In cartesian coordinates, we can write the position vectors as-
a) → r = 12.4 m , θ = 170° ↔ - 12.21 i + 2.15 j
b) → r = 4 cm , θ = 50° ↔ 2.57 i + 3.06 j
c) → r = 20 inches , θ = 210° ↔ - 17.32 i - 10 j
What are polar coordinates?It is two-dimensional coordinate system which uses a straight line distance (from a reference point) and the angle made by it (with respect to reference direction) to represent a point in the X-Y plane.
Given are the position vectors in polar coordinates of three points in X-Y coordinate system.
The transformation from polar coordinates (r, θ) into cartesian coordinates (x, y) is done using the following formulae -
x = r cosθ
y = r sinθ
a) → r = 12.4 m , θ = 170°
x = 12.4 x cos (170°) = 12.4 x -0.98480775301 = -12 .21
y = 12.4 x sin (170°) = 12.4 x 0.17364817766 = 2.15
In cartesian form → ( -12.21 i + 2.15 j )
b) → r = 4 cm , θ = 50°
x = 4 x cos (50°) = 4 x 0.64278760968 = 2.57
y = 4 x sin (170°) = 4 x 0.76604444311 = 3.06
In cartesian form → ( 2.57 i + 3.06 j )
c) → r = 20 inches , θ = 210°
x = 20 x cos (210°) = 20 x -0.86602540378 = -17.32
y = 20 x sin (210°) = 20 x -0.5= -10
In cartesian form → ( -17.32 i - 10 j )
Therefore, in cartesian coordinates, we can write the position vectors as -
a) → r = 12.4 m , θ = 170° ↔ - 12.21 i + 2.15 j
b) → r = 4 cm , θ = 50° ↔ 2.57 i + 3.06 j
c) → r = 20 inches , θ = 210° ↔ - 17.32 i - 10 j
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outlet and at the reactor inlet are of 14.4 m s−1 and 10.7 m s−1, respectively. What is the change of rate of kinetic energy (in W )? a. 102.68 b. −698.78 c. −696.53 d. 696.60 e. −102.68
We find that the change in kinetic energy is positive and equal to 696.60 W, option d. The formula for kinetic energy is given by KE = 1/2 * mv^2, where m is the mass of the fluid and v is its velocity.
In this case, we are given the velocities at the outlet and the reactor inlet, which are 14.4 m/s and 10.7 m/s, respectively. Since the mass of the fluid is not provided, we can assume it to be constant.
The change in kinetic energy is given by the difference in kinetic energies at the outlet and the reactor inlet, which can be calculated using the formula:
ΔKE = (1/2 * m * v_outlet^2) - (1/2 * m * v_inlet^2)
Simplifying this expression, we get:
ΔKE = 1/2 * m * (v_outlet^2 - v_inlet^2)
Plugging in the given values, we have:
ΔKE = 1/2 * m * (14.4^2 - 10.7^2)
Calculating this expression, we find the answer to be approximately 696.60 W. Therefore, the correct option is d. 696.60.
In summary, the change in the rate of kinetic energy is approximately 696.60 W. This is calculated by taking the difference between the kinetic energy at the outlet and the kinetic energy at the reactor inlet using the formula ΔKE = 1/2 * m * (v_outlet^2 - v_inlet^2). Plugging in the given velocities of 14.4 m/s and 10.7 m/s, we find that the change in kinetic energy is positive and equal to 696.60 W.
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According to Newton’s first law of motion, when will an object at rest begin to move?
when its inertia decreases to zero
when an unbalanced force acts upon it
when the action and reaction forces are equal
when two equal and opposite forces act upon it
According to Newton’s first law of motion, an object at rest will begin to move, when an unbalanced force acts upon it.
option B is the correct answer.
What is Newton's first law of motion?Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by an external force.
In other words, an object will maintain its state of motion (whether it is at rest or moving in a straight line at a constant speed) unless a force acts upon it.
Thus, according to Newton’s first law of motion, an object at rest will begin to move, when an unbalanced force acts upon it.
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Answer:
its B
Explanation:
A JFET has a drain current of 5mA. If IDSS = 10mA and VGS ( off )= -6 v. find The Value Of
( 1 ) VGS
( 2 ) VP
\(\begin{gathered} \: \: \\ \\ \\ \\ \end{gathered} \)
\( \underline {\huge \boxed{ \sf \color{skyblue}Answer : }}\)
Given :
\( \tt \large {\color{purple} ↬ } \: \: \: \: \: I_{D} = 5mA\)
\( \: \: \)
\( \tt \large {\color{purple} ↬ } \: \: \: \: \: I_{DSS} = 10mA\)
\( \: \: \)
\( \tt \large {\color{purple} ↬ } \: \: \: \: \: V_{GS(off)} = -6V\)
\( \: \: \)
\( \tt \large {\color{purple} ↬ } \: \: \: \: \: V_{GS} = {?}\)
\( \: \: \: \)
Let's Slove :
\( \tt \large I_{D} = I_{(DSS)} (1 - \frac {V_{GS}}{V_{GS(off)}} )^{2} \)
\( \: \: \: \)
\( \tt \large \: V_{GS} = (1 - \frac{ \sqrt{I_D} }{ \sqrt{I_{DSS}} } ) \times V_{GS(off)}\)\( \: \: \: \)
\( \tt \large \: V_{GS} = (1 - \frac{ \sqrt{5m} }{ \sqrt{10m} } ) \times { - 6}\)\( \: \: \)
\( \underline \color{red} {\tt \large \boxed {\tt V_{GS} = 1.75 ✓}}\)Protons and electrons are ejected from the sun in large quantities. These charge particles, that travel to the earth from the sun along with electromagnetic radiation, are called the solar wind. The solar wind penetrates the atmosphere of the earth much more at the geopmagnetic north and south poles than anywhere else on the earth. Why
The solar wind penetrates the Earth's atmosphere much more at the geomagnetic north and south poles due to the configuration of Earth's magnetic field lines.
Earth's magnetic field is generated by its core and creates a protective shield called the magnetosphere. This shield is important because it deflects harmful solar wind particles away from Earth's atmosphere. The magnetic field lines are shaped like loops that extend from the geomagnetic north and south poles. The field lines are more concentrated and closer to the Earth's surface at the poles, which allows solar wind particles to follow these lines and penetrate deeper into the atmosphere at the poles compared to other regions. This increased penetration at the poles is what causes phenomena such as auroras, where charged particles interact with the Earth's atmosphere to create beautiful light displays.
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The organisms and environments that make up a community, called an Response area, are constantly changing. Sudden and violent events, such as Response area from the ocean and Response area, that often cause these changes are called Response area. Response area results when rainfall exceeds the holding capacity of a drainage system.
Answer:
ecosystem; hurricanes and tornadoes; catastrophic events.; Fooding; moving water; soil
Explanation:
After using the word bank to fill in the blanks in the passage, the passage reads;
"The organisms and environments that make up a community called an ecosystem are constantly changing. Sudden and violent events, such as hurricanes and tornadoes that often cause these changes are called catastrophic events. Fooding results when rainfall exceeds the holding capacity of a drainage system. The energy of the fast-moving water and the layers of sediment carried by it can uproot or bury plants, reshape the soil and destroy roads and buildings."
I’m pretty sure it’s a,h I just need a second opinion
The vectors are said to be equal if they have same magnitude as well as same direction.
In case of C and G,
The direction of both the vectors are same but the magnitude of G is more than C.
Thus, C and G are not equal vectors.
In case of E and D,
Both the vectors have opposite direction to each other and the magnitude of D is more than E.
Thus, E and D are not equal vectors.
In case of B and C,
Both the vectors have same direction but the magnitude of C is more than the magnitude of B.
Thus, B and C are not equal vectors.
In case of A and H,
Both the vectors have same direction and both the vectors cover three boxes, thus, the magnitude of the vectors is same.
Hence, A and H are equal vectors.
You rev your car's engine to 2500 rpm (rev/min). What is the period of the engine? T = ??s What is the frequency of the engine? f = ??Hz If you change the period of the engine to 0.038 s , how many rpms is it doing? f = ??rpm
The speed of the car's engine, n = 2500 rev/min. In order to find the period of the engine, we use the formula;T = 1/f, where f = frequency.
Substituting the value of n into the formula, we can write;f = 2500 rev/min = (2500 rev/min) / (60 s/min) = 41.67 rev/s.
Therefore,T = 1/f = 1/41.67 rev/s = 0.024 s.
The period of the engine is 0.024 s.
To find the frequency of the engine; We use the formula f = 1/T.
Substituting the value of T, we get;f = 1/0.024 s = 41.67 Hz.
The frequency of the engine is 41.67 Hz. When T=0.038 s. We can use the formula f = 1/T to find the frequency when T = 0.038 s.
Substituting the value of T, we get;f = 1/T = 1/0.038 s = 26.32 Hz.
Frequency of the engine is 26.32 Hz.
We know that;f = n / 60.
Therefore,n = f × 60.
Substituting the value of f, we get;n = 26.32 Hz × 60 = 1579.3 rev/min.
Therefore, the engine is running at 1579.3 rpm when T = 0.038 s.
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i am having trouble with writing a 2 paragraph summary about this vidio can someone help me
Picture of the Big Bang (a.k.a. Oldest Light in the Universe)
Answer:
where is the video?
Explanation:
determine which part of the electromagnetic spectrum each of the following waves lies in. waves with a frequency f = 10.0 khz.
a. UV
b. Microwave
c. IR
d. X-ray
e. Visible
f. Radio
The waves with a frequency f = 10.0 kHz lie in the radio part of the electromagnetic spectrum.
The electromagnetic spectrum is the range of all types of electromagnetic radiation. It includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. The position of a wave on the spectrum is determined by its frequency and wavelength. The waves with a frequency f = 10.0 kHz have a wavelength of approximately 30,000 meters, which falls within the radio part of the spectrum.
Radio waves have the longest wavelengths and the lowest frequencies in the electromagnetic spectrum. They are used for broadcasting and communications, such as radio and TV signals. Therefore, the waves with a frequency f = 10.0 kHz belong to the radio part of the electromagnetic spectrum.
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Cyclist 1 pedals 40 kilometers east in 2 hours. Cyclist 2 pedals 10 kilometers west in half an hour. Based on this information, which statement about cyclists is correct?
Answer:
See Explanation
Explanation:
Given
Cyclist 1:
\(Distance = 40km\)
\(Time = 2hr\)
\(Direction = East\)
Cyclist 2:
\(Distance = 10km\)
\(Time = 0.5hr\)
\(Direction = West\)
The question requires options. Since none is given, I'll answer on a general term.
First, calculate the speed of both cyclists
\(Speed = \frac{Distance}{Time}\)
Cyclist 1:
\(Distance = 40km\)
\(Time = 2hr\)
\(Speed = \frac{40km}{2hr}\)
\(Speed = 20km/hr\)
Cyclist 2:
\(Distance = 10km\)
\(Time = 0.5hr\)
\(Speed = \frac{10km}{0.5hr}\)
\(Speed = 20km/hr\)
The following can be deduced from above:
Both cyclists travel at the same speed of 20km/hrBoth cyclists travel in opposite directions
Determine whether the following scenarios are either random or systematic errors:
When recording buret volumes, Wonda notices that their buret volume falls between 16.1 and 16.2 mL. Because buret volumes need to have 2 decimal places, Wonda uses their best judgement to estimate the volume to be 16.15 mL.
Daisy uses the analytical balance in order to measure the mass of the empty beaker. However, it turns out that the balance adds 0.0015 g to all measurements.
When performing his pipet trials, Remy look down at the meniscus to determine if it was in line with the calibration mark on the pipet. This meant the actual volume he transferred was always lower than volume he recorded.
The first and second scenario is a systematic error. The third scenario is a random error.
The first scenario is a systematic error because Wonda consistently estimates the buret volume to be between 16.1 and 16.2 mL, leading to a bias in the measurements.
The second scenario is a systematic error because the analytical balance consistently adds 0.0015 g to all measurements, leading to a bias in the measurements.
The third scenario is a random error because Remy's reading of the meniscus is subject to variation and does not consistently lead to an over or underestimation of the volume transferred. This can be reduced by using a standardized technique to read the meniscus, but the variation will still exist.
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Ammonia is a common____?
Answer:
Base
Hope this helps! :)
At any given time, ____ of the earth is illuminated by the sun. Select one: a. one-fourth b. one-third c. one-half d. two-thirds
At any given time, one-half of the Earth is illuminated by the sun (sunlight). The correct answer is option c).
This is because the Earth rotates on its axis once every 24 hours, causing different parts of the Earth to be exposed to sunlight at different times. As the Earth rotates, the half facing the sun experiences daytime, while the half facing away from the sun experiences nighttime.
The amount of sunlight that reaches the Earth's surface at any given location also depends on the tilt of the Earth's axis and its orbit around the sun. The Earth's axis is tilted at an angle of approximately 23.5 degrees relative to its orbit around the sun, which causes the seasons.
During the summer solstice, the hemisphere tilted towards the sun receives the most direct sunlight and experiences the longest day of the year, while the opposite hemisphere experiences the shortest day of the year.
During the winter solstice, the opposite occurs. During the equinoxes, the Earth's axis is neither tilted towards nor away from the sun, and both hemispheres experience equal amounts of daylight and darkness.
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Question 5 of 10
Which option is a potential environmental benefit of adopting a new
technology?
A. Increased research and development time
B. Preservation of habitat
C. Improved medical outcomes
D. Increased customer satisfaction
SUBMIT
Answer:
preservation of habitat
Explanation:
i just took the test
What is the environmental advantage of technology?
Renewable energy has enabled us to capture this naturally occurring energy and convert it into electricity or useful heat through devices such as solar panels, wind and water turbines, which reflects a highly positive impact of technology on the environment.
What are the impact of technology on environment?
The environmental impact of technology does not end with the raw materials and where they have come from.
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diagram for terrestial weather
The correct answer of terrestial weather:
The solar insolation in the visible and infrared regions of the solar electromagnetic spectrum is much more than the energy that space weather occurrences release into the troposphere and stratosphere. Despite claims to the contrary, there may be some connection between the Earth's climate and the 11-year sunspot cycle. There is no proof of this. For instance, it has frequently been suggested that the Maunder minimum, a 70-year period almost devoid of sunspots, is correlated to a cooler climate, but these correlations have vanished after further research. Changes in cosmic ray flux are hypothesized to affect how much cloud formation occurs.
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Please I need help kindly answer it fast.
Answer:
a
Explanation:
Answer:
3
Explanation:
period=1\time
period=1\3
period=0.3
Which motor and body should Devon use to build the car with the greatest acceleration? motor 1, with body 1 motor 1, with body 2 motor 2, with body 1 motor 2, with body 2
Answer:
hello your question is incomplete below is the complete question
Devon has several toy car bodies and motors. The motors have the same mass, but they provide different amounts of force, as shown in the table.
Which motor and body should Devon use to build the car with the greatest acceleration?
motor 1, with body 1
motor 1, with body 2
motor 2, with body 1
motor 2, with body 2
answer: Motor 2 body 1
Explanation:
F = ma
hence a ( acceleration ) = F / m
force of motor 2 = 15 N since the mass of the motor is the same and that of the bodies aren't given
The motor and body that would produce the greatest acceleration would be : Motor 2 Body 1 if the mass of Body 1 is less than the mass of Body 2
Answer:
c
Explanation:
Which best explains why a pyramid is used to represent energy flow within an ecosystem? Hint: what happens to available energy as you go up?
Explain the significance of the pyramid shape in the representation of the energy, biomass, or number pyramids. The pyramid is utilized because it can depict the energy present at each trophic level.
What does an energy pyramid serve?BACKGROUND: How energy moves through an ecosystem is depicted by an energy pyramid. Students can easily understand how energy is transmitted from consumers to producers by demonstrating the trophic (feed) levels of the ecosystem.
What aspect of the energy pyramid is accurate?The decline in energy as we pass thru every feeding (trophic) stage in an ecosystem is represented by an energy pyramid. And because 90% of energy is wasted at each stage of the pyramid's structure, energy gradually decreases from the producers at the base to the predators at the top.
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Which of the following particle is responsible for the transfer of static charge?
A. Neutron
B. Electron
C. Proton
D. A & C
Answer:
B. Electron
Static charge is produced by electron transfer.
Explanation:
Answer A: The neutron does not possess a charge and is said to be neutral.
Answer D: Protons and neutrons never move from object to object.
Only negative charges can move freely from one object to another. The energy that comes from these charges particles is called electrical energy.
....
Hope this answer can help you.
The answer is an electron.
ben starts waling at 2 mi/h. after an hour and a half amanda begins jogging at 6 mi/h. how long until amanda catches ben
Amanda would need to catch up to Ben in 6/10 hours, or 0.6 hours.
What is distance?Use the distance equation d = st, which reads distance equals speed times time, to find the distance. Given that both rate and speed denote a specific amount of travel per unit of time, such as miles per hour or kilometers per hour, they are comparable. R = s = d/t indicates that rate r is equal to speed s.
At 7 miles per hour, Amanda starts jogging down the same path.
Thus, following t hours, Amanda's position is determined by:
A(t) = 7t
Ben begins moving at a 2mph pace along a path.
Ben will be at position 2×1.5 = 3 when Amanda departs in an hour and a half. Ben's position therefore after t hours is as follows:
B(t) = 3+2t
A(t) = B(t)
7t = 3+2t
5t = 3
t = 3/5
t = 0.6hrs
So, Amanda will catch up Ben after 0.6 hours.
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Complete question " Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?".
if molecule gains heat energy it converts liquid to gas
Answer:
Actually, the substance is the one that changes from liquid to gas.
The molecule just gains energy which overcomes the attraction force between it and neighboring molecule.
Name all the energy transfers that occur to make a solar-powered traffic light work (name what generates the energy, and what kind of energy it turns to):
if the volume of a fixed mass of hydrogen in a container is 30cm³ at a pressure of 50mmHg find the volume of the gas if the pressure is 60mmHg at constant pressure
25
Explanation:
P1V1=P2V2 hence 50×30=60v
V=1500÷60
V=25
If I triple the mass per unit length of guitar string, its natural frequency changes by what factor?
If you triple the mass per unit length of guitar string, the natural frequency changes by a factor of 0.63.
The natural frequency of a stretched string is given by the formula:
f=\frac{1}{2L}\sqrt{\frac{T}{\mu}}
where f is the frequency, L is the length of the string, $T$ is the tension in the string and \mu is the mass per unit length of the string.
Therefore, if you triple the mass per unit length of the guitar string, then the frequency changes by a factor of: \frac{f_2}{f_1}=\sqrt{\frac{\mu_1}{\mu_2}}
where f_1 is the original frequency and \mu_1 is the original mass per unit length, f_2 is the new frequency and \mu_2 is the new mass per unit length.
Substituting the values, we get:
\frac{f_2}{f_1}=\sqrt{\frac{\mu_1}{3\mu_1}}\frac{f_2}{f_1}=\sqrt{\frac{1}{3}}\frac{f_2}{f_1}=0.63
Therefore, if you triple the mass per unit length of guitar string, its natural frequency changes by a factor of 0.63.
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What causes comets to move through the solar system?.
I study in astronymy in College I had a question like this.
Long-period comets are set in motion towards the Sun from the Oort cloud by gravitational perturbations caused by passing stars and the galactic tide. Hyperbolic comets may pass once through the inner Solar System before being flung to interstellar space. The appearance of a comet is called an apparition.
Two point charges are placed at the following points on the x-axis. +2.0 C at
×=0, -3.0.C at 0.40m. Find the electric field strength at 1.20m?
The electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.
To find the electric field strength at a distance 1.20 m on the x-axis, we can use Coulomb's law:
\($$F=k\frac{q_1q_2}{r^2}$$\)
where F is the force between two charges, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb constant.For a single point charge q located at the origin of the x-axis, the electric field E at a distance r is given by:
\($$E=\frac{kq}{r^2}$$\) where k is the Coulomb constant.
So, let's calculate the electric field due to each charge separately and then add them up:
For the +2.0 C charge at x = 0, the electric field at a distance of 1.20 m is:\($$E_1=\frac{kq_1}{r^2}=\frac{(9\times10^9)(2.0)}{(1.2)^2}N/C$$\)
For the -3.0 C charge at x = 0.40 m, the electric field at a distance of 1.20 m is:
\($$E_2=\frac{kq_2}{r^2}\)
\(=\frac{(9\times10^9)(-3.0)}{(1.20-0.40)^2}N/C$$\)
The negative sign indicates that the direction of the electric field is opposite to that of the positive charge at x = 0.
To find the net electric field, we add the two electric fields\(:$$E_{net}=E_1+E_2$$\)
Substituting the values of E1 and E2:
\($$E_{net}=\frac{(9\times10^9)(2.0)}{(1.2)^2}-\frac{(9\times10^9)(3.0)}{(0.8)^2}N/C$$E\)
net comes out to be -1.5×10⁴ N/C.
Therefore, the electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.
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A mountain climber has a mass (with all of their equipment) of 95, point, 0, k, g,95.0kg. If they were perfectly efficient, and ate 500, g,500g of chocolate (providing 11, point, 1, M, J,11.1MJ of chemical energy), how high could they climb?
Answer:
11900 meters
Explanation:
Use the Potential energy = mgh formula, substituting these in to get 11.1x10^6 = 95 x 9.81 x h.
Rearrange to make h the subject and the answer given is 11900 (3sig.fig.)
The maximum height to which he can climb will be 1.168 x 10⁴ meters.
What is potential energy?
The potential energy of a body is the energy of the body due it position. The potential energy always exist for two bodies which are in mutual interaction with each other for example by a force. For body a on earth, the potential energy of the body - earth system is -
E[P] = mgh
Given is a mountain climber that has a mass of 95 kg.
We can write -
Mass of climber = [M] = 95 kg
Energy gained by eating the chocolate = [E] = 11.1 MJ = 1.11 x 10⁷ joules
Assume that the height achieved achieve by the climber is [h] meters
Therefore, the potential energy gained at that height will be equal to 11 MJ
Therefore -
mgh = 1.11 x 10⁷
95 x 10 x h = 1.11 x 10⁷
95 x 10 x h = 1110 x 10⁴
h = (1110 x 10⁴)/950
h = 1.168 x 10⁴ meters
Therefore, the maximum height to which he can climb will be 1.168 x 10⁴ meters.
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If Calcium has 2 valence electrons and Chlorine has 7 valence electrons, how many Cl-1 ions would need to combine with 1 Ca+2 ion?
Answer:
CALCIUM IDENINE ADEININE AND PHOSPHATE
Explanation:
Make a super villain out of these resources
Answer:the super villain would have the ability to control electricity and could take any Metal object or weapons that anyone points at him because he is magnetic
Explanation:
At today's market value, how much gold is dissolved in the ocean?
Based on the current gold spot price of $42.51 USD per gram, that amount of gold would be worth approximately $771 trillion.
When we compare that to the 2016 US Gross Domestic Product (GDP) of 18.57 trillion and its 41 times. It can also be compare to global domestic product of $78.28 trillion in 2014, which is nearly 10 times the entire world's domestic product.
We can clearly see that world's oceans contain a lot of money in terms of the gold inside it. The enormous process of extracting the gold from enormous quantities of seawater, however is tedious. There would be about 13 billionths of a gram of gold in each liter of water.
There is currently no profitable way to extract the gold from seawater that is also cost-effective. Nevertheless, many enthusiastic investors and inventors, including dishonest ones, persisted. In a fever dream in the 1890s, preacher Ford Jernegan came up with the idea for a "Gold Accumulator." The idea was to use a procedure using mercury and electricity treatments to remove gold from the Long Island Sound.
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