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The measure of in degrees, is approximately 34.38 side lengths are 4, 5.3 ,and 7

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Draw the triangle as shown in the figure below.
a=5.3, b=7, c=4.

The smallest angle is ∠C because it is opposite the shortest length of 4.
From the Law of Cosines,
c² = a² + b² – 2ab cosC
or
cos C = (a² + b² – c²)/(2ab)
           = (5.3² + 7² – 4²)/(2*5.3*7)
           = 0.823

∠C = arcos(0.823) = 34.58°
This answer agrees reasonably with 34.38°
 

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Your body is approximately _______ percent water. A. 30 B. 45 C. 60 D. 75

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Your body is approximately _______ percent water. A. 30 B. 45 C. 60 D. 75

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In England approximately 177,568,123 tonnes of waste is generated every year. What is this number rounded to the nearest hundred thousand

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In England approximately 177,568,123 tonnes of waste is generated every year. What is this number rounded to the nearest hundred thousand

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There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)

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If a quantity A is decreased by 15%, it means that what is left is 85% of it.

85%A= frac{85}{100}A=0.85A

Part A.

Consider the 150 marigolds.

After the first month, 0.85*150 are left
After the second month, 0.85*0.85*150= (0.85)^{2} *150
After the third month, 0.85*0.85*0.85*150 =  (0.85)^{3}*150
.
.
so After n months,  (0.85)^{n}*150 marigolds are left.

in functional notation: M(n)=(0.85)^{n}*150 is the function which gives the number of marigolds after n months

consider the 125 sunflowers.

After 1 month, 125-8 are left
After 2 months, 125-8*2 are left
After 3 months, 125-8*3 are left
.
.
After n months, 125-8*n sunflowers are left.

In functional notation: S(n)=125-8*n is the function which gives the number of sunflowers left after n months

Part B.

M(3)=(0.85)^{3}*150=0.522*150=78 marigolds are left after 3 months.

S(3)=125-8*3=125-24=121 sunflowers are left after 3 months.

Part C.

Answer : equalizing M(n) to S(n) produces an equation which is very complicated to solve algebraically.

A much better approach is to graph both functions and see where they intersect.
 
Another approach is by trial, which gives 14 months

M(14)=(0.85)^{14}*150=15

S(14)=125-8*14=125-112=13

which are close numbers to each other.

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The amount of time it takes to fill a whirlpool tub is inversely proportional to the square of the radius of the pipe used to fill it. If a pipe of radius 2.5 inches can fill the tub in 8 minutes, how long will it take the tub to fill if a pipe of radius 3.5 inches is used? How many inches would the tub fill approximately in minutes?

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The amount of time it takes to fill a whirlpool tub is inversely proportional to the square of the radius of the pipe used to fill it. If a pipe of radius 2.5 inches can fill the tub in 8 minutes, how long will it take the tub to fill if a pipe of radius 3.5 inches is used? How many inches would the tub fill approximately in minutes?

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The half-life of helium-5 is 7.6 x 10^-22 seconds, and the half-life of helium-9 is 7 x 10^-21 seconds. Approximately how many times greater is the half-life of helium-9 than that of helium-5?

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(7X10^-21)/(7.6X10^-22)  is equal to:

(7/7.6)(10^-21/10^-22)

Rule for division of similar bases with exponents…

(a^b)/(a^c)=a^(b-c)

In this case we have (10^-21)/(10^-22)=10^(-21–22)=10^1

And 7/7.6≈0.921, and we only had two significant figures so 0.92 works

0.92X10^1

9.2

So the half life of helium-9 is about 9.2 times greater than the half life of helium-5

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The muscular system is composed of approximately 600 smooth, cardiac or skeletal muscles ?

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The muscular system is composed of approximately 600 smooth, cardiac or skeletal muscles ?

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Calculate the speed with which the moon orbits the earth given the distance from earth to moon as R = 3.84 · 108 m. (Astronomers note that the true orbital period of the moon, is 27.3 Earth days. Interestingly, this would mean that there are approximately 13 months in a year. Use the 27.3 days/month for T – the time required for one revolution in your calculation.)

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This sounds pretty easy, in fact. The orbital motion can be assumed to be circular and with constant speed. Then, the period is the time to do one revolution. The distance is the length of a revolution. That is 2*pi*R, where R is the distance between the Moon and the Earth (the respective centers to be precise). In summary, it’s like a simple motion with constant speed:

v = 2*pi*R/T,

you have R in m and T is days, which multiplied by 86,400 s/day gives T in seconds.

Then v = 2*pi*3.84*10^8/(27.3*86,400) = 1,022.9 m/s ~ 1 km/s (about 3 times the speed of sound 🙂

For the Earth around the Sun, it would be v = 2*pi*149.5*10^9/(365*86,400)~ 29.8 km/s!

I know it’s not in the problem, but it’s interesting to know how fast the Earth moves around the Sun! And yet we do not feel it (that’s one of the reasons some ancient people thought crazy the Earth not being at the center, there would be such strong winds!)

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Alcohol consumption in teenagers is a problem for families, society and the teens themselves. Approximately 5,000 adolescents die each year as a result of underage drinking. What are other consequences for teens who experiment or abuse alcohol? (HIGH SCHOOL)

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Alcohol consumption in teenagers is a problem for families, society and the teens themselves. Approximately 5,000 adolescents die each year as a result of underage drinking. What are other consequences for teens who experiment or abuse alcohol? (HIGH SCHOOL)

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During heart transplants, the _____ nerves are severed resulting in a faster resting heart rate (approximately 100 beats per minute) after the transplant. glossopharyngeal cardiac accelerator vagus phrenic cervical spinal

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During heart transplants, the _____ nerves are severed resulting in a faster resting heart rate (approximately 100 beats per minute) after the transplant. glossopharyngeal cardiac accelerator vagus phrenic cervical spinal

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A company is setting its direct materials and direct labor standards for its leading product. basic wages of the assembly line personnel are $19 per hour. payroll taxes are approximately 23% of wages. how much is the direct labor cost standard per hour? (round your answer to the nearest cent.)

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A company is setting its direct materials and direct labor standards for its leading product. basic wages of the assembly line personnel are $19 per hour. payroll taxes are approximately 23% of wages. how much is the direct labor cost standard per hour? (round your answer to the nearest cent.)

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In a right triangle, angle a measures 20°. the side opposite angle a is 10 centimeters long. approximately how long is the hypotenuse of the triangle? 3.4 centimeters 10.6 centimeters 27.5 centimeters 29.2 centimeters

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In a right triangle, angle a measures 20°. the side opposite angle a is 10 centimeters long. approximately how long is the hypotenuse of the triangle? 3.4 centimeters 10.6 centimeters 27.5 centimeters 29.2 centimeters

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The Geologic Time Scale begins at the formation of Earth approximately _____ years ago.

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Answer:

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²    

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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After the United States declared war to Germany approximately how long did it take for over a million Americans troops to arrive in Europe?

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It took one year for over a million Americans troops to arrive in Europe after the United States declared war to Germany.

On 11 December 1941, four days following the Japanese attack on Pearl Harbor and the United States declaration of war against the Japanese Empire, Nazi Germany declared war against the United States, in reaction to what was considered to be a series of provocations by the United States government when the US was still officially neutral during World War II.

On December 11, 1941, the United States Congress declared war upon Germany, hours after Germany declared war on the United States after the attack on Pearl Harbor by the Empire of Japan.

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In the important industrial process for producing ammonia (the Haber Process), the overall reaction is: N2(g) + 3H2(g) → 2NH3(g) + 100.4 kJ A yield of NH3 of approximately 98% can be obtained at 200°C and 1,000 atmospheres of pressure. This reaction is: exothermic endothermic

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In the important industrial process for producing ammonia (the Haber Process), the overall reaction is: N2(g) + 3H2(g) → 2NH3(g) + 100.4 kJ A yield of NH3 of approximately 98% can be obtained at 200°C and 1,000 atmospheres of pressure. This reaction is: exothermic endothermic

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PLEASE HELP ILL GIVE 40 PTS There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp. Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points) Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? (2 points) Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically. (4 points)

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The polinomials only can have positive whole exponents, that is: 1, 2, 3, 4, 5, 6, … (you can include 0 also, because it iis the independent term).

So, if you are told that one term of the polynomial is 9 x ^ (negative something), it is necessary that the number after the negative sign be negative, given that negative times negative is positive.

Therefore, the only possible option from the answer choices is the option 3) -9.

Answer: 3) – 9

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There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp. Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically.

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There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp. Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically.

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Gina looks at the architectural plan for a four-walled roomie the walls meet each other at right angles. The length of one wall is 17 inches. The length of the diagonal floor of the room in the plan is approximately 18.79 inches. Is the room in the shape of a square? Explain how you determined your answer. Show your work.

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Gina looks at the architectural plan for a four-walled roomie the walls meet each other at right angles. The length of one wall is 17 inches. The length of the diagonal floor of the room in the plan is approximately 18.79 inches. Is the room in the shape of a square? Explain how you determined your answer. Show your work.

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Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be Approximately 25,500 people Approximately 24,8500 people Approximately 25,150 people

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Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be Approximately 25,500 people Approximately 24,8500 people Approximately 25,150 people

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The following table shows the currently accepted half-life values for six parent isotopes. Parent Isotope Currently Accepted Half-Life Values Uranium-238 4.5 billion years Uranium-235 704 million years Thorium-232 14.0 billion years Rubidium-87 48.8 billion years Potassium-40 1.25 billion years Samarium-147 106 billion years Earth is approximately 4.5 billion years old. Given this information and the data in the table, which of the following isotopes could today contain less than 50 percent of its parent isotope? Potassium-40 Rubidium-87 Samarium-147 Uranium-238

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25) Answer is: less metallic and more nonmetallic.

Electronegativity increases from left to right across a period, atoms have tendency to attract electrons.

Electronegativity (χ) is a property that describes the tendency of an atom to attract a shared pair of electrons.

26) Answer is: radioisotope.

Radioisotope has an unstable atomic nucleus and emit energy and particles when it changes to a more stable form.

Francium (Fr) is element with atomic number 87 (87 protons and 87 electrons).

27) Answer is: boils.

Boiling is the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere.

The Celsius scale was based on 0°C for the freezing point of water and 100°C for the boiling point of water at 1 atm pressure.

28) Answer is: endothermic.

There are two types of reaction:  

1) endothermic reaction (chemical reaction that absorbs more energy than it releases, ΔH>0).

2) exothermic reaction (chemical reaction that releases more energy than it absorbs).  

For example, the breakdown of ozone is an endothermic process. Ozone has lower energy than molecular oxygen (O₂) and oxygen atom, so ozone need energy to break bond between oxygen atoms.  

29) Answer is: kinetic.

The average kinetic energy of molecules depends on the temperature.  

As temperature increases, molecules gain more energy from surrounding and move faster.  

Kinetic energy (standard unit is the joule J) depends on speed of the molecule.  

Solid gains kinetic energy to become a liquid and then becomes a gas.

30) Answer is: alpha particles.

This was famous Rutherford’s Gold Foil Experiment: he bombarded thin foil of gold with positive alpha particles.

Rutherford observed the deflection of alpha particles on the photographic film.  

Alpha particles are helium atom particles, consist of two protons and two neutrons.  

According to Rutherford model of the atom: atoms have their charge concentrated in a very small nucleus.  

31) Answer is: highest.

For example, calcium oxide.

Calcium oxide (CaO) has ionic bonds between calcium cations (Ca²⁺) and oxygen anions (O²⁻).

Because it has strong ionic bonds, it has high melting point (around 2600°C).

Ionic bond is the electrostatic attraction between oppositely charged ions (cations and anions).

32) Answer is: a scientific model.

A scientific model is a representation of an idea, an object, a process or a system that is used to describe and explain phenomena that cannot be experienced directly.

33) Answer is: the superscript is mass number and the subscript is atomic number.

Atomic number(Z) is the number of protons, which is characteristic of a chemical element..

Mass number (A) is the total number of protons and neutrons in a nucleus.

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Determine the equation of the graph and select the correct answer below. parabolic function going up from the left through the point approximately negative two and three fourths comma zero and turning at the point negative one comma three and going down through the point zero comma two and through the point approximately three fourths comma zero and continuing towards infinity

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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Enzo read this passage from “The Smithville Gazette: Neighborhood Thief Strikes Again.” Another episode in the recent spate of neighborhood thefts occurred on Saturday at Ferguson’s department store. Several pieces of jewelry were taken at approximately 12:30 in the afternoon. Mrs. Jane Dickson, the employee working the jewelry counter reported that she did not initially see the theft, but realized shortly before 1 p.m. that several necklaces were missing from inside the jewelry case, which she had accidentally left unlocked while moving away to help another customer. Instead of taking notes on the central idea, Enzo copied the passage down exactly. What is the best way to revise the passage into notes that reveal the central idea? a) Saturday @ 12:30 p.m., Ferguson’s, Mrs. Jane Dickson, jewelry, necklaces b) robbery @ Ferguson’s jewelry on Sat.—necklaces stolen c) On Saturday at Ferguson’s, there was a robbery and some jewelry was stolen. d) Mrs. Jane Dickson says there was a jewelry robbery.

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Hey there!

Correct answer is D. Comma or Period Inside Rule

A. Question mark or exclamation point inside: those are not really necessary.

B. Colon or semicolon: not, a semicolon would divide the whole sentence and it would be shorten; a colon would work but after requested, when there is already a comma.

C. Question mark or Exclamation Point Outside Rule: would not work, becase it is an very polite and affirmative sentence.

D: A comma or period inside rule: actually, just a comma would work. Please, Cooper’s dad requested, go… Cooper’s dad requested must be in between commas as it is a vocative.

Hope this helps

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According to a study of paddle sport accident statistics from 1995-2000, approximately half of all victims of canoeing and kayak related fatalities were doing what at the time?

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The answers to the given blanks above are NORMS, and CONFORMITY PRESSURES CHANGE ATTITUDES, respectively.
This research is actually based from Jean Watson (1950), an American nurse theorist who is known for her theory of Human Caring. According to her, when the given standards in an environment are changed, this also affects how a person deals with the people around his or her environment. Given above that there is lesser prejudice, this also changed their attitude by being less prejudiced.

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If, on average, Bob can make a sale to every 3rd person that comes into his store, how many people must come into Bob�s store if he wanted to make approximately fifteen (15) sales?

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=  x+y=84.8 …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

H^2=P^2+B^2

(44.8)^2=x^2+z^2  ………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

H^2=P^2+B^2

(72)^2=y^2+z^2 …………[3]

Subtract [2] and [3]

(72)^2-(44.8)^2=y^2+z^2-x^2-z^2

5184-2007.04=(x+y)(x-y)

3176.96=(84.8)(x-y)

37.464=x-y ……….[4]

Add equation [1] and [4], to get values of x and y

x+y+x-y=84.8+37.464

2x=122.264

x=61.132

Substitute x in [1]

x+y=84.8

61.132+y=84.8

y=23.668

Substitute value of x in equation [2], to get z

(44.8)^2=x^2+z^2

(44.8)^2=(23.668)^2+z^2

2007.04-560.174224=z^2

z=sqrt{1446.865776}

z=38.06

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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If you double the radius of the earth and keep the mass of the earth the same, the acceleration of gravity on the surface of the earth will be approximately …

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Answer:

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²    

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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