Categories

## Suppose you are able to manipulate a plants access to components in the photosynthesis equation. drag each label to the appropriate bin to predict how that action will affect plant growth. for each increase or decrease, assume that every other component of the photosynthesis equation is unlimited.

We know that the word equation for the reaction taking place during photosynthesis is:

carbon dioxide + water + sunlight → glucose + oxygen

Therefore, the more the reactants are provided, the more the plant will grow. The lesser the reactants, the lesser the growth. Providing products will not alter the rate of photosynthesis. The factors may be grouped as:

Increase plant growth:
-increase sunlight
-increase carbon dioxide
-increase water

No effect on plant growth:
-increase glucose
-increase oxygen
-decrease glucose
-decrease oxygen

Decrease plant growth:
-decrease water
-decrease sunlight
-decrease carbon dioxide

Categories

## Ryan was 8 when his parents invested \$4000 in a certificate of deposit that pays 6%. if ryan leaves the account alone until it reaches \$10,000, how old will he be? (assume that the interest is not compounded annually.)

Ryan was 8 when his parents invested \$4000 in a certificate of deposit that pays 6%. if ryan leaves the account alone until it reaches \$10,000, how old will he be? (assume that the interest is not compounded annually.)

Categories

## Assume there are 365 days in a year 1.) What is the probability that ten students in a class have different birthdays? 2.) What is the probability that at least ten students in a class share their birthday

Assume there are 365 days in a year 1.) What is the probability that ten students in a class have different birthdays? 2.) What is the probability that at least ten students in a class share their birthday

Categories

## What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of \$6.88 per basket. assume that the standard deviation is known to be \$1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop

Given:
Sample size, n = 40
Sample mean, xb = \$6.88
Population std. deviation, σ = \$1.92 (known)
Confidence interval = 90%

Assume normal distribution for the population.
The confidence interval is
(xb + 1.645*(σ/√n), xb – 1.645*(σ/√n)
= (6.88 + (1.645*1.92)/√40, 6.88 – (1.645*1.92)/√40)
= (7.38, 6.38)

Answer: The 90% confidence interval is (7.38, 6.38)

Categories

## Consider college officials in admissions registration, counseling, financial aid campus ministry, food services, and so on. How much money do these people make each year? Suppose you read in your local newspaper that 45 officials in student services earn an average of \$50,340 each year. Assume that the standard deviation is \$10,780 for salaries of college officials and student services. Find a 90% confidence interval for the population mean salaries of such personnel. Round your answer to the nearest dollar and don;t forget to use the \$ sign.

Since sample size is > 40, we use the z-score
in calculating for the confidence interval.

The formula is given as:

Confidence Interval = X ± z * σ / sqrt (n)

Where,

X = mean = \$50,340

z = z-score which is taken from standard distribution
tables at 90% confidence interval = 1.645

σ
= standard deviation = \$10,780

n = sample size = 45

Substituting to the equation:

Confidence Interval = 50,340 ± 1.645 * 10,780 / sqrt (45)

Confidence Interval = 50,340 ± 1,607

Confidence Interval = \$48,733 to \$51,947

Therefore the salary range of the personnel is \$48,733 to \$51,947.

Categories

## Franklin deposited \$75 in a no-interest bank account when he opened it. After that, he deposits \$50 per month in the account. Assume he makes no other withdrawls or deposits. The equation below can be used to find m, the number of months it take him to save a total of \$175 . What number should he use as the coefficient of m ??

Franklin deposited \$75 in a no-interest bank account when he opened it. After that, he deposits \$50 per month in the account. Assume he makes no other withdrawls or deposits. The equation below can be used to find m, the number of months it take him to save a total of \$175 . What number should he use as the coefficient of m ??

Categories

## A golf ball is hit from the ground with an initial velocity of 208 ft per second assume the starting height of the ball is 0 ft how long will it take the golf ball to hit the ground

A golf ball is hit from the ground with an initial velocity of 208 ft per second assume the starting height of the ball is 0 ft how long will it take the golf ball to hit the ground

Categories

## My grandfather, who lost his short-term memory sometime during the first Eisenhower Administration, calls me into his study because he wants to tell me the story he’s never told anybody before again. . . . My grandfather slams the door and motions me to the chair in front of his desk. I’ll be thirteen in two weeks. “There’s something I want to tell you, son,” he says. “Something I’ve never told anybody. You think you’re ready? You think you’ve got the gumption?” “I think so.” “Think so?” “I know so, sir. I know I’ve got the gumption.” . . . “It was late,” he says. “Someone knocked on my stateroom door. I leaped up. In those days I slept in uniform—shoes, too.” My grandfather smiles. His face is so perfectly round that his smile looks like a gash in a basketball. I smile back. “Don’t smile,” he says. “Just because I’m smiling, don’t assume I couldn’t kill you right now. Know that about a man.” Source: Orner, Peter. “The Raft.” The Atlantic Online. The Atlantic Monthly Company, Apr. 2000. Web. 10 May 2011. Which point of view does the text use?

My grandfather, who lost his short-term memory sometime during the first Eisenhower Administration, calls me into his study because he wants to tell me the story he’s never told anybody before again. . . . My grandfather slams the door and motions me to the chair in front of his desk. I’ll be thirteen in two weeks. “There’s something I want to tell you, son,” he says. “Something I’ve never told anybody. You think you’re ready? You think you’ve got the gumption?” “I think so.” “Think so?” “I know so, sir. I know I’ve got the gumption.” . . . “It was late,” he says. “Someone knocked on my stateroom door. I leaped up. In those days I slept in uniform—shoes, too.” My grandfather smiles. His face is so perfectly round that his smile looks like a gash in a basketball. I smile back. “Don’t smile,” he says. “Just because I’m smiling, don’t assume I couldn’t kill you right now. Know that about a man.” Source: Orner, Peter. “The Raft.” The Atlantic Online. The Atlantic Monthly Company, Apr. 2000. Web. 10 May 2011. Which point of view does the text use?

Categories

## Find the area of the shaded region. Round answers to the nearest tenth. Assume all inscribed polygons are regular.

We can calculate for the area of the shaded region by 1)
calculating the area of circle, 2) calculating for area of triangle, and 3)
calculating for area of the segment below the triangle. Then subtract 2 and 3
from 1.

1) Area of circle, Ac = π r^2

Ac = π (6)^2

Ac = 113.10

2) Area of triangle, At

The triangle is an equilateral triangle with angles on each
corner equal to 60 degrees. Meanwhile, the 3 angles at the center is 120
degrees each since a circle is 360 degree. We know that the radius (line from
centerpoint to corner) is equivalent to 6. Using the cosine law, we can calculate
for the length of one side.

s^2 = 6^ + 6^2 – 2 (6) (6) cos 120

s^2 = 108

s = 10.4

Since this is an equilateral triangle therefore all sides
are equal. The area for this is:

At = (sqrt3 / 4) * s^2

At = 46.77

3) Area of segment, As is given as:

As = [ (r^2) / 2 ] ( θ rad – sin θ )

As = [(6^2) / 2] (120 * π / 180 – sin 120)

As = 22.11

Therefore the area of shaded region is:

A = 113.10 – 46.77 – 22.11

A = 44.22

Categories

## Assume that a multispecialty medical group has decided to segment their market area (community) by income level. the group has decided to target a small niche of middle-aged, white-collar professionals who are married, with both spouses working outside the home. how might this medical group tailor its marketing mix to appeal to this segment?

A multispecialty medical group is a group medical practicing professionals (mostly doctors) who cater to different medical needs. Since the company targets that specified income level mentioned above, their marketing mix should be based on servicing busy individuals. They should make sure that their service is fast and offer delivery or online results.

Categories

## An action movie production team needs glass spheres to hold a green liquid that looks like an explosive l. if all of the available 3,392’92 cubic inches of the liquid is to be poured into 30 glass spheres l, what should the diameter of each sphere be. assume that each sphere is filled to the top

We need 30 glass spheres whose TOTAL volume = 3,392.92 cubic inches.
Therefore each of the 30 spheres must have a volume of  3,392.92 / 30 =

113.0973333333

cubic inches
Sphere Volume   =   4/3 • π • r³
Sphere Volume / (4/3 • π)

4.1887902048

26.9999994758

diameter = 6 inches

Categories

## Calculate the ph of 0.375 l of a 0.18 m acetic acid-0.29 m sodium acetate buffer after the addition of 0.0090 mol of koh. assume that the volume remains constant.

To calculate the pH of this solution, we use the
Henderson-Hasselbalch equation:

pH = pKa + log ([A-]/[HA])

Where,

[A-] = Molarity of the conjugate base =
CH3COO- = 0.29 M
[HA] = Molarity of the weak acid  = CH3COOH = 0.18 M

pKa = dissociation constant of the weak acid =
4.75

When KOH is added to the buffer, the chemical
reaction is:

CH3COOH + KOH = CH3COO-K+ + H2O

Therefore when 0.0090 mol KOH is added, 0.0090
mol acid is neutralized, and 0.0090 mol CH3COO- is produced.

[CH3COO-] = [0.0090 mol + 0.375 L (0.29 mol/L) ]
/ 0.375 L = 0.314 M

[CH3COOH] = [-0.0090 mol + 0.375 L (0.18 mol/L) ]
/ 0.375 L = 0.156 M

Going back to Henderson-Hasselbalch
equation:

pH = 4.75 + log (0.314 / 0.156)

pH = 5.054

Categories

## If you put \$1,500 in a savings account that pays 4% interest compounded continuously, how much money will you have in your account in 5 years? Assume you make no additional deposits or withdrawals. A. \$3,286.68 B. \$1,832.10 C. \$1,824.98 D. \$9,160.52

If you put \$1,500 in a savings account that pays 4% interest compounded continuously, how much money will you have in your account in 5 years? Assume you make no additional deposits or withdrawals. A. \$3,286.68 B. \$1,832.10 C. \$1,824.98 D. \$9,160.52

Categories

## What net force is required to push a sofa with a mass of 59 kilograms so that it accelerates at 9.75 meters/second2? (Assume a flat, frictionless surface.)

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

Categories

## A student gets a cut on his hand. Within a week, the cut has healed and there is little evidence of the original injury. What can we assume about the cells surrounding the cut?

A student gets a cut on his hand. Within a week, the cut has healed and there is little evidence of the original injury. What can we assume about the cells surrounding the cut?

Categories

## What would be your estimate of the age of the universe if you measured a value for hubble’s constant of h0 = 30 km/s/mly ? you can assume that the expansion rate has remained unchanged during the history of the universe. express your answer using two significant figures. yr?

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

Categories

## Department w had 2,400 units, one-third completed at the beginning of the period; 16,000 units were transferred to department x from department w during the period; and 1,800 units were one-half completed at the end of the period. assume the completion ratios apply to direct materials and conversion costs. what is the equivalent units of production used to compute unit conversion cost on the cost of production report for department w? assume the company uses fifo.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

Categories

## A continuous random variable is a random variable that can: ?assume any value in one or more intervals ?assume no continuous random frequency ?have no random sample ?assume only a countable set of values

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

Categories

## An employee earns \$36 per hour and 1.5 times that rate for all hours in excess of 40 hours per week. assume that the employee worked 60 hours during the week, and that the gross pay prior to the current week totaled \$52,200. assume further that the social security tax rate was 6.0%, the medicare tax rate was 1.5%, and federal income tax to be withheld was \$605.

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       \$6,800   \$10,500  \$8,400    \$66,000   \$4,700

Pay subject to FICA S.S.         \$421.60  \$651.00  \$520.80 \$4092.00 \$291.40
6.2%, (First \$118,000)

Pay subject to FICA Medicare \$98.60 \$152.25    \$121.80    \$957.00    \$68.15
1.45% of gross

Pay subject to FUTA Taxes      \$40.80  \$63.00     \$50.40    \$396.00  \$28.20
0.6%

Pay subject to SUTA Taxes   \$367.20  \$567.00  \$453.60  \$3564.00 \$253.80
5.4% (First \$7000)

Totals                                     \$928.20 \$1,433.25 \$1,146.60 \$9,009.00 \$641.55

Categories

## Civics Assume the European Euro is increasing in exchange value compared to the U.S. dollar. Who will benefit most in this situation? A U.S. family traveling throughout Europe A European company that imports electronics from the U.S. A European company that imports Asian foods An international travel agency based in Florida

The Reformation actually started after Columbus’s landing in North America.

Treaty of Tordesillas in 1494 was forced on Spain and Portugal by the Pope. The Pope basically said that all lands in the New World belonged to Spain and all new non-Christian lands in the Eastern Hemisphere belong to Portugal. No other Catholic countries can do anything in those areas without the approval of the owner.

The pope basically drew two lines on the globe setting the border. The western line started at the north pole cut half way through Greenland and ended at the south pole. The new world was everything to the west. Problem is that it ran through a chunk of Brazil which is why Brazil is an ex-Portuguese colony.

The Eastern line starts at the North Pole runs through siberia, through the pacific just west of Japan, and cuts Australia in half. Of course, Australia hadn’t been discovered yet. Everything to the the east of this line is the new world.

Obviously, this treaty didn’t hold up well, but the reformation gave the protestant countries an excuse to explore the new world since they didn’t have to take orders from the Pope. Even so, France, a catholic country, ignored it too.

Really, the only country that was effected by the reformation in the exploration of the Americas was England. All the other countries, changed their religion once and then went to war with the nearest catholic country. Sweden became Lutheran and stayed that way. The Dutch Republic became Calvinists and stayed that way.

England kept switching. First it was Catholic. Then, Henry VIII made it protestant. Then, Henry’s daughter Mary I made it catholic again. Henry’s other daughter Elizabeth I (with the two hit movies) made it Protestant again.

Years latter, Oliver Cromwell over through the monarchy, executed the King Charles I, and established a Protestant fundamentalist religious military dictatorship. He outlawed drinking,smoking, gambling, theater, dirty books, sports, prostitution, and anything generally fun. He would have made Saudi Arabia proud. Basically, all you could do is work, pray, and die. Sex was allowed for creating children, but you couldn’t enjoy it.

When Cromwell died, the people of England said enough was enough and brought back the King. Charles II kicked out the fundamentalists and brought back drinking, smoking, gambling, dirty books, sports, prostitution, and having fun during sex. Incidentally, those were also all his hobbies.

This brings us to the famous Pilgrims. They were part of Cromwell’s crowd. They kept agitating a return to the no-fun policy. They annoyed everybody. They weren’t persecuted for practicing their religion, they were persecuted because they kept trying to force their religion on everyone else. Sort of like Southern Baptists.

Charles II was the most easy going monarch in British history. Do realize how annoying you have to be to get him to throw you out.

Charles’s brother James II was obsessed with turning Great Britain catholic again. After four years of trying, they kicked him and his followers out.

Categories

## Which term best describes a proof in which you assume the opposite of what you want to prove? A. Proof by syllogism B. Proof by contradiction C. Proof by contrapositive D. Proof by converse

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

Categories

## If a Killer whale is feeding at the fourth trophic level, how much phytoplankton mass is required to add each gram of new mass to the whale? Assume that 10% of the energy at one trophic level is transferred to the next level. a. 1000 grams b. 100 grams c. 500 grams d. 1 gram

The correct answer is option C, that is, 30 minutes.

It is essential to get a good night sleep for good mental, physical, and emotional health. It is as essential as consuming a healthy diet and doing enough exercise. It has been found that about half of the adults do not shut their eyes, with many admitting that they lie awake at night fretting about their worries.

Thus, to tackle the situation, one should be preparing to go to sleep before 30 minutes of light out. One needs to put the body and brain in the right state where sleep can take place easily.

Categories

## A howler monkey is the loudest land animal and, under some circumstances, can be heard up to a distance of 4.6 km. assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is 1.0 × 10-12 w/m2. what is the acoustic power emitted by the howler?

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

Categories

## Two children standing on opposite sides of a merry-go-round are trying to rotate it. they each push in opposite directions with forces of magnitude 10.2 n. (a) if the merry-go-round has a mass of 180 kg and a radius of 1.8 m, what is the angular acceleration of the merry-go-round? (assume the merry-go-round is a uniform disk.)

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s