We may not consider the use of** hair samples **today because **DNA **analysis is more modern.

The term **DNA **refers to the molecule that contains the** genetic material **of the living things. Hence, we could use the DNA sample to be able to solve very difficult cases. This is because the DNA sample can be able to tell the exact identity of the person that involved,

Before the advent of the DNA, the hair sample was one of the very reliable ways be which evidence could be gathered to solve crimes. Hence; Modern** DNA analyses** have made testimony using hair samples obsolete.

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Missing parts;

Which of the following statements is most true regarding the use of testimony on hair samples in courts today?

Hair samples are replacing DNA as an easily available, go-to source for identifying suspects

Modern changes in the discipline mean that any police officer can provide testimony on hair samples

Modern DNA analyses have made testimony using hair samples obsolete

There’s solid research that should lead us to be skeptical of testimony based on hair samples

If it takes 20 N to move a box, how much power will be needed to move the box a distance of 5meters in 5 seconds?

**Answer:**

It will need **20 Watts** power to move the box 5 meters in 5 seconds.

**Step-by-step explanation:**

The** power** is defined as the **work per** unit **time** or the rate of doing work:

W=dL/dt

Where de **work** L, can be calculated by multiplying the** force** by the displacement d:

L=F.d

To this example, F and D are known, therefore the work is:

L=20N . 5m=40 Nm

We know that the work is doing within a time of 5 seconds:

W= 40 Nm / 5s = 20 Nm/s = **20 Watts**

a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg , what is the momentum of the tackling dummy after the hit assuming the lineman stops instantly after impact?

A 115 kg lineman is working on tackling drills. if he is **running **at 2.8 m/s and hits a tackling dummy with a mass of 55 kg, then the **momentum **of the tackling dummy would be 322 kg-m/s.

It can be defined as the product of the **mass **and the speed of the **particle**, it represents the combined effect of mass and the speed of any particle, and the **momentum **of any particle is expressed in Kg m/s unit.

As given in the problem a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg ,

By using the **conservation **of the momentum,

Momentum before the collision = momentum after the collision

The **momentum **of the tackling dummy = m × v

= 2.8 × 115

=322 kg-m/s

Thus, the **momentum **of the tackling dummy would be 322 kg-m/s.

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what factors affect skill-related fitness and how does each affect it?

Several factors affect your **skill-related fitness **and your skills, including heredity, practice etc .

Skill-related fitness is have six different components; agility, speed, power, balance, coordination, reaction time.

Several factors affect your skill-related fitness and your skills, including **heredity**, practice etc

for example some people are able to run faster than others or react quick because they inherited these traits from their parents. A person who did not inherited a tendency in these areas from their ancestors ,may have more difficulty performing skills that require those abilities.

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Hydrochloric acid and sodium hydroxide can be combined to form sodium chloride and water. Which best explains the reaction?

The mass of sodium hydroxide will result in the same mass of sodium chloride.

The total mass of hydrochloric acid and sodium hydroxide will result in a lower total mass of sodium chloride and water.

The mass of hydrochloric acid will result in the same mass of sodium chloride.

The total mass of hydrochloric acid and sodium hydroxide will result in the same total mass of sodium chloride and water.

THE ANSWER IS D

The statement that best describes the reaction is as follows: The total **mass** of hydrochloric acid and sodium hydroxide will result in the same total **mass** of sodium chloride and water (option D).

The **law** of **conservation** of **matter** states that matter can neither be created nor destroyed. This law means that the **mass** that enters and leave a system is accounted for.

The **law** of **conservation** of **mass** explains the input and output of **mass** in a chemical reaction such that the mass of the reactants must be equal to the **mass** of the products.

According to this question, hydrochloric acid (HCl) and sodium hydroxide (NaOH) can be combined to form sodium chloride and water.

This means that the total amount of **matter** of the **reactants** (hydrochloric acid and sodium hydroxide) must equate the total amount of **matter** of the products (sodium chloride and water).

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Heat waves are defined by the difference in temperature compared to the normal _________ typical of a region.

The difference in **temperature **from the average temperature for a region defines a **heat wave**.

A **heat wave **is an extended period of unusually hot weather that usually lasts longer than days.

**Heat waves **can occur in both low and high humidity conditions. They have the capacity to cover a wide area, exposing too many **people **to harmful heat.

An extremely dangerous weather event known as a heat wave occurs when **temperatures **rise considerably above 90° F. Due to the extreme heat and high **humidity **levels, an area becomes extremely warm for an extended period of time.

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gas giants have many moons than terristcal planets due to having higher ___ ?

Gas giants have more moons than terrestrial **planets **due to having higher masses.

Giant **planets **are composed of low boiling point substances rather than other solid substances but massive solid **planets **can also exist. There are four giant **planets **in the Solar System i.e. Jupiter, Saturn, Uranus, and Neptune. They are composed of hydrogen and helium atom i.e. Jupiter and Saturn whereas Uranus and Neptune are composed of ice, rock, hydrogen, and helium.

The giant **planets **have more moons as compared to the terrestrial planets because of their big masses which leads to stronger gravitational fields. Giant **planets **also occupy greater space and have larger volumes of mass in their surrounding atmosphere.

So we can conclude that due to having higher masses, Gas giants have many moons as compared to terrestrial **planets**.

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X 24. A man drives a car and records the distance he travels on a distance- *0/2

time graph. At one point he gets stuck in traffic and does not move for

one hour. This point on the graph the slope will be horizontal. Why is this correct?

The distance-time **graph **will show the **slope **as horizontal for the time in which the man don't move.

**How to find slope of a graph?**

The **slope **formula rise/run is used to get the slope from a **graph**. The first thing we must do when given a line's graph and asked to determine its equation is to determine its slope. In order to determine the **slope **from a **graph**, we can take any two points on the line (x1, y1) and (x2, y2) and use the formula (y2 - y1) / (x2 - x1).

In the distance-time **graph **the distance is represented at y-axis and the time is represented at x-axis. So, In the time in which the man stops moving (stuck in the traffic) there is no change in distance but the times keeps changing or increasing that's why at the point he gets stuck in traffic and does not move for one hour. This point on the **graph** the **slope **will be horizontal.

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a singly charged positive ion has a mass of 3.3x10-26 kg. after being accelerated from rest through a potential difference of 933 v, the ion enters a magnetic field of 1.43 t along a direction perpendicular to the field. calculate the radius of the circular path of the ion in the field.

A singly charged positive ion has a** **mass of 3.3x10-26 kg. after being accelerated from rest through a** potential difference** of 933 v, the ion enters a magnetic field of 1.43 t along a direction perpendicular to the field. The** **radius of the circular path of the ion in the field is (r)= 1.982 cm.

Energy is a term that means the object is affected by some amount of force and move a distance. That is called the **energy**. It can be measured in Joule.

To calculate the radius we are using the formula here,

r= mu/Bq

Where we are given,

m = The mass of single positive charged ion.= 3.3×10⁻²⁶kg.

q= The charge of the single positive charged ion.= 1.602×10⁻¹⁹ C

B = The magnetic field for the electric field. = 0.92 T

But we don't know the term, u= the velocity of the single positive charged ion.

So we have to calculate the velocity of the single positive charged ion. To calculate the velocity we are using the formula,

(1/2)mu²=qv

Here we are given,

v= The potential difference of the electric field. = 933v.

We have to calculate the velocity=u, as Conservation of energy we know,

(1/2)mu²=qv

Or,(1/2)mu²=ev

Or, u²= (2×1.602×10⁻¹⁹×933)/(3.3×10⁻²⁶)

Or, u=91325.9 m/s.

So from this we know the velocity of the ion, u=91325.9 m/s.

Now, we have to calculate the radius in a magnetic field= r,

r= mu/Bq =mu/Be

Or, r= 3.3×10⁻²⁶×91325.9/0.92×1.602×10⁻¹⁹

Or, r=0.01982m

Or, r=1.982 cm.

So from the calculation we can surely say that, The radius of the circular path of the ion in the field is (r)= 1.982 cm.

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A scientific model can be used to

**Scientific models** area unit accustomed make a case for and predict the behaviour of real objects or systems.

A system of ideas, events, or processes is described physically, mathematically, conceptually, or conceptually in an exceedingly **scientific model**. By victimisation their scientific experience to produce explanations that create it doable to forecast the patterns, scientists work to recognise and comprehend the patterns that exist in the environment.

**Scientific model** illustrations include:

a simulation of the sun, moon, and earth's motions (which you participated in last year) a way for statement eclipses. The weather will be foretold victimisation models that describe weather events.

**Models** will assist you in mentally imagining one thing that's difficult to ascertain or comprehend. Models will aid in scientific prediction, understanding of processes, and communication of ideas.

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Two electromagnetic waves are traveling through a material. Wave 1 has a maximum electric field strength that is three times the maximum field strength of wave 2. How do the average intensities of the waves compare?.

Wave 1's intensity is nine times greater than Wave 2's. An **electromagnetic wave** carries both magnetic and electric energy when it moves.

An electromagnetic wave carries both magnetic and **electric energy** when it moves. Both waves contribute equally to the energy of electromagnetic waves. It is assumed that wave 1 has an electric field E that is three times greater than wave 2's maximal electric energy E'.

Thus, we can state:

E/E' = 3

We are aware,

The wave's intensity is determined by,

I = 1/2eE²c

Where,

I represents the wave's power,

e is a free space permittivity,

E represents the wave's energy.

The speed of light is c.

the strength of wave 1 right now

I1 = 1/2eE1²c

second wave

I2 = 1/2eE²c

Currently, dividing the two intensities,

I1/I2 = E1²/E2²

We are aware,

E/E' = 3

So,

I1/I2 = 9

I1 = 9I2

Thus, we can state:

Wave 1's **intensity **is nine times greater than Wave 2's.

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a rigid bar with mass m, length l, and a uniformly distributed positive charge q is free to pivot about the origin in the presence of a spatially uniform electric field e⃗

a. V(y)=V-E(y) b. U=vq-1/2QEL.cosФ c. V=EL/2 d. **angular speed** of the bar as it passes Ф=0° is W=[tex]\sqrt{3QE/ML}[/tex]

You were already familiar with the ideas of **velocity **and speed. The idea of** angular speed** and velocity, however, is what needs to be understood in terms of physical numbers. Angular motion is the term for when an item is expected to travel along a circular path while making a specific angle. The idea of angular speed and angular **velocity **is derived from the object's angular motion. Let's examine these ideas in greater depth. Assuming you are rotating a ball in a circular orbit, the angular speed can be defined as follows.

A body's rate of angle change over time as it rotates in a circular orbit is known as its angular speed. The definition of angular **velocity **is similar to that of linear velocity when an object is moving with some speed in a circular orbit.

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A cougar with a mass of 80 kg is standing at the edge of a cliff. Find the cougar's potential energy if the cliff is 70 m high. show your work !!!

The **potential energy **of the 80kg **cougar **at a height of 70m is 54880 Joules.

**Potential energy **is simply the energy a body possesses due to its position.

It is expressed mathematically as;

P.E = mgh

Where m is mass, h is height and g is acceleration due to gravity ( g = 9.8m/s² )

Given the data in the question;

Mass of the cougar m = 80kgHeight h = 70mPotential energy P.E = ?Plug the given values into the potential energy formula above and solve.

P.E = mgh

P.E = 80kg × 9.8m/s² × 70m

P.E = 54880kgm²/s²

P.E = 54880 Joules.

Therefore, the **potential energy **of the **cougar **is 54880 Joules.

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A 11.0kg ball traveling at 13.0m/s is crashed into from behind by a 14.0kg ball traveling at 22.0m/s in the same direction. What is the velocity of the first ball if the second slows down to 16.2m/s after the collision?

Let **p **be the total linear momentum of the system before the collision and **p'** the total linear momentum of the system after the collision. Let **p₁₁** and **p₁₄** be the linear momentum of the 11.0kg ball and the 14.0kg ball before the collision, and let **p₁₁'** and **p₁₄' **be their linear momenta after the collision.

According to the **Law of Conservation of Linear Momentum**, the total linear momentum of the system before and after the collision remains the same. Then:

Let **v** be the unknown speed of the 11.0kg ball after the collision. Find the value of **p₁₁, p₁₄, **and** p₁₄'**. Find an expression for **p₁₁'** in terms of **v** and replace all the values into the above equation. Solve for **v**.

The linear momentum of a particle with mass **m** and velocity **v** is:

Then:

[tex]\begin{gathered} p_{11}=(11kg)(13.0\frac{m}{s})=143kg\cdot\frac{m}{s} \\ \\ p_{14}=(14kg)(22.0\frac{m}{s})=308kg\cdot\frac{m}{s} \\ \\ p^{\prime}_{11}=(11kg)\cdot v \\ \\ p^{\prime}_{14}=(14kg)(16.2\frac{m}{s})=226.8kg\cdot\frac{m}{s} \end{gathered}[/tex]Then:

[tex]\begin{gathered} p_{11}+p_{14}=p_{11}^{\prime}+p_{14}^{\prime} \\ \\ \Rightarrow143kg\cdot\frac{m}{s}+308kg\cdot\frac{m}{s}=(11kg)\cdot v+226.8kg\cdot\frac{m}{s} \\ \\ \Rightarrow143kg\cdot\frac{m}{s}+308kg\cdot\frac{m}{s}-226.8kg\cdot\frac{m}{s}=(11kg)\cdot v \\ \\ \Rightarrow224.2\cdot\frac{m}{s}=(11kg)\cdot v \\ \\ \Rightarrow v=\frac{224.2kg\cdot\frac{m}{s}}{11kg}=20.381818\ldots\frac{m}{s} \\ \\ \therefore v\approx20.4\frac{m}{s} \end{gathered}[/tex]**Therefore, the velocity of the first ball after the collision is 20.4m/s.**

a cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. if the diameter and height of the cylinder are d and l, respectively, derive an expression for the velocity of the cylinder as a function of time, t. discuss what will happen as t → [infinity]. can this device serve as a viscometer?

When there is relative motion between the fluid layers or between the fluid and solid surface, the fluid's internal property known as viscosity is created. This relative motion is being resisted by **viscosity**.

Derivations of the equations of motion—the connections for the conservation of mass and momentum—in rectangular,

coordinates that are spherical and cylindrical. The entire body of experimental data suggests that the fundamental equations of fluid mechanics are in fact those listed below, and that they apply to any circumstance where a Newtonian **fluid **is flowing, in theory.

**Viscosity**, a characteristic of fluids, is produced when there is relative motion between the fluid layers or between the **fluid **and solid surface. **Viscosity **prevents this relative motion from happening.

Unfortunately, due to their all-encompassing nature, their analytical solution is challenging or impossible unless the circumstances are quite straightforward.

However,

These "Navier-Stokes equations" must be understood for the following reasons.

reasons:

1. They result in the analytical and precise resolution of some basic yet significant problems.

issues.

2. They serve as the foundation for additional chemical engineering research in various fields.

3. A few reasonable simplification assumptions can frequently result in

for many engineering problems, approximation solutions are eminently acceptable purposes. Typical examples can be found in the study of boundary layers, the use of films to cover substrates, waves, lubrication, and inviscid (irrotational) flow.

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an initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 n. the coefficient of static friction between the box and the floor is 0.35. (a) what should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

a) The **angle **between the cable and the horizontal in order to pull the greatest possible amount of sand is 19°. b) The weight of the sand and box in that situation is 3.3x10³ N.

A similar scenario is depicted with a free-body diagram and in the textbook's illustration, where the unknown angle is represented by the symbol. We employ the same system of coordinates as in that figure.

a) Newton's second law thus results in

x : T cosФ - f = ma

y : T sinФ + Fn-mg = 0

With a = 0 and f = f s, max = s F N, we may solve for the **mass **of the box-and-sand (as a function of **angle**) as follows:

m = T/g (sinФm + cosФm/us )

Hence, in order to determine the **angle **m that corresponds to the greatest **mass **that may be drawn, we will solve using calculus techniques.

dm/dt = T/g (sinФm + cosФm/us ) = 0

As a result, tan m = s is obtained, and for s = 0.35, m = 19 is obtained.

(b) The result of entering our value for m into the formula we discovered for the **mass **of the box and sand is m=340 kg. This is equivalent to a weight of mg=3.3x10³ N.

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Is the exoplanet like earth in terms of its distance from its star? Explain your answer

Every planet in the **solar** **system** orbits the Sun. Planets known as **exoplanets** orbit other stars. **Astronomers** search for exoplanets by observing the effects that these **planets** have on the **stars **they **orbit**.

Any planet outside of our solar system is an exoplanet. The **majority** of **exoplanets** orbit other **stars**, while rogue planets—free-floating exoplanets that are unattached to any star—orbit the galactic center.

Since **liquid** **water **is necessary for all known forms of life, an **exoplanet** that is too near or too far from its host star is less likely to support life. Additionally, some primordial compounds may require **ultraviolet** light to form, but a **hyperactive** host star can blast the nascent planet, removing its atmosphere.

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electromagnetic radiation with a maximum wavelength of 540 nm(5.4×10−7 m) is needed for the study of the photoelectric effect in potassium atoms. what is the approximate frequency that corresponds to this wavelength?

At a speed of two times ten to the eighth and violent. 5, 40 times 10 to the power -9 meters is written as. This leads to the conclusion that frequency F is equivalent to 5.6 times. Turn 14 times every second. Therefore, the given **electromagnetic radiation** requires this frequency.

In this problem, we have a given violent electromagnetic radiation, and we need to determine the frequency that corresponds to that **violent electromagnetic radiation**.

The chosen wavelength is lambda. I called at five minutes and forty nanometers—540 times 10 to the power—or nine meters. Considering that one nanometer equals 10 to the power -9 meters. Now, sea upon lambda finds frequency.

The value of C is three in 2, ten to the power eight meters per second, **violent**, and the speed of light in a vacuum. 5, 40 times 10 to the power -9 meters is written as. This leads to the conclusion that frequency F is equivalent to 5.6 times. Turn 14 times every second. Therefore, the given **electromagnetic radiation **requires this frequency.

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__________________________1. She is caught in a wind that blows toward the

equator from about 30° N and 30° S of the

equator. She is in the_______________

This is science

She is caught in a **wind** that blows toward the **equator** from about 30° N and 30° S of the equator. She is in the **trade wind**. This science is called **Hadley cell**.

It follows the movement of wind blows from one **direction** to the other such as the one which blow from north to **south** or **east** to west. The trade wind are produced by **warm moist air** rising near the equator.

Now, within the context of the task given above, when the movement wind which blows toward the equator from about 30° N and 30° S of the equator is known as the trade wind.

So therefore, the **movement** of wind from the same certain degrees from North and South is called **trade** wind.

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17. A ball rolls off a lab table at 5 m/s horizontally. The table is 1.2 meters tall.

a. How long is it in the air?

b. How far from the table does it hit the ground?

c. What are the x and y speeds just before it hits the ground?

The ball is in the air for 0.24 seconds, the ball hits the ground 2.46 meters far from the table and the** x speed** is 0m/s and** y speed** is 5m/s.

**Velocity **of the ball is 5m/s and the height of the table is 1.2 meters.

a. We know,

**Velocity = distance/time**

5 = 1.2/time

Time = 1.2/5

Time = 0.24 seconds.

The time taken by the ball to reach the ground is 0.24 seconds.

b. The ball after rolling of the table will behave like **Horizontal projectile.**

**Horizontal range R** formula,

R = V.√(2h/g)

Putting all the values,

R = 5.√(2×1.2/9.8)

R = 5×0.49

R = 2.46 meters.

c. When the ball reaches the ground,

**X speed** is 0m/s and **Y speed **is 5m/s.

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if you are on top of mount Everest and do a small hop without moving forward, would you still be pulled down by gravity? explain it and also answer my other newest question.

**Explanation:**

Gravity would still pull you down although it wouldn't affect you as much because there is less gravitational pull in high places such as Mt. Everest.

rank the capacitors on the basis of the charge stored on the positive plate. rank from largest to smallest. to rank items as equivalent, overlap them.

Capacitors on the basis of charge stored on positive plates become stable. Large ones should be more wild, smaller ones are less large an urgent. When overlapped, the plates collide causing earthquakes.

A rod pr is balanced on a pivot at the end r while a string is used to support the rod at p. the weight of the rod is 9n, acts at a point q where qr=30cm and pq=15cm. the tension in the string is

The **tension in the string** if a rod PR is balanced on a pivot at the end R while a string is used to support the rod at P is 6 N

**Moment = Force * Perpendicular Distance**

Let us consider the pivot side be initial point,

Since the rod is balanced,

CM = ACM

CM = Clockwise moment

ACM = Anticlockwise moment

F = 9 N

PQ = 15 cm = 0.15 m

QR = 30 cm = 0.3 m

PR = PQ + QR

PR = 0.15 + 0.3

PR = 0.45 m

**CM = W * QR**

CM = 9 * 30

CM = 2.70 N m

ACM = T * PR

ACM = 0.45 T N m

2.70 = 0.45 T

T = 6 N

Therefore, the tension in the string is **6 N**

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what is temperature?

how temperature can be measured

**Answer:**

**Temperature is the kinetic energy of the particles of a substance.**

**Explanation:**

**The more kinetic energy a particle has the higher it's temperature. In the case of the atmosphere, which is what we are primarily concerned with in Meteorology, we measure this using a mercury thermometer (in certain situations we use an alcohol thermometer and of course modern times have given us things like dewcells and digital thermometers but we always go back to the mercury thermometer for accuracy).**

You are instructed by your supervisor to move 20 boxes—each of which has a weight of 11.34 N—onto an awaiting truck. The back of the truck is 1.65 m above the loading dock. How much work must you perform to do your assignment?

The amount of **work done** to move 20 boxes each of weight 11.34 N onto an awaiting truck with back 1.65 m above the loading dock is **374.22 Joule**.

Work done is calculated by the product of total **force** and **displacement**.

According to the question, total force done to lift the boxes is twenty times the weight of each box. So, the force required to lift all the blocks is,

Force = 20 × 11.34 = 226.8 N

As the back of the truck is 1.65 m above the loading dock, displacement done to move the boxes is 1.65 m.

So, the work done is,

Work = 226.8 × 1.65 = 374.22 **Joule**

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A frog leaps from flat ground at 6.32 m/s

at a 36.3 angle. What maximum height

does it reach?

(Unit = s)

At hmax, Vy=0

vy=v0y-gt

0=6.32sin(36.3)-9.81t

t=.381 seconds

Δy=v0yt-.5gt^2

Δy=6.32sin(36.3)*.381-.5(9.81)(.381)^2

maximum height=.714 m

Suppose you are in a car that is going around a curve. The speedometer reads a constant 30 miles per hour.

Which of the following is NOT true?

a) Your velocity is constant.

b) You and the car are accelerating.

c) Your acceleration is constantly changing

d) Your direction is constantly changing.

e) Your speed is constant.

The true statement is "Your **speed** is constant".

An object is moving at a **constant speed** when its speed is constant, that is the speed does not increase or decrease.

**Constant speed** also refers to the movement of a body at a uniform rate in a fixed steady-state moving with an average speed.

If you are in a car that is going around a curve and the speedometer reads a constant 30 miles per hour, you will notice that the direction of your motion is changing and but the **distance** travelled in a given **time** does not change.

Thus, only the **speed** is constant but velocity and acceleration is not constant.

The correct option is E.

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How could infrared imaging be used to find a lost hiker? Answer in 2-3 complete sentences.

When you scan the **hiker's body**, you will notice a **warm spot**. Unless that person was dead, they would not be **emitting heat.**

What is hiking?According to

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consider a resistor-inductor circuit where a 10v force is applied for a period of 2 seconds. the equation for the current in the circuit is given: \f$\displaystyle \small \frac{di}{dt} 5i

A **step function** is defined U(t)=0,1 [tex]\left \{ {{t < 0} \atop {t > 0}} \right.[/tex] **i(t)=e^-5t + 2** if t=2&3 & **i(t)=3e^-5t ** if 2>t>3.

A **step function**, sometimes known as a staircase function, is a piecewise constant function with a limited number of parts, according to the definition given in mathematics. In other words, one can think of a function on the real numbers as a finite linear combination of indicator functions of given intervals. In addition, it goes by the names floor function and biggest** integer function.** There is no continuity in the step function. In mathematics, a step function is a function whose graph resembles a series of steps because it is made up of numerous horizontal line segments interspersed with jumps. The biggest** integer function** is a frequent illustration of step functions in mathematics.

When provided intervals are used, a step function has a constant value, but the constant varies for each interval. A function that returns the biggest integer that is less than or equal to x is known as the greatest **integer function.**

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anne is working on a research project that involves the use of a centrifuge. her samples must first experience an acceleration of 100???? , but then, the acceleration must increase by a factor of eleven. by how much will the rotational speed have to increase? express your answer as a fraction of the initial rotation rate.

if the final **acceleration** increases by a factor of 11, then the final rotation should be** 3.32**[tex]w_{1}[/tex]** times **the initial rotation.

The relation between the centripetal **acceleration** and rotation speed of the particle is given as

a=rω²

Where ω is the angular speed and r radius of the circle

Now, rearranging the above equation we will get

ω = √[tex]\frac{a}{r}[/tex]

The initial acceleration is given by

a₁ =100g

But then, the acceleration increases by a factor of 11. Which means the final acceleration of the particle is

a₂ = 11 (100g)

= 1100g

The final and initial rotation speeds are related as

[tex]\frac{w1}{w2}[/tex] = √[tex]\frac{a2}{a1}[/tex]

[tex]w_{2}[/tex] = √[tex]\frac{1100g}{100g}[/tex] x [tex]w_{1}[/tex]

[tex]w_{2}[/tex] = 3.32 [tex]w_{1}[/tex]

The **final rotation **should be** 3.32**[tex]w_{1}[/tex]** times **the initial rotation.

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A girl is outside walking on level ground. First she walks 829 m to the east, then 223 m north, and finally 387 m west. What is the magnitude of her displacement? Give your answer in meters correct to at least 1 decimal place. Do not include units in your answer.

**Answer:**

not enough information need more information to answer the question

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