastic part will affect the mean (average) value if it is used as a central tendency for comparison. This same thing will affect the mode and the range of the value of strength.

The best measure of central of tendency to use is median since the affected cracked part in the plastic is minimal.

Give the largest positive number that can be represented in 13 bits for the two cases:
a) Unsigned number, and b) Signed number
Show the binary, decimal, and hexadecimal representations of the number for each case

Answers

The largest positive number that can be represented in 13 bits for the two cases are

A) Unsigned number

The largest unsigned no can be represented with 13bits as

\((2)^n - 1 = (2)^{13} - 1 = 8191\)

In Binary - \((1111111111111)_2\)

In decimal - \((8191)_{10}\)

In hexadecimal - \((1FFF)_{16\)

B) Signed number

The largest signed no can be represented with 13bit as

\(2^n = 2^{13} = 8192\)

The range is from \((2^n-1)\)

therefore, the maximum value is \((4096)_{10}\)

In binary - \((1000000000000)_2\)

In hexadecimal - \((1000)_{16}\)

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As you encounter unfamiliar key torms in your eText, how can you leamn their definitions? Note that key terms may oppoar in boid or in a diferent color in your eted Select all that apply. O Select the Search icon and enter the term into the seurch feld. A definitian will show up in the Key torms saction of Eie fesulfs. O Select the Playlist icon and select the module you want to hear O Select the Table of Contents or the Navigation icon and navigate to the Glossary. O Select the key term in your eText and a pop-up defintion wel appear

Answers

A) Select the Search icon and enter the term into the search field. A definition will show up in the Key Terms section of the search results.

What is Key Terms?

Key Terms are words or phrases used to describe a concept or idea. They are often used in the field of academia to help define the scope of a particular study or research project. Key Terms are also used in business and legal documents to provide a concise and precise description of a concept or idea. By providing clear definitions for each key term, it helps to ensure that all parties involved in a discussion or agreement are on the same page.

C) Select the Table of Contents or the Navigation icon and navigate to the Glossary.
D) Select the key term in your eText and a pop-up definition will appear.

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As more and more lamps are connected in series to a battery, the brightness of each lamp goes ____.

Answers

When lamps are connected in series to a battery, the brightness of each lamp decreases. This is due to the nature of a series circuit and the principles of electrical current flow.

In a series circuit, the components (in this case, lamps) are connected one after another in a single path. This means that the same current flows through each lamp in the circuit. When lamps are connected in series, the total resistance in the circuit increases because the individual resistances of the lamps add up. As a result, the current flowing through the circuit remains the same, but it gets divided among the lamps.

According to Ohm's Law, the brightness of a lamp is directly proportional to the current passing through it. Therefore, as the current is divided among multiple lamps connected in series, each lamp receives a smaller portion of the total current. This reduced current results in a decrease in the brightness of each lamp.

Additionally, lamps have a certain operating voltage, which is the voltage required to produce their optimal brightness. In a series circuit, the total voltage of the battery is distributed across the lamps. As more lamps are added in series, the voltage available for each lamp decreases. Consequently, the lamps operate at a lower voltage than their optimal level, leading to a further decrease in brightness.

It's important to note that this explanation assumes the lamps have the same resistance and are designed to operate under the same voltage. If the lamps have different resistances or are designed for different voltages, the brightness may be affected differently.

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Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in) and tip radius of curvature of 1.2 x 10-3 mm (4.7 x 10-5 in.) when a stress of 1200 MPa (174,000 psi) is applied.

Answers

Answer:

the theoretical fracture strength of the brittle material is 5.02 × 10⁶  psi

Explanation:

Given the data in the question;

Length of surface crack α = 0.25 mm

tip radius ρ\(_t\) = 1.2 × 10⁻³ mm

applied stress σ₀ = 1200 MPa

the theoretical fracture strength of a brittle material = ?

To determine the the theoretical fracture strength or maximum stress at crack tip, we use the following formula;

σ\(_m\) = 2σ₀\((\) α / ρ\(_t\) \()^{\frac{1}{2}\)

where α is the Length of surface crack,

ρ\(_t\) is the tip radius,

and σ₀ is the applied stress.

so we substitute

σ\(_m\) = (2 × 1200 MPa)\((\) 0.25 mm / ( 1.2 × 10⁻³ mm ) \()^{\frac{1}{2}\)

σ\(_m\) = 2400 MPa × \((\) 208.3333 \()^{\frac{1}{2}\)

σ\(_m\) = 2400 MPa × 14.43375

σ\(_m\) = 34641 MPa

σ\(_m\) = ( 34641 × 145 )psi

σ\(_m\) = 5.02 × 10⁶  psi

Therefore, the theoretical fracture strength of the brittle material is 5.02 × 10⁶  psi

what will be the power absorbed by an electric heater, which takes a current of 6A and has a voltage rating of 110 volts​

Answers

The power absorbed by the electric heater is;

P = 660 Watts

We are given;

Current; I = 6 A

Voltage; V = 110 V

Now, we want to find the power that is absorbed by the electric heater.

The formula for electric power is;

P = IV

Where;

I is current

I is current V is voltage

Thus:

P = 6 × 110

P = 660 Watts

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Tech A says that a faulty vacuum booster can affect engine operation. Tech b says that steal brake Ponce can be replaced with a copper line, as it easier to bend into shape. Who is correct ?

Answers

Answer:

Tech A

Explanation:

A faulty vacuum booster can actually affect the operation of an engine. Engine stalls when brakes are applied. And this can happen when the diaphragm that is inside the brake booster fails. The failing thus allows air to bypass the seal. When the brakes are then pressed, the engine will actually feel like it will stall, and the idle will most probably drop. Also, asides a reduction in the break performance quality, a stalling engine is very bad and can result to many negative effects.

3. Why do plastic and composite fenders require different bolts?

Answers

Plastic and composite fenders require different bolts because fenders combine energy absorption and deflection qualities.

What are plastics?

Plastics are defined as a class of substances, either artificial or natural, that can be molded while still soft and subsequently hardened to maintain the desired shape. The thickness grade for plastic sheeting most frequently used is 6 mil. This is 0.006 inch, or six thousandths of an inch.

Fasteners are regarded as tools that are used in a variety of applications to form a solid junction. While some fasteners are permanently linked, the majority allow joints to be broken apart or withdrawn without harming the pieces that were joined.

Thus, plastic and composite fenders require different bolts because fenders combine energy absorption and deflection qualities.

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(20 pts) At a given input to the thrust lever, after passing through the compressor, air enters to the
combustor of a jet engine with M1 (see data table) p1=7 atm and T1=570 K. Fuel is supplied through the
fuel nozzles with a fuel-air ratio by mass of 0. 5. The heat released during the combustion is HR (see data
table) J per kilogram of fuel. Assuming =1. 4 for fuel-air mixture, calculate the M2 ,p2 and T2 at the exit
of the combustor. Also, calculate the maximum fuel-air ratio beyond which the flow will be choked at the
exit. INFORMATION

M1(MACH)=0. 4

HR=9. 4*106

Answers

Answer:

To calculate M2, p2, and T2 at the exit of the combustor, we can use the isentropic relations for a nozzle, assuming that the flow through the combustor is adiabatic and isentropic.

Using the isentropic relations, we can relate the Mach number, pressure, and temperature at the exit of the combustor to their values at the inlet of the combustor.

M2 = sqrt((2/(gamma-1))*((T1/(1+((gamma-1)/2)*M1^2))*(1+((gamma-1)/2)*M1^2*0.5*(gamma+1)*0.5*(1+0.5*(gamma-1)*M1^2)^(-1)*(1-0.5*(gamma-1)*M1^2*0.5*(gamma+1)*0.5*(1+0.5*(gamma-1)*M1^2)^(-1)*(1+0.5*(gamma-1)*M1^2*0.5*(gamma+1)*0.5*(1+0.5*(gamma-1)*M1^2)^(-1)*((gamma+1)/(2*gamma))^((gamma+1)/(2*(gamma-1))))))^(-1))

where gamma = 1.4 is the specific heat ratio of the fuel-air mixture.

Substituting the given values, we get:

M2 = sqrt((2/(1.4-1))*((570/(1+((1.4-1)/2)*0.4^2))*(1+((1.4-1)/2)*0.4^2*0.5*(1+0.5*(1.4-1)*0.4^2)^(-1)*(1-0.5*(1.4-1)*0.4^2*0.5*(1+0.5*(1.4-1)*0.4^2)^(-1)*(1+0.5*(1.4-1)*0.4^2*0.5*(1+0.5*(1.4-1)*0.4^2)^(-1)*((1.4+1)/(2*1.4))^((1.4+1)/(2*(1.4-1))))))^(-1)) = 0.818

p2 = p1*(1+0.5*(gamma

Explanation:

2.12.5: Four Corners

Answers

Answer:

speed(0)

square_length = int(input("What is the length of the square?"))

def draw_square():

   pendown()

   for i in range(4):

       forward(square_length)

       left(90)

   penup()

   

penup()

setposition(-200, -200)

draw_square()

penup()

setposition(-200, 200 - square_length)

draw_square()

penup()

setposition(200 - square_length, 200 - square_length)

draw_square()

penup()

setposition(200 - square_length, -200)

draw_square()Explanation:

Statement and decision testing exercise
Scenario: A vending machine dispenses either hot or cold drinks. If you choose a hot drink (e.g. tea or coffee), it asks if you want milk (and adds milk if required), then it asks if you want sugar (and adds sugar if required), then your drink is dispensed.

a. Draw a control flow diagram for this example. (Hint: regard the selection of the type of drink as one statement.)

b. Given the following tests, what is the statement coverage achieved? What is the decision coverage achieved? Test 1: Cold drink Test 2: Hot drink with milk and sugar

c. What additional tests would be needed to achieve 100% statement coverage? What additional tests would be needed to achieve 100% decision coverage?

Answers

To achieve 100% statement coverage, additional tests are needed to cover different combinations of drink preferences (milk and sugar). For 100% decision coverage, tests should cover both the selection of drink type and the decisions related to adding milk and sugar.

a. Control Flow Diagram:

Start

|

V

Choose Drink Type (Hot or Cold)

|

V

IF Hot Drink

|   |

|   V

|   Ask for Milk Preference

|   |

|   V

|   IF Milk Required

|   |   |

|   |   V

|   |   Add Milk

|   |   |

|   |   V

|   |   Ask for Sugar Preference

|   |   |

|   |   V

|   |   IF Sugar Required

|   |   |   |

|   |   |   V

|   |   |   Add Sugar

|   |   |   |

|   |   |   V

|   |   V

|   V

|   Dispense Hot Drink

|

V

ELSE (Cold Drink)

   |

   V

   Dispense Cold Drink

|

V

End

b. Given the tests:

Test 1: Cold drink

Test 2: Hot drink with milk and sugar

Statement Coverage achieved: The statement coverage achieved would be 10 out of 15 statements (66.7%).

Decision Coverage achieved: The decision coverage achieved would be 2 out of 3 decisions (66.7%).

c. Additional tests for 100% statement coverage:

Test 3: Hot drink without milk and sugar

Test 4: Hot drink with milk only

Test 5: Hot drink with sugar only

Test 6: Hot drink without milk and without sugar

Additional tests for 100% decision coverage:

Test 7: Cold drink

Test 8: Hot drink with milk and sugar

Test 9: Hot drink without milk and sugar

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What historic event / period marked the beginning of the manufacturing boom in the mid-
to-late 18th century (1700s)?

Answers

Answer:

Industrial  revolution too bad at english languge not fleunt so if say a whole story of this i will not make secene but answer is to it industrial revolution.

Explanation:

Machines: The housings for aircraft engines, wind turbine generators, and the Enterprise's warp drives are all referred to by what French loanword?

Answers

Nacelle is a French loanword is to describe the housings for aircraft engines, wind turbine generators, and the Enterprise's warp drives.

What more can be said about the word Nacelle?

Generally speaking, a "nacelle" is an aerodynamic enclosure or housing that is used to describe an aircraft, wind turbine, or spacecraft's engine, generator, or gearbox.

The nacelle, which is said to be found at the top of the tower of a wind turbine, houses the generator, gearbox, and other vital parts of the turbine.

To reduce drag and increase the effectiveness of the turbine, the nacelle is aerodynamically built. For upkeep and repairs, it also offers a secure, contained environment. When it comes to jet engines in airplanes, the nacelle provides a similar function by acting as an aerodynamic housing for the engine and other equipment.

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We have a credit charge that is trying to process but we do not remember signing up and email login is not working? Is there a way to check?

Answers

Answer:

Yes

Explanation:

In such a case, one way to check the credit charge is to contact your bank, doing so would allow the bank to check your account properly to determine where the transaction was originated from.

Another way you could check is to contact the online merchant where such a transaction was initiated.

Draw the logic circuit for each of the following. For each gate, determine if it generates either EVEN or ODD parity bit and finds the output for the given input data: (Remember: A XOR generates EVEN parity bit. A XNOR generates Odd Parity bit, whatever how many inputs they have.)
Data Inputs Which kind parity bit can it generate?
4-input XOR, input data-1001 Even Parity Bit ODD Parity Bit
5-input XOR, input data-10010
6-input XOR, input data-101001
7-input XOR, input data 1011011

Answers

Answer:

a) 4-input XOR, input data-1001  = 0 Even parity Bit

b)  5-input XOR, input data-10010 = 0 Even parity Bit  

c) 6-input XOR, input data-101001 = 1 Even parity Bit

d) 7-input XOR, input data 1011011 = 1 Even parity Bit

Explanation:

a) 4-input XOR, input data-1001  ;  generates 0 Even parity Bit

b)  5-input XOR, input data-10010 ; generates 0 Even parity Bit  

c) 6-input XOR, input data-101001 ; generates 1 Even parity Bit

d) 7-input XOR, input data 1011011 ; generates 1 Even parity Bit

Attached below is the Logic circuits of the data inputs

Draw the logic circuit for each of the following. For each gate, determine if it generates either EVEN

Which of the following sentences correctly uses commas after prepositional phrases

Answers

Answer:

You didn't write full questions

Explanation:

Where are options? You say following but there is no any option

Describe the differences between case hardening and through hardening, insofar as engineering applications of metals are concerned.

Answers

Answer:

The answer is below

Explanation:

Case hardening is a form of steel hardening that is applied on mild steel with a high temperature of heat.

It results in material forming a hard surface membrane, while the inner layer is soft.

It is mostly used for universal joints, construction cranes, machine tools, etc.

On the other hand, Through hardening is a form of steel hardening in engineering that involves heat treatment of carbon steel.

It increases the hardness and brittleness of the material.

It is often used for axles, blades, nuts and bolts, nails, etc.

A soil sample, taken from a borrow pit has a specific gravity of soil solids of 2.66. The sample was taken to a materials laboratory and tested. The results of a standard Proctor test are tabulated below.

Weight of Soil (lb) Moisture Content (%)
3.20 12.8
3.78 13.9
4.40 15.0
4.10 15.7
3.70 16.6
3.30 18.1

The maximum dry density in lb/ft3 is most nearly:_______

Answers

Answer:

115 Ib/ft^3

Explanation:

To determine the maximum dry density in Ib/ft3 we have to calculate :

Bulk unit weight ( yb ) ; W / v

Dry unit weight ( yd. ) :  yb / ( 1 + w )

For every set of data given

assuming  v = 1/30 ft^3

calculating for the 3 data set ( maximum dry density )

weight of soil (W) = 4.40

moisture content (%) (w) = 15.0 = 0.15

Bulk unit weight (yb) = 4.40 / (1/30)  = 132 Ib/ft^3

Dry unit weight ( yd. ) = 132 / ( 1 + 0.15 ) = 114.702 Ib/ft^3

therefore after calculations the maximum dry density in Ib/ft^3 ≈ 115 Ib/ft^3

will give brainliest what are 3 good projects to do with wood or cardboard or paper or an old drone when you are a beginner



if you do not have 3 good projects then please dont answer and just comment them but if you have more than 3 that would be great for you to answer.

Answers

I have some ideas!

1. A simple wall shelf
2. Cup holder
3. Candle holder

Hope this helps!

Answer:the inflating Ballon expirement

Explanation:

Which of the following Tosca elements need to be added to requirements as per best practice 

Answers

Templates are tosca elements that need to be added to requirements as per best practices.

Why do Templates need to be added?

Before you can run your tests, you must perform tasks manually that Template Selection enables you to automate. You can carry out the following actions in Step 3:

• The Test Case templates you want to employ for your tests should be chosen.

• Make a list of the test cases that will be executed or an execution list.

• Make a set of functional or non-functional criteria called a requirement set to evaluate the business risk of a test project.

What are Templates?

A file used as a model for a new document is known as a template. Templates have pre-filled placeholder fields and expertly crafted styles and layouts. When creating a new file, many word processors, presentations, desktop publishing products, and even website providers include template galleries that you can peruse.

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T/F docker containers give the exact same isolation properties as type 2 virtual machines

Answers

False, Docker containers do not give the exact same isolation properties as type 2 virtual machines.

Both Docker containers and type 2 virtual machines provide a certain level of isolation, Docker containers have a lighter-weight isolation mechanism, sharing the host operating system's kernel, whereas type 2 virtual machines use a hypervisor to provide more complete separation between the host system and the virtualized environment.

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why is it important to know where your online information comes from?

Answers

It is very important to know where online information comes from in order to validate, authenticate and be sure it's the right information

What are online information?

Online informations are information which are available on the internet such as search engines, social handles and other websites

In conclusion, it is very important to know where online information comes from in order to validate, authenticate and be sure it's the right information

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So i have a Question so if you have somebody in your family and you dont share nothing with that person what do that person feel like so if they dont do nothing how would you feel.

Answers

Answer:

Who care

Explanation:

Lol

Consider the flow of mercury (a liquid metal) in a tube. How will the hydrodynamic and thermal entry lengths compare if the flow is laminar

Answers

Answer:

Explanation:

Considering the flow of mercury in a tube:

When it comes to laminar flow of mercury, the thermal entry length is quite smaller than the hydrodynamic entry length.

Also, the hydrodynamic and thermal entry lengths which is given as DLhRe05.0= for the case of laminar flow. It should be noted however, that Pr << 1 for liquid metals, and thus making the thermal entry length is smaller than the hydrodynamic entry length in laminar flow, like I'd stated in the previous paragraph

The term route of entry on an SDS refers to the way a _____ enters the body

Answers

Answer:

No matter what u post on a football page, some fatherless dude will either say "pessi" or "penaldo"

The term route of entry on an SDS refers to the way a _____ enters the body

draw the fbd that is required to determine the internal forces at point j. (you must provide an answer before moving on to the next part.) the fbd that is required to determine the internal forces at point j is

Answers

The FBD (Free Body Diagram) that is required to determine the internal forces at point J should include all external forces acting on the system and any reactions or forces present at point J.

This FBD will allow for the determination of the internal forces, such as shear forces and bending moments, at point J.
To determine the internal forces at point J, you need to draw a Free Body Diagram (FBD). In this FBD, you should include all the external forces acting on the object at point J, such as gravitational force, tension, friction, and any applied forces. Once you have drawn the FBD, you can use equilibrium equations (sum of forces in horizontal and vertical directions equals zero) to solve for the unknown internal forces. After finding the internal forces at point J, you can move on to the next part of your problem. Forces are physical quantities that describe the interactions between objects or systems. They can cause a change in motion or deformation in an object. Some common types of forces include gravitational force, electromagnetic force, frictional force, and normal force. Forces can be described by their magnitude, direction, and point of application. Newton's laws of motion provide a framework for understanding the behavior of objects under the influence of forces. Understanding forces is essential in many fields, including physics, engineering, and biomechanics, as it allows for the prediction and control of the behavior of systems under different conditions.

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A small ship capable of making a speed of 6 knots through still water maintains a heading due east while being set to the south by an ocean current. The actual course of the boat is from A to B, a dis- tance of 10 nautical miles that requires exactly 2 hours. Determine the speed vC of the current and its direction measured clockwise from the north.

Answers

This question is incomplete, the missing diagram is uploaded along this answer below;

Answer:

the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively

Explanation:

Given the data in the question and as illustrated in the diagram below;

The absolute velocity of the ship Vs is 6 Knots due east

so we convert to meter per seconds

Vs = 6 Knots × \(\frac{0.51444 m/s}{1 Knots}\) = 3.0866 m/s

Next we determine the relative velocity of the ship Vs/c

Vs/c = AB / t

given that distance between A to B = 10 nautical miles which requires 2 hours

so we substitute

Vs/c = 10 nautical miles / 2 hrs

Vs/c = [10 nautical miles × \(\frac{1852 m}{1 nautical-miles}\) ] / [ 2 hrs × \(\frac{3600s}{1hr}\) ]

Vs/c = 18520 / 7200

Vs/c = 2.572 m/s

Now, from the second diagram below, { showing the relative velocity polygon }

Now, using COSINE RULE, we calculate the velocity current.

Vc = √( V²s + V²s/c - 2VsSs/ccos10 )

we substitute

Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × cos10 ) )

Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × 0.9848 ) )

Vc = √( 9.527099 + 6.615184 - 15.6361 )

Vc = √0.506183

Vc = 0.71 m/s

Next, we use the SINE RULE to calculate the direction;

Vc/sin10 = Vs/c / sinθ

we substitute

0.71 / sin10 = 2.572 / sinθ

0.71 / 0.173648 = 2.572 / sinθ

4.0887 = 2.572 / sinθ

sinθ  = 2.572 / 4.0887

sinθ = 0.62905

θ = sin⁻¹( 0.62905 )

θ = 38.98°

So, angle measured clock-wise will be;

θ = 270° - 38.98°

θ = 231.02°

Therefore, the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively

A small ship capable of making a speed of 6 knots through still water maintains a heading due east while
A small ship capable of making a speed of 6 knots through still water maintains a heading due east while
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