The difference quotient that best approximates the instantaneous rate of change is 1.
What do you mean average rate of change?Average rate of change is rate at which one value within a function changes in relationship to another. The average rate of change is usually used to determine slope of a graphed function.
Let's explore how to find average rate of change and use linear and nonlinear functions to demonstrate it.
The average rate of change the formula is used to find the slope of a graphed function. To find average rate of change, divide the change in y-values by the change in x-values.
Finding average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.
We can define average rate of change of a function f(x) in interval [a, b] as:
[tex]r=\frac{f_{b}-f_{a} }{b-a}[/tex]
Particularly, if we want to find an approximation of rate of change for a particular value x', we can choose:
a < x' < b
Such that a and b are close to x'.
Then if we want to find the instantaneous rate of change of g at x = 0, we need to find the values of a and b really close to zero.
Looking at the table, we can choose:
a = -0.001
b = 0.001
(are two closer ones to zero)
Then rate of the change can be written as:
[tex]f(x)=\frac{g(0.001)-g(-0.001)}{0.001-(-0.001)}=\frac{2.001-1.999}{0.002}=1[/tex]
From that, we can conclude that a good approximation of instantaneous rate of change is 1.
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With your hand parallel to the floor and your palm upright, you lower a 3-kg book downward. If the force exerted on the book by your hand is 20 n, what is the book’s acceleration?.
According to the net force, the acceleration of the book is 16.47 m/s².
We need to know about force to solve this problem. According to second Newton's Law, the force applied to an object will be proportional to mass and acceleration. Hence, it can be written as
∑F = m . a
where F is force, m is mass and a is acceleration
From the question above, we know that
m = 3 kg
g = 9.8 m/s²
F1 = 20 N
Find the net force
∑F = F1 + W
∑F = 20 + m . g
∑F = 20 + 3 . 9.8
∑F = 20 + 29.4
∑F = 49.4 N
Find the acceleration
∑F = m . a
49.4 = 3 . a
a = 16.47 m/s²
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The area of an equilaterla triangle is increasing at a rate of 5 m^2/hr. find the rate at witch the height is chganging when the areai is:_________
The rate at which the height is changing is ( 5 / x ) m / hr
We know that,
Area of an equilateral triangle A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4
h = [tex]\sqrt{3}[/tex] x / 2
Where,
x = Side
h = Height
Given that,
dA / dt = 5 [tex]m^{2}[/tex] / hr
h = [tex]\sqrt{3}[/tex] x / 2
Differentiate both sides with respect to t
dh / dt = ( [tex]\sqrt{3}[/tex] / 2 ) ( dx / dt )
dx / dt = ( 2 / [tex]\sqrt{3}[/tex] ) ( dh / dt )
A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4
Differentiate both sides with respect to t
dA / dt = ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( dx / dt )
5 = ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( 2 / [tex]\sqrt{3}[/tex] ) ( dh / dt )
dh / dt = ( 5 / x ) m / hr
Rate of change of height is defined as the rate at which height of an object changes with respect to time. It is represented as dh / dt
Therefore, the rate at which the height is changing is ( 5 / x ) m / hr
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Explain briefly the trnsmission of radio waves
Answer: A radio wave is generated by a transmitter and then detected by a receiver. An antenna allows a radio transmitter to send energy into space and a receiver to pick up energy from space. Transmitters and receivers are typically designed to operate over a limited range of frequencies.
Explanation:
If the bar oa is rotating clockwise with a constant velocity and the collar slides freely, the direction of the reaction force on the collar will be:_______
The direction of the reaction force on the collar will be Non constrained motion direction .
What is the relationship between the magnitude of the angular velocity ω and that of the velocity v ?ω = v / r
Since the cylinder is wrapped about the string, it rolls without slipping with respect to the string. The constraint relationship to assure this kind of motion can be obtained by considering the relative velocity of the point on the cylinder that is in contact with the string with respect to the string it should be zero.
The velocity of the center of the cylinder,
v = dy (t) / dt, r and the rotation rate of the cylinder, ω
We have to first find the velocity of the contact point relative to the center of the cylinder. Since this ignores the translational motion of the entire cylinder with respect to the ground, we then need to add back in the cylinder's center of mass velocity to find the velocity of the contact point with respect to the ground.
So, v (contact) = ωr - v where,
ω is the angular velocity
v is the linear velocity
r is the radius
ω = v / r
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When an object falls through the air, its velocity increases and its acceleration:_________
a. increases.
b. decreases.
c. remains the same whether in air or in vacuum.
When an object falls through the air, its velocity increases and its acceleration decreases.
What is velocity ?A vector measurement of the rate and direction of motion is what is meant by the term "velocity." Simply said, velocity is the rate of movement in a single direction. Velocity may be used to gauge both the speed of a rocket launching into space and the speed of a car traveling north on a busy freeway.
As you might have anticipated, the velocity vector's scalar (absolute value) magnitude corresponds to the motion's speed. The first derivative of position with respect to time is known as velocity in calculus. There is a straightforward formula that combines rate, distance, and time to calculate velocity.
The following method is the most typical approach to get the constant velocity of an item traveling straight ahead:
r = d / t
The rate or speed is r. (sometimes denoted as v for velocity)
d is the traveled distance.
t is the amount of time needed to finish the movement
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What is the maximum number of comparisons that a binary search should do for a sorted array of 81,014 elements ?
The maximum number of comparison is 4502
Binary array : it is an array consist of only 0s and 1s only.
Binary search - an efficient algorithm for finding items from a sorted list.
it is called binary because it divide array into tow halves.
It is used to excess data more faster when the space is tight.
binary search will search the array by dividing it into two halves till it find the value.
The main advantage of it is that is more quicker than a serial search.
binary search algorithm can be implemented in the two ways :
1. Iteration method
2. Recursive method
the maximum number of comparisons is 4502.
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which are ways of transferring thermal energy? multiple select question. conduction radiation transference emission convection
The ways of transferring thermal energy are Conduction, Convection and Radiation.
Heat transfer is the movement of molecules from a region of higher temperature to a lower temperature. It can be done in three ways:
ConductionConvectionRadiationConduction is the heat transfer done through direct contact between two bodies. Convection is the heat transfer done by movement of fluids such as water or air. Radiation is the heat transfer done by electromagnetic waves.
Therefore, the ways of transferring thermal energy are Conduction, Convection and Radiation.
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A set of measurements that has high precision but low accuracy represents what sort of error?
In a lab setting, a systematic error frequently causes high precision with low accuracy. Either the measurer consistently makes the same error, or the measuring device has a fault. Even while a badly calibrated balance might consistently read the same mass, it will be far lower than the actual mass of the object.
What do you understand by accuracy?Accuracy is defined as "the degree to which the outcome of a measurement adheres to the correct value or a standard. basically refers to how closely a measurement fits the established value." The degree to which the outcome of a measurement complies to the proper value or a standard," is how accuracy is defined.
The more traditional term is "accuracy of measurement," which is defined as "... the degree to which the outcome of a measurement agrees with the genuine value of the thing being measured."
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Which of the solvents given is not commonly used for acquiring a 1h nmr spectrum?
The solvents that are not commonly used for acquiring a 1H NMR spectrum are the ones that contain [tex]^{1} H[/tex] nuclei.
[tex]^{1} H[/tex] NMR is also called as Proton Nuclear Magnetic Resonance. It is a method used to determine the structure of molecules of a substance.
For this [tex]^{1} H[/tex] NMR to work perfectly, the solvents must not contain [tex]^{1} H[/tex] nuclei. That is why Deuterated solvents are used. Some of the examples of deuterium solvents are chloroform, dimethyl sulfoxide, heavy water, etc.
Therefore, the solvents that are not commonly used for acquiring a 1H NMR spectrum are the ones that contain [tex]^{1} H[/tex] nuclei.
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What is one important difference between the glyoxylate cycle and the citric acid cycle?
The major difference is the cleavage of isocitrate by isocitrate lyase, resulting in succinate and glyoxylate, as opposed to the breakdown of isocitrate by isocitrate dehydrogenase.
What is glyoxylate cycle?A variant of the tricarboxylic acid cycle called the glyoxylate cycle is an anabolic mechanism that may be found in fungus, bacteria, protists, and plants. In order to synthesize carbohydrates, acetyl-CoA is converted to succinate in the glyoxylate cycle. When simple sugars like glucose or fructose are not available, the glyoxylate cycle in microorganisms enables cells to employ two carbons (C2 molecules) like as acetate to meet cellular carbon needs. Animals are often thought to lack the cycle, with the exception of nematodes during the early stages of embryogenesis.
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Match each problem with the correct utility.
the computer is running slowly
sensitive information is not secure
sending a large video file through email
computers in a small business that can't share
information
:: SOHO
:: compression utility
III I
:: encryption :: defragmentation utility
An encryption can be defined as a form of cryptography and it typically involves the process of converting or encoding information in plain text into a code, known as a ciphertext. Generally speaking, an information or data that has been encrypted it can only be accessed and deciphered by an authorized user.
This ultimately implies that, an encryption simply refers to a utility which can be used by an end user to to secure his or her sensitive information from unauthorized access or theft by a hacker (attacker).
In Computer programming, some examples of encryption algorithms include the following:
3DESAESRC4RC5RSAIn Computer technology, a defragmentation utility helps to reorganize (rearrange) the data stored on a disk drive and as such, it would make a computer system to run faster. Also, a compression utility is a type of utility which can be used to reduce the size of a large video file that is to be sent through an email.
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The four phases of matter include all of the following except _____.
a. water
b. gas
c. liquid
d. plasma
e. solid
The correct answer is option A. Water is not a state/ phase of matter
What are the states of matter?States are those phases that describe its physical attributes as well as how its constituent particles are arranged. Solid, liquid, gas, and plasma are the four main states of matter that can exist.
When something melts, it transitions from a solid to a liquid condition.
Water has a freezing point of 0°C.The melting point of flour is around 220 degrees Celsius, which is greater than that of salt and sugar. Sublimation is the process by which a solid transforms into a gaseous state, as in the case of camphor. Examples of changes in the states of matter include the melting of ice, the freezing of water, the burning of camphor, the melting of wax, and the production of precipitates.
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While passing a slower car on the highway, you accelerate uniformly from 17.5 m/s to 29.5 m/s in a time of 11.1 s. how far do you travel during this time?
When I accelerate uniformly from 17.5 m/s to 29.5 m/s in a time of 11.1 s, I travel 260.85 m
The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:
x = [(vi + vf) /2] * t
Where:
x = distancevf = final velocityvi = initial velocityt = timeInformation about the problem:
vi= 17.5 m/svf = 29.5 m/s t = 11.1 sx= ?Applying the distance formula, we have:
x = [(vi + vf) /2] * t
x = [(17.5 m/s + 29.5 m/s ) /2] * 11.1 s
x = [(47 m/s ) /2] * 11.1 s
x = (23.5 m/s) * 11.1 s
x = 260.85 m
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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An object that is dropped from a height H falls with a constant acceleration of g. The final
speed, v, just before it reaches the ground can be expressed as v = sqrt(2gh). By how much does the height need to change double the final velocity?
The height has to change by a factor of 1.
What is the height?We can obtain the height from which the object falls using the equations of kinematics under gravity. We can see that the object was dropped from a height thus u = 0 m/s.
We can the write;
v= √2gh
h1 = v^2/2g
When the final velocity is doubled, we have;
2v= √2gh
h2 =4v^2/2g
h2 = 2v^2/g
The height changes by;
2v^2/g - v^2/2g = v^2/g
Thus the height has to change by a factor of 1.
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What branch of science is the system-
atic study of God's physical creation
and how it works?
Answer:
Physical science
Explanation:
You accidentally drop an eraser out of the window of an apartment 15 m above the groun
e. How long will it take for the Eraser to reach the ground?
Answer:
1.8 seconds
Explanation:
Ignoring air friction
d = 1/2 at^2
15 = 1/2 (9.81) t^2 shows t = 1.75 = 1.8 seconds
You ride your bike at a constant speed of 5 for 300 a from your house to the mailbox What was your acceleration for the trip? (1 point)
00
05
O 300 s
Since the speed is the same through out, acceleration for the trip will be zero.
What is Acceleration ?Acceleration is the rate at which velocity is changing. It is a vector quantity.
If you ride your bike at a constant speed of 5 m/s for 300 s from your house to the mailbox, your acceleration for the trip will be equal to zero.
Because Acceleration = Change in speed ÷ time
Since the speed is constant, acceleration = 0/time = 0
Therefore, the acceleration for the trip is zero.
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Answer:
0 m/s^2
Explanation:
No change in speed or direction = constant velocity = no acceleration.
Which persuasive writing strategy involves quoting a consumer, who is satisfied with a specific product or service, in a news release?
In a news release, using a consumer who is happy with a particular good or service as a testimonial might be persuasive.
What do you understand by consumer?Consumers are described as people or organizations who utilize or consume goods and services. Customers might be consumers or exist solely as customers; they are the buyers of products and services inside the economy.
Businesses may select how to promote their goods and services most effectively by comprehending how consumers think, feel, and make decisions. This aids in predicting consumer behavior and helps marketers promote their already-available goods and services.
Consumer behavior is the study of how consumers choose things based on their needs, wants, and desires as well as how they purchase and utilize them.
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If the device produces 8.5 kw of power on a day when the waves are 1.4 m high, how many kilowatts will it produce when they are 0.625 m high?
The power generated by 1.4 m high waves is 1.69 kW.
We need to know about power to solve this problem. The power generated by waves can be determined as
P = 1/2 . μ . ω² . A² . v
where P is power, μ is the constant of wave media, ω is angular speed, A is amplitude and v is wave speed.
Power is proportional to amplitude squared. Hence
P ~ A²
From the question above, we know that
P1 = 8.5 kW
A1 = 1.4 m
A2 = 0.625 m
By using the ratio of power, we can write
P1 / P2 = A1² / A2²
8.5 / P2 = 1.4² / 0.625²
P = 1.69 kW
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Observations and inferences are important in science. How would you explain the difference between these two words?
Answer:
The difference between observations and inferences is observations uses one or more of your five senses to know or determine something. However, inferences are where you make an explanation for the observation. For example, you see steam rising off a coffee cup ( this is an observation). The coffee is hot ( this is an inference).
Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (let |a| = 22 lb and |b| = 16 lb. round your answers to one decimal place.)
Given,
The magnitude of the resultant force is 39.7 N and makes an angle of 49.5° with the x-axis.
The two given forces are vectors, thus they have to be resolved horizontally and vertically to determine their resultant.
So that:
Horizontal component = F Cos θ
Vertical component = F Sin θ
Thus, given that: a = 28 lb at 45° on x & y axis, and b = 12 lb at 30° below x-axis.
i. Resolving the vector horizontally, we have:
horizontal component = 28 Cos 45° + 12 Cos 30°
= 19.80 + 10.39
horizontal component, x = 30.19
ii. Resolving the vectors vertically, we have:
vertical component = 28 Sin 45° + 12 Sin 30°
= 19.80 + 6.0
vertical component, y = 25.80
a. Magnitude of the resultant force, |R| = [tex]\sqrt{x^{2} + y^{2} }[/tex]
= [tex]\sqrt{(30.19)^{2} +(25.80)^{2} }\\\\[/tex]
= 39.7124
|R| = 39.7 Newtons
b. The angle that the resultant makes with the positive x-axis can be determined by:
[tex]Tan\ \theta = \frac{x}{y} \\\\\theta = Tan^{-1} \frac{30.19}{25.80} \\\\= 49.4832\\\\\theta = 49.5\textdegree[/tex]
Therefore, the magnitude of the resultant force is 39.7 N and makes an angle with the x-axis.
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A car is decelerating at the rate of 3 km/s 2. if its initial speed is 66 km/s, how long will it take the car to come to a complete stop?
The car with an initial speed of 66 km/s will come to a complete stop at 22 s
The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:
t = (vf - vi) /a
Where:
vf = final velocityvi = initial velocityt = timea = accelerationInformation about the problem:
vi= 66 km/svf = 0 m/sa= - 3 km/s2t = ?Applying the time formula, we have:
t = (vf - vi) /a
t = (0 m/s - 66 km/s) / - 3 km/s2
t = (- 66 km/s) / - 3 km/s2
t = 22 s
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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PLEASE HELP, i really need the help because i dont understand
The y-component of the vector is 4.97 m.
What is a vector?A vector is a quantity that has both magnitude and direction.
To calculate the y-component of the vector in the diagram above, we use the formula below.
Formula:
Y = Hcos∅.......... Equation 1From the question,
Given:
H = 22.3 m∅ = 77.1°Substitute these values into equation 1
Y = 22.3(cos77.1)Y = 22.3×0.223Y = 4.97 m.Hence, the y-component of the vector is 4.97 m.
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Three identical capacitors are connected in parallel to a potential source (battery). if a charge of q flows into this combination, how much charge does each capacitor carry?
Each capacitor carries a charge of 1/3q as they are identical.
These capacitors are identical and the combination is connected in parallel to each other.So each should receive an equal portion of the total charge when received from the power source.If the combination is connected in series to each other, then each one would receive the same amount of charge, not a portion of the total charge (in such a case the total charge would be 3q).To know this more precisely, consider the simple formula used for a capacitor: [tex]Q = CV[/tex].In a parallel arrangement, the potential is the same for each one and since the capacitance is equal, the charge one would carry is the same as well.Then the total charge [tex]q[/tex] is the sum of each capacitor's charge which yields [tex]q = 3Q\,\,\to\,\,Q = \frac{q}{3}[/tex] .#SPJ4
Find the work done by a force f=8i-6j 9k that moves an object from the point (0,10,8) to the point (6,12,20) along a straight line. the distance is measured in meters and the force in newtons.
Work done is 158 joule
Given that, the force of a moving object is,
F = (8i - 6j + 9k) N
The object is moving from point (0,10,8) to the point (6,12,20)
Now we can calculate the displacement by the formula,
dr = (x2-x2)i + (y2 - Y2)j + (z2 - z2)k
Put all the values from the given values.
dr = (6 - 0)x + (12 - 10)j + (20 - 8)k
dr = (6i-2j+12k) meters
Now, the work done can be calculated as,
W = F.dr
W = (8i - 6j + 9k).(6i-2j+12k)
W = 158 J
Hence, work done is 158 joule
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Which has zero acceleration?
a. at rest.
b. moving at constant velocity.
c. in mechanical equilibrium.
d. all of these
e. none of these
At rest, when travelling at a constant speed, and when in mechanical equilibrium, there is no acceleration and answer choice D is correct.
How would you define acceleration?In mechanics, acceleration describes the rate at which a driving object's velocity changes over time. They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Depending on whether an object is moving faster, slower, or in a different direction, its velocity may change. Examples of acceleration include a falling apple, the moon orbiting the earth, and a car that has stopped at a stop sign. The car is positively accelerating if the speed is increasing. As the car slows down, its speed decreases. A decline in speed is referred to as negative acceleration. In both situations, the car is traveling ahead, yet one has a positive acceleration and the other a negative one.
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What differences would rutherford have observed if he used aluminum foil instead of gold foil?.
The gold sheet used was around 1000 atoms thick.
What differences would Rutherford have observed if he used aluminum foil instead of gold foil?The Rutherford observed that the use of aluminium foil will be better instead of gold foil, the reason is given below. The gold is very cheap metal so due to this property it can be easily turned into thin thin foil, Rutherford wants the thinnest layer as thin as possible. If any other metal foil is used in place of gold then also there will be no change in the observations if the metal foil to be used is as thin as gold foil.
So we can conclude that the gold sheet used was around 1000 atoms thick.
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A measure of central tendency called the _____ can be a particularly biased or misleading measure of central tendency when there are a few extreme scores.
A measure of central tendency called the mean can be a particularly biased or misleading measure of central tendency when there are a few extreme scores.
"The statistical metric that identifies a single value as representative of an entire distribution" is the definition of central tendency. It strives to give a precise account of all the facts. It is the lone value that best typifies or reflects the information gathered.
The mean, median, mode, and the midrange are the four indicators of central tendency. The arithmetic mean of the maximum and minimum values in a data set is used here to describe the midpoint or mid-extreme of a set of statistical data values.
A dataset's arithmetic mean (which is distinct from its geometric mean) is calculated by dividing all of the values by the total number of values. Due to the fact that the computation takes into account all values, it is the most widely used central tendency measure.
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A semiconductor device containing transistors, capacitors, and resistors is called a:____.
a. difference engine.
b. a diode.
c. an integrated circuit.
d. a radio.
e. a transformer.
Option C: A semiconductor device containing transistors, capacitors, and resistors is called an integrated circuit.
TransistorThe semiconductor device known as a transistor is used to switch or amplify electrical impulses.
One of the fundamental components of contemporary electronics is the transistor. It is made of semiconductor material and typically has at least three terminals for connecting to an electronic circuit.
The current flowing through another pair of the transistor’s terminals is controlled by the voltage or current provided to one set of those terminals.
A transistor can magnify a signal because the regulated (output) power can be greater than the controlling (input) power. Although many more transistors are found embedded in integrated circuits, some are packaged individually.
The first field-effect transistor was developed in 1947 by American physicists John Bardeen and Walter Brattain while working for William Shockley at Bell Labs.
The concept of a field-effect transistor was first proposed by the Austrian-Hungarian physicist Julius Edgar Lilienfeld, but it was not possible to actually build a working device at that time. The three received a shared 1956 Nobel Prize in Physics for their achievement.
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With an increase in strain rate, ductility ______ and tensile strength _____. a) decreases, decreases b) decreases, increases c) increases, increases d) increases, decreases
With an increase in strain rate, ductility decreases and tensile strength increases. Option b. decreases, increases is the correct answer
The ductility of materials decreases as the strain rate rises. The reason is that the material exhibits brittle behaviour. Material increases in tensile strength.
Ductility: A material's ductility refers to its capacity to withstand plastic deformation or drawing without breaking. As a result, it provides information on how "soft" or pliable the material is.
Tensile strength: Maximum load a material can bear without breaking when it is stretched, divided by the material's initial cross-sectional area.
Therefore, option b. is the correct answer for the given question
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