A boat moves through the water with two forces acting on it. One is a 1,575-N forward push by the water on the propeller, and the other is a 1,200-N resistive force due to the water around the bow. (Review attachment)

(a) What is the acceleration of the 1,100-kg boat?

______ m/s2

(b) If it starts from rest, how far will the boat move in 20.0 s?

______ m


(c) If it starts from rest, how far will the boat move in 20.0 s?

______ m/s

A Boat Moves Through The Water With Two Forces Acting On It. One Is A 1,575-N Forward Push By The Water

Answers

Answer 1

(a) The acceleration of the 1,100-kg boat is 0.341 m/s².

(b) The distance covered by the boat is 68.2 m.

(c) The speed of the boat is 6.82 m/s.

Acceleration of the boat

Net force on the boat = 1,575 N - 1,200 N = 375 N

F(net) = ma

a = F(net)/m

a = 375/1100

a = 0.341 m/s²

Distance moved in 20 s

s = ut + ¹/₂at²

s = 0 + ¹/₂(0.341)(20)²

s = 68.2 m

Speed of the boat in 20 s

v = u + at

v = 0 + 0.341(20)

v = 6.82 m/s

Thus, the acceleration of the 1,100-kg boat is 0.341 m/s², the distance covered by the boat is 68.2 m and the speed of the boat is 6.82 m/s.

Learn more about acceleration here: https://brainly.com/question/14344386

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Related Questions

The speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.3 m long, and the nerve impulse speed is 33 m/s, how long (in s) does it take for the nerve signal to travel this distance?

Answers

Answer:

Explanation:

Speed of electrical nerve signal = 33 m /s

Distance travelled = 1.3 m

time taken = distance / speed

= 1.3 / 33  

= .039 s

= 39 ms ( millisecond )  .

A vertical wire carries a current straight up in a region of the magnetic field directed north. What is the direction of the magnetic force on the current due to the magnetic field

Answers

Answer:

The direction of the force on the vertical wire is towards the East or right.

Explanation:

Using Fleming's right hand rule, the current is the middle finger pointing straight up, the magnetic field is the fore-finger pointing Northwards and then the thumb is the direction of the force on the vertical wire.

Following these conventions, the thumb points towards the East. So, the direction of the force on the vertical wire is towards the East or right.

Which of the following statements is true?
A. Friction primarily affects objects that contain iron.
B. Friction pulls objects toward the center of the Earth
C.
Friction does not affect objects in motion.
D.
Friction slows down or stops objects in motion.

Answers

Answer:

D. Friction slow down or stop objects in motion.

Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of vi, g, h, and t. (Take upward to be the positive direction.)
(a) What is the time interval between when the first ball strikes the ground and the second ball strikes the ground?
?t = ______
(b) Find the velocity of each ball as it strikes the ground.
For the ball thrown upward vf = ______
For the ball thrown downward vf = ______
(c) How far apart are the balls at a time t after they are thrown and before they strike the ground?
d = _______

Answers

Answer:

Explanation:

 a )

Time for first ball to reach top position

v = u - gt

0 = vi - gt

t = vi / g

Time to reach balcony  while going downwards

= vi /g

Total time = 2 vi / g

Time to go down further to the ground = t₁

Total time = 2 vi / g + t₁

Time for the other ball to go to the ground = t₁

Time difference = ( 2 vi / g + t₁ ) - t₁

= 2vi / g .

( b )

v² = u² + 2gh

For both the throw ,

final displacement = h , initial velocity downwards = vi

( For the first ball also  , when it go down while passing the balcony , it acquires the same velocity vi but its direction is downwards.)

vf² = vi² + 2gh

vf = √ ( vi² + 2gh )

(c )

displacement of first ball after time t

s₁ = - vi t + 1/2 g t²  [ As initial velocity is upwards , vi is negative ]

displacement of second ball after time t

s₂ = vi t + 1/2 g t²

Difference = d =  s₂ - s₁

= vi t + 1/2 g t² - ( - vi t + 1/2 g t² )

d = 2 vi t .

PLZZZZ HELPPPPPPPPPppppp​

Answers

What grade are you in?!!??

pls help me this is a major SOS pls help pls btw this is IXL

Answers

Explanation:

the object with the higher temperature has greater thermal energy

So the answer is

the stick of butter with less thermal energy.

Hope it will help :)

Answer:

The stick of butter with less thermal energy

Explanation:

I am pretty sure

Problem 4.13: Sound waves travel through air at a speed of 330 m/s. A whistle blast at a frequency of about 1.0 kHz lasts for 2.0 s. (a) Over what distance in space does the "wave train" representing the sound extend? (b) What is the wavelength of the sound? (c) Estimate the precision with which an observer could measure the wavelength. (d) Estimate the precision with which an observer could measure the frequency.

Answers

Answer:

a)  x = 660 m, b)  λ = 0.330 m, c) Δλ = 0.1 cm, d)    Δf = 104

Explanation:

a) the distance in which the train of waves extends can be obtained from the uniform movement

             v = x / t

             x = v t

             x = 330 2

             x = 660 m

b) the speed of sound is related to the wavelength and frequency

             v = λ f

              λ = v / f

              λ = 330/1000

              λ = 0.330 m

c) The precision in the measurement of the wavelength refers to the error or uncertainty in the measurement, if the measurement is direct with a tape measure the precision is the appreciation of the tape measure, in general it is 0.1 cm

d) the accuracy of the frequency in general the frequency is calculated from the measurements of period T

                f = 1 / T

The precision of the period is data by the chronometer used, in general time a press of 0.01s, by the response time of the people

               Δf = df / dT    ΔT

               Δf = 1 / T² ΔT

                Δf = 1 / (0.001)² 0.01

                 Δf = 104

As we can see, a much more precise system is needed to reduce the error

An insulated, vertical piston-cylinder assembly contains 50 L of steam at 105 oC. The outside pressure is 101 kPa. The piston has a diameter of 20 cm and the combined mass of the piston and the load is 75 kg. The electrical heater and the paddle wheel are turned on and the piston rises slowly by 25 cm with a constant pressure. The total internal energy increases by 3.109 kJ.

Determine:

a. The pressure of air inside the cylinder during the process.
b. The boundary work performed by the gas.
c. The combined work transfer by the shaft and electricity.

Answers

Answer:

Explanation:

From the given information:

The pressure of the air during the process = [tex]P_{atm} + P_{due \ to \ wt \ of \ piston}[/tex]

[tex]= 101 \ kPa + \dfrac{75 \ kg \times 9.8 \ m/s^2 \times \dfrac{1 \ N }{1 \ kg.m/s^2} }{\dfrac{\pi}{4}(0.2 \ m)^2} ( \dfrac{1 \ N }{m^2} \times \dfrac{1 \ kPa}{1000 \ n/m^2})[/tex]

The pressure of the air during the process = 124.42 kPa

The boundary work = P × ΔW

The boundary work = 124.42  kPa × (π/4) × (0.2 m)² × 0.25 m × (1 kJ/1 kPa.m³)

The boundary work = 0.977 kJ

The combined work transfer = [tex]W_{boundary} + \Delta U[/tex]

The combined work transfer = 0.977 + 3.109 kJ

The combined work transfer = 4.086 kJ

Communication satellites are placed in a geosynchronous orbit, i.e., in a circular orbit such that they complete one full revolution about the earth in one sidereal day (23.934 h), and thus appear stationary with respect to the ground. Determine the altitude of these satellites above the surface of the earth in both SI and U.S. customary units.

Answers

Answer:

Explanation:

Let the radius of orbit of geostationary satellite be R .

Time period of satellite = 2πR / V₀ where V₀ is orbital velocity

T = 2πR / √gR

T= 2πR / √(GM / R )

T = 2πR¹°⁵ / √GM  

R¹°⁵ = T x √GM  / 2π

T = 23.934 h = 23.934 x 60 x 60 s = 86126.4 s

R¹°⁵ = 86126.4 x √ ( 6.67 x 10⁻¹¹ x 5.972 x 10²⁴ )  / 2π

= 86126.4 x √ ( 398.33 x 10¹²  )  / 2π

= 86126.4 x 19.95 x 10⁶  / 2π

= 273.428 x 10⁹

R = 42.92 x 10⁶ m

= 42920 km

Radius of orbit = 42920 km

radius of earth = 6370 km

Altitude of satellite = 42920 - 6370 = 36550 km .

In US customary unit = 36550 x 10³ /.9144 yards

= 36550 x 10³ /(.9144 x 1760 ) miles

= 22771 miles .

Concept Simulation 4.1 reviews the central idea in this problem. A boat has a mass of 4490 kg. Its engines generate a drive force of 4520 N due west, while the wind exerts a force of 890 N due east and the water exerts a resistive force of 1210 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign

Answers

Answer:

-0.54m/s²

Explanation:

According to Newton's second law of motion

F = ma

Force = mass * acceleration

Given

Mass m = 4490kg

Take the sum of forces

Sum of force along the east = 890+1210 = 2100N

Sum of forces along the west = -4520N

Net force = -4520+2100

Net force = -2420N

Acceleration = Net force/Mass

Acceleration = -2420/4490

Acceleration = -0.54m/s²

Hence the boat acceleration is -0.54m/s²

|:Give one word answer
1. An object that allows whole light to pass through it _______​

Answers

Answer:

Translucent object

Explanation:



The electric field from two charges in the plane of the paper is represented by the dashed lines and arrows below.

Select a response for each statement below. (Use 'North' towards top of page, and 'East' to the right)


The magnitude of the E-field at Ris .... than at M.

The force on a (+) test charge at P is zero.

The magnitude of the charge on the left is .... that on the right.

The force on a (+) test charge at L is directed ....

The force on a (-) test charge at J is directed

The force on a (-) test charge at N is directed ....

The sign of the charge on the right is negative.

Answers

Answer:

a) electric field at point P must be zero

b) harged must be positive

c) force ais in the direction of the electric field

d)  force is in the opposite direction to the electric field

e)  force is in the opposite direction to the field

Explanation:

After reading your exercise, it is unfortunate that the diagram did not come out, but we are going to answer the questions in general.

a) force on a charge (+) is zero

this implies that the electric field at point P must be zero

        F = q E

b) the magnitude of the charge on the left is on the right

this indicates that the charged must be positive since the lines must exit the charge

c) force on load directed towards (direction not indicated)

since the charge is positive the force at point L is in the direction of the electric field at this point

d) force on test load (-) does not indicate direction

The force on a negative charge is in the opposite direction to the electric field at point J

e) Force on a test load (-) at point N

the force is in the opposite direction to the field at point N

If you stand on a trampoline, it depresses under your weight. When you stand on a hard stone floor, __________. If you stand on a trampoline, it depresses under your weight. When you stand on a hard stone floor, __________. the floor deforms very slightly under your weight only if you are heavy enough does the floor deform at all under your weight the floor does not deform at all under your weight

Answers

Answer:

the floor deforms very slightly under your weight

Explanation:

A trampoline is made up of a large piece of strong cloth held by springs on which you jump up and down as a sport. So, If you stand on a trampoline, it depresses under your weight.  However, the floor does not deform under your weight as it is too stiff.

Therefore,

when you stand on a hard stone floor, the floor deforms very slightly under your weight.

Which two statements help explain why digital storage of data is so reliable?

A. Memory chips are sturdy.

U B. Digital data usually deteriorate over time.

C. It is usually possible to recover data from a memory chip even

when the device containing it is broken.

D. Digital data are easier to copy than analog data are, making them

more accessible to thieves.

Answers

Answer:

A. Memory chips are sturdy.

C. It is usually possible to recover data from a memory chip even when the device containing it is broken.

Explanation:

Digital storage of data refers to the process which typically involves saving computer files or documents on magnetic storage devices usually having flash memory. Some examples of digital storage devices are hard drives, memory stick or cards, optical discs, cloud storage, etc.

A reliable storage ensures that computer files or documents are easily accessible and could be retrieved in the event of a loss.

The two statements which help explain why digital storage of data is so reliable are;

A. Memory chips are sturdy: they are designed in such a way that they are compact and firm.

C. It is usually possible to recover data from a memory chip even when the device containing it is broken.

Answer:

A and C

Explanation:

got it right on a p e x

How can you drop two eggs the fewest amount of times, without them breaking?

Answers

Because the shell didn’t crack.

I hope this helps.

Answer:

get 2 jugs of water put an egg in each one drop the jugs with parachutes on them in long grass on a sunny non windy day

Explanation:

egg+ground=broken

egg-ground= egg+air

egg+air=unbroken

egg+water= egg+wet

egg+water= unbroken

egg+egg= 2 egg

egg+egg+air= egg+egg+unbroken+unbroken

egg+egg+unbroken+unbroken=(egg+unbroken)2

longgrass+egg= 40%unbroken+60broken+egg

longgrass+egg+egg=20%unbroken+80%broken+2egg

ground+water=mud

mud+egg=unbroken+egg+muddy

air+water=raining

egg+raining+air=wet+egg+slip+50%broken+50%unbroken

ask if need more proof

Which one of Newton’s Laws best explains a bottle flip?

Answers

Answer:

the 2nd law-

Hope this helps <3

Explanation:

who is bill cypher and what is his origin?

Answers

Answer:

Bill Cipher is the true main antagonist of Gravity Falls. He is a Dream-Demon with mysterious motives and seems to have a vendetta against the Pines family, especially his old rival Stanford Pines

Explanation:

attraction is seen between the poles of two bar magnet in the case of​

Answers

Answer:

he magnetic field of a bar magnet is strongest at either pole of the magnet. It is equally strong at the north pole when compared with the south pole. The force is weaker in the middle of the magnet and halfway between the pole and the center

Explanation:

If a wave has a speed of 1000 m/s and frequency of 500 Hz, what is the wavelength?

• 1500 Hz
• 2 m
• 0.05 m

Answers

Answer:

2 m

Explanation:

speed=frequency×wavelength

wavelength=speed/frequency

wavelength=1000/500

=2 m

You are trying to push a 30 kg canoe across a beach to get it to a lake. Initially, the canoe is
at rest, and you exert a force over a distance of 3 m until it has a speed of 1.2 m/s.

a. How much work was done on the canoe?

b. The coefficient of kinetic friction between the canoe and the beach is 0.2. How much work was done by friction on the canoe?

c. How much work did you perform on the canoe?

d. What force did you apply to the canoe?

Answers

Answer:

m = 30, g = 9.8, coefficient = 0.2, so force due to friction = 30 x 9.8 x 0.2 = 58.8 N, so work done by friction = 58.8 x 1.2 = 70.56 J

Explanation:

Calculate the ratio of the drag force on a passenger jet flying with a speed of 1200 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at one-fourth the speed and half the altitude of the jet. At 10 km the density of air is 0.38 kg/m3 and at 5.0 km it is 0.67 kg/m3. Assume that the airplanes have the same effective cross-sectional area and the same drag coefficient C. (drag on jet / drag on transport)

Answers

Answer:

[tex]2.267[/tex]

Explanation:

Drag force is given by

[tex]F=\dfrac{1}{2}\rho Av^2C[/tex]

C = Drag coefficient is constant

A = Area is constant

[tex]v_1[/tex] = Velocity of the passenger jet = 1200 km/h = [tex]\dfrac{1200}{3.6}\ \text{m/s}[/tex]

[tex]v_2[/tex] = Velocity of the prop plane = [tex]\dfrac{1}{4}v_1[/tex]

[tex]\rho_1[/tex] = Density of the air where the jet was flying = [tex]0.38\ \text{kg/m}^3[/tex]

[tex]\rho_2[/tex] = Density of the air where the prop plane was flying = [tex]0.67\ \text{kg/m}^3[/tex]

[tex]F\propto \rho v^2[/tex]

[tex]\dfrac{F_1}{F_2}=\dfrac{\rho_1 v_1^2}{\rho_2 v_2^2}\\\Rightarrow \dfrac{F_1}{F_2}=\dfrac{0.38 v_1^2}{0.67 (\dfrac{1}{4}v_1^2)}\\\Rightarrow \dfrac{F_1}{F_2}=2.267[/tex]

The ratio of the drag forces is [tex]2.267[/tex].

Explain the difference in the function of plant and animal cell organelles, including cell membrane, cell wall, nucleus, cytoplasm, mitochondria, chloroplast, and vacuole

Answers

Answer:

Plant cell Animal cell

2. Have a cell membrane. 2. Have no chloroplasts.

3. Have cytoplasm. 3. Have only small vacuoles.

4. Have a nucleus. 4. Often irregular in shape.

5. Often have chloroplasts

containing chlorophyll. 5. Do not contain plastids.

A radio transmitting station operating at a frequency of 125 MHz has two identical antennas that radiate in phase. Antenna B is 9.05 m to the right of antenna A. Consider point P between the antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For what values of x will constructive interference occur at point P?

Answers

Answer:

Explanation:

The formula for frequency is:

[tex]f = \dfrac{c}{\lambda}[/tex]

If we make [tex]\lambda[/tex] the subject; we have:

[tex]\lambda = \dfrac{c}{f}[/tex]

[tex]\lambda = \dfrac{3\times 10^6 \ m/s}{125 \ MHz (\dfrac{10^6 \ Hz}{1 \ MHz})}[/tex]

[tex]\lambda = 2.4 \ m[/tex]

Let assume that there is a point P between antenna A  to B.

where;

A to B = 9.05

A to P = x  and

P to B = 9.05 - x

Then, the condition for the constructive inteference is:

Δx = nλ

x - (9.05 - x) = nλ

2x - 9.05 = n(2.4)

So, we need to start assigning values to n so that the value of x becomes less than or equal to 9.05 m

If n = -1

Then;

2x - 9.05 = (-1)(2.4)

x = 3.325 m

If n = -2

Then;

2x - 9.05 = (-2)(2.4)

x = 2.125 m

If n = -3

Then;

2x - 9.05 = (-3)(2.4)

x = 0.925 m

If n = 0

Then;

2x - 9.05 = (0)(2.4)

x = 4.525 m

If n = 1

2x - 9.05 = (1)(2.4)

x = 5.725 m

If n = 2

Then;

2x - 9.05 = (2)(2.4)

x = 6.925 m

Hence, there exist 7 points in which constructive interference occurs.

who has brown hair and brown eyes but is a boy

Answers

Answer:

I have strawberry blonde/brown hair blue eyes and a girl lol

Explanation:

what is the formular for force​

Answers

Answer:

f=m*a

Explanation:

The formula for force says force is equal to mass (m) multiplied by acceleration (a)

A shuttle bus slows down with an average acceleration of -2.4 m/s2. How long does it
take the bus to slow from 9.0 m/s to rest?

Answers

Answer:

[tex]\boxed {\boxed {\sf 3.75 \ seconds }}[/tex]

Explanation:

Average acceleration is found by dividing the change in acceleration by the time.

[tex]a=\frac{ v_f-v_i}{t}[/tex]

The shuttle bus has an acceleration of -2.4 meters per square second. It slows from 9.0 meters per second to rest, or 0 meters per second. Therefore:

[tex]a= -2.4 \ m/s^2 \\v_f= 0 \ m/s \\v_i= 9 \ m/s[/tex]

Substitute the values into the formula.

[tex]-2.4 \ m/s^2=\frac{0 \ m/s - 9 \ m/s}{t }[/tex]

Solve the numerator.

[tex]-2.4 \ m/s^2 = \frac{-9 \ m/s}{t}[/tex]

We want to solve for t, the time. We have to isolate the variable. Let's cross multiply.

[tex]\frac{-2.4 \ m/s^2}{1} = \frac{-9 \ m/s}{t}[/tex]

[tex]-9 \ m/s *1= -2.4 \ m/s^2 *t[/tex]

[tex]-9 \ m/s=-2.4 m/s^2*t[/tex]

t is being multiplied by -2.4. The inverse of multiplication is division, so divide both sides by -2.4

[tex]\frac{-9 \ m/s }{-2.4 \ m/s^2} =\frac{ -2.4 \ m/s^2*t}{-2.4 \ m/s^2}[/tex]

[tex]\frac{-9 \ m/s }{-2.4 \ m/s^2} =t[/tex]

[tex]3.75 \ s=t[/tex]

It takes 3.75 seconds.

Which of the following choices is the best example of potential energy?

Answers

Answer:

A basketball sitting still in a players hands

Explanation:

The other 3 answers have the ball in motion (going towards the basket, bouncing, and rolling) so that would be kinetic energy.

When the basketball is sitting in the player's hands, it has the potential to be in motion.

Answer:

it is D not B it D

Explanation:

How far can a bus carrying small children, travel at a rate of 60 km per hour travel in 2 1/2 hours?

Answers

150km

Explanation:

speed = 60km/hr.time = 2¹/2 hr = 5/2 hrdistance = speed × time = 60 ×5/2 = 150km

MARK ME AS BRAINLIST

How long will it take an object traveling at 90 kilometers per hour to travel 910 kilometers?

Answers

Explanation:

time = distance / velocity

We know that distance = 910 km and velocity = 90 km/h.

t = d / v

t = 910 km / 90 km/h

t = 10.11 hrs

The object traveled for 10.11 hours long. Hope this helps, thank you !!

The physics of wind instruments is based on the concept of standing waves. When the player blows into the mouthpiece, the column of air inside the instrument vibrates, and standing waves are produced. Although the acoustics of wind instruments is complicated, a simple description in terms of open and closed tubes can help in understanding the physical phenomena related to these instruments. For example, a flute can be described as an open-open pipe because a flutist covers the mouthpiece of the flute only partially. Meanwhile, a clarinet can be described as an open-closed pipe because the mouthpiece of the clarinet is almost completely closed by the reed.
Consider a pipe of length 80.0 cm open at both ends. What is the lowest frequency f of the sound wave produced when you blow into the pipe?

Answers

Answer:

Explanation:

Lowest frequency will be the fundamental frequency . For fundamental note

λ /2 = L where λ is wavelength of sound produced and L is length of open end pipe .

Given L = 80 cm

λ /2 = 80

λ = 160 cm .

= 1.6 m

frequency of note = velocity of sound / wavelength

= 330 / 1.6

= 206.25 Hz .

206 Hz approx.

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Ursula's mother spanks Ursula for hitting her younger brother. According to observational learning principles, the mother is _____. An intravenous hypertonic solution containing dextrose, proteins, vitamins, and minerals is known as? Substance A is transported from the plasma of the peritubular capillary into the fluid of the renal tubule. Substance A is said to be __________. A race track is miles long. If the car race is 200 laps then how many miles will the drivers travel during the race? Which of the following actions constitutes the unauthorized practice of law if performed by a real estate licensee who isn't a licensed attorney How can a speaker break the law by delivering a speech find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cmstep by step pls When Ocean Spray decided to make its Craisins (a dried cranberry snack food) available in convenience stores, supermarkets, and vending machines, it was involved with determining _____ strategy. If a firm's ROA and ROE are equal, it can be concluded that the firm is a. losing money. b. liquid enough to pay some extra dividends. c. financed by all equity. d. financed by a high proportion of debt. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| 2 x < 5} {x| 1 x 5} The free exercise clause states that the national government will not interfere with which of the following The Securities and Exchange Commission is the federal agency that has responsibility for regulating ______. The price index was 120 in Year 1 and 126 in Year 2. What was the inflation rate Find the measure of Angle E if Arc AB = 80 degrees and Arc CD = 38. Round to the nearest tenth. A scientist testing the effects of a chemical on apple yield (apples/acre) sprays an orchard with the chemical. A second orchard does not receive the chemical. In the fall, the yield is determined (number of apples harvested per acre). What is the dependent variable 2sin^2(x)+sin(2x)=2please help!! A gym class has $12$ students, $6$ girls and $6$ boys. The teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. If the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys Diagram 1 shows a tangent to a circle, centre O. Find x and y; 40 y Diagram 1 A nuclear reaction can be controlled using which of the following?Select one or more:a. control rodsb.water to disperse the heatc.large containersd. small containers Which equation represents this number sentence?Nine more than the quotient of a number and 3 is 21.n3+9=21fraction n over 3 end fraction plus 9 equals 213n+9=21fraction 3 over n end fraction plus 9 equals 21n+93=21fraction numerator n plus 9 end numerator over 3 end fraction equals 219n+3=21