Which definition describes a scientific theory?
OA. A claim, assumption, or method that is commonly thought to be
based on science but is not scientific
B. The pursuit of knowledge about the natural world and the
application of that knowledge
C. An explanation for a natural phenomenon that is based on facts
and is supported by the results of many experiments
D. A method of carefully examining an idea, using a variety of
thought processes to construct and evaluate knowledge
OA: A. A claim, assumption, or method that is commonly thought to be based on science but is not scientific.
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
A claim, assumption, or method that is commonly thought to be based on science but is not scientific is called pseudoscience. Pseudoscience is often presented as being scientific, but it does not meet the criteria of science. For example, pseudoscience may be based on speculation or personal opinion, rather than on evidence. It may also be based on experiments that are not properly controlled or that are not reproducible.
Pseudoscience can be harmful because it can lead people to make decisions that are not based on evidence. For example, people who believe in pseudoscience may be more likely to avoid proven medical treatments or to use unproven treatments that could actually be harmful.
It is important to be able to identify pseudoscience so that you can make informed decisions about your health and your life. If you are unsure whether something is pseudoscience, you can ask a scientist or do some research to find out more.
a satellite revolves around the earth in an orbit of radius 42000000m. find the value of g and its orbital speed at this hieght.
Answer:
Step 1: Given data
Acceleration due to gravity on the surface of the earth is g.
The radius of the earth is R and x is the height of the satellite above the earth's surface.
The mass of the satellite is m.
Step 2: Calculate the orbital speed of the satellite.
We know that,
mv2R+x=GMmR+x2
v=GMR+x
v=GMR2×R2R+x
Step 3: Final answer
v=gR2R+x
We can also write it as
v=gR2R+x12
convert 750W into kilowatts
Ans. 0.75
To convert watts into kilowatts we must divide it by 1000
so dividing 750W by 1000
we get,
750/1000 = 0.75
hence 750W in kilowatts equals to 0.75
The softest sound a human ear can hear is at 0 dB (Io = 10-12 W/m2). Sounds above 130 dB cause pain. A particular student's eardrum has an area of A = 51 mm2. What is the most power, in watts, the ear can receive before the listener feels pain?
Im so confused on how to even start with this problem, my main question is how sound and power are related.
Answer:
Sound and power are related through intensity, which is the amount of power per unit area. The intensity of a sound wave is proportional to the square of its amplitude, which is a measure of how far the wave oscillates from its equilibrium position.
To solve this problem, you can use the formula for sound intensity:
I = P/A
where I is the intensity of the sound wave in watts per square meter (W/m^2), P is the power of the sound wave in watts (W), and A is the area of the eardrum in square meters (m^2).
You are given that the softest sound a human ear can hear is 0 dB, which corresponds to an intensity of 10^-12 W/m^2. You are also given that sounds above 130 dB cause pain. To find the maximum power the ear can receive before the listener feels pain, you can rearrange the formula for intensity to solve for power:
P = AI
where A is the area of the eardrum in square meters.
Substituting the given values, you get:
P = (51 x 10^-6 m^2)(10^-12 W/m^2 x 10^(130/10))
Simplifying this expression, you get:
P = 1.8 x 10^-3 W
Therefore, the most power the ear can receive before the listener feels pain is 1.8 x 10^-3 watts.
Can the potential of a non uniform charged sphere be the same as that of a point charge? Explain in details
No. The potential of a non-uniform charged sphere cannot be the same as that of a point charge.
Non-uniform charged sphere as a point chargeThe potential at any point in space is determined by the distribution of charge within the system, and a non-uniform charged sphere has a different charge distribution than a point charge.
A point charge has all of its charges concentrated at a single point, while a non-uniform charged sphere has charge distributed throughout its volume.
As a result, the electric field and potential will be different for these two systems, even if they have the same total charge. Therefore, the potential of a non-uniform charged sphere cannot be the same as that of a point charge.
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The velocity of three particles of masses 20g, 30g and 50g are 2i, 10j and 10k respectively. The velocity of the centre of mass the three particle) is
Answer:
The velocity of the center of mass (Vcm) of a system of particles can be calculated using the formula:
Vcm = (m1v1 + m2v2 + m3v3 + ... + mnvn) / (m1 + m2 + m3 + ... + mn)
where m1, m2, m3, ... mn are the masses of the particles and v1, v2, v3, ... vn are their velocities.
In this problem, we have three particles with masses of 20g, 30g, and 50g and velocities of 2i, 10j, and 10k respectively. We can convert the masses to kg to make the calculations easier:
m1 = 20g = 0.02kg
m2 = 30g = 0.03kg
m3 = 50g = 0.05kg
Using the formula above, we can calculate the velocity of the center of mass:
Vcm = (m1v1 + m2v2 + m3v3) / (m1 + m2 + m3)
Vcm = (0.02kg * 2i + 0.03kg * 10j + 0.05kg * 10k) / (0.02kg + 0.03kg + 0.05kg)
Vcm = (0.04i + 0.3j + 0.5k) / 0.1kg
Vcm = 0.4i + 3j + 5k m/s
Therefore, the velocity of the center of mass of the three particles is 0.4i + 3j + 5k m/s.
mark me brilliant
Price $15 12 9 6 3 Quantity Demanded per Month 1 2 3 5 7 Price $15 12 9 6 3 In the BOX what you would expect to see if you plotted the numbers on the graph. The quantit demand pe month dec 0 1 2 3 4 5 6 7 Quantity b. It costs Charlene $2.00 to ride to bus to the dog owners house each time she goes. What number of dog walks will give her the most profit?
From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.
How to solve
Based on the provided data, we can create a demand schedule for the prices and the quantity demanded per month.
Let's first organize the data in a table:
Price ($) Quantity Demanded per Month
15 1
12 2
9 3
6 5
3 7
If you plotted these numbers on a graph, you would expect to see a downward-sloping curve, illustrating the inverse relationship between price and quantity demanded. As the price decreases, the quantity demanded per month increases.
Now let's consider Charlene's costs and profits from walking dogs. It costs her $2.00 for each bus ride to the dog owner's house.
To calculate her profit, we need to find her total revenue at each price point, then subtract her total costs.
Price ($) Quantity Demanded per Month Total Revenue ($) Total Costs ($) Profit ($)
15 1 15 2 13
12 2 24 4 20
9 3 27 6 21
6 5 30 10 20
3 7 21 14 7
From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.
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The boy biked 600 m at a speed of 10 m/s, how long did it take him to bike the total distance?
Answer:60 seconds
Explanation: Since we have the boy's initial location si (0m), final location sf (600m) and his velocity v, we can have our position equation like so:
sf = si + vt
600 = 0 + 10t
Solve for t by dividing 600 by 10 and your time t = 60s
A force acts on a particle that has a mass of 1.5 kg. The force is related to the position x
of the particle by the formula = 0.503 where if x is in meters and F is in newtons. (a)
What are the SI units of C? (b) Find the work done by this force as the particle moves from
= 3.0 to = 1.5 (c) At = 3.0, the force points opposite the direction of the
particle’s velocity (speed is 12.0m/s). What is its speed at = 1.5? (d) Can you tell its
direction of motion at using only the work–kinetic energy theorem? Explain your
calculations.
(a) F(x) = 0.503 x, where x is in meters and F is in newtons, is the formula given for the force. We can see that this equation's proportionality constant, C, must be expressed in newtons per meter. C is therefore measured in N/m in the SI.
The work done and direction(b) The work done by the force as the particle moves from x = 3.0 m to x = 1.5 m can be calculated using the formula for work, which is W = ∫ F(x) dx, where the integral is taken over the distance moved. Therefore, we have:
W = ∫ 0.503 x dx from x = 3.0 to x = 1.5
W = [0.503/2 x^2] from x = 3.0 to x = 1.5
W = [0.503/2 (1.5^2 - 3.0^2)]
W = -1.129 J
The work done by the force is -1.129 joules.
(c) At x = 3.0, the force is given to be in the opposite direction to the particle's velocity. Therefore, the force is opposing the motion of the particle. We can use the work–kinetic energy theorem to determine the change in kinetic energy of the particle between x = 3.0 and x = 1.5, and hence its speed at x = 1.5. The work–kinetic energy theorem states that the net work done on an object is equal to its change in kinetic energy. Therefore, we have:
W_net = ΔK
In this case, the only force acting on the particle is the given force, and we have already calculated the work done by this force as -1.129 J. Therefore, we have:
W_net = -1.129 J
ΔK = 1.129 J (since the work done is negative, indicating a decrease in kinetic energy)
We can use the formula for kinetic energy, K = (1/2)mv^2, to find the particle's speed at x = 1.5. Therefore, we have:
ΔK = (1/2)m(v^2 - v_0^2)
1.129 = (1/2)(1.5)(v^2 - 12^2)
v^2 = 12^2 - (2/1.5)(1.129)
v^2 = 56.49
v = 7.52 m/s
The particle's speed at x = 1.5 is 7.52 m/s.
(d) kinetic energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done by the given force Is -1.129 J, the initial kinetic energy of the particle (since we are told its speed at x = 3.0).
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When a wave reaches a surface, the new material absorbs all the energy of the wave.
O True
O False
Answer: true
Explanation: if the current element is above the current water level then it is true
A bicyclist travels 69.05 kilometers in 4.332 hours. What is the cyclist's average speed?
Answer:
v = 15.939 km/h
Explanation:
distance (d) = 69.05 km
time (t) = 4.332 hours
Speed (v) = ?
v = d / t
v = 69.05 / 4.332
v = 15.939 km/h
estimate the work you do to mow a lawn 10m by 20m with a 50 cm wide mower. Assume you push with a force of about 15 N.
Answer:
W = 6000 Joule
Explanation:
Work is defined as force times distance
W = F * d
We know that F = 15N, we just need the distance (d)
Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.
The width of the mower is only 50 cm = 0.5 m.
This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,
d = 10 (meter) * 40 (times) = 400 meter
Therefore:
W = (15) * (400) = 6000 J
4-What is the equivalent resistance of this circuit?
( )32 Ω
( )43 Ω
( )48 Ω
( )74 Ω
Explanation:
The parallel resistors ( 10 and 40 Ω) have an equivalent resistance of
( 40 * 10 ) / ( 40 + 10 ) = 8 Ω
Then you can add all of the series resistances to find the total resistance
15 + 25 + 8 Ω = 48 Ω
Remember V = IR ....then V/R = I
Current = V/ R = 55 v / 48 Ω = 1.15 A
13. If the supply of gasoline rises, name a substitute that will increase in demand? 14. How do you think each of the following affected the world price of oil? List if it will effect supply or demand, and the price change if any. Use basic supply and demand analysis. a. Tax credits were offered for expenditures on home insulation. b. The Alaskan oil pipeline was completed. c. Oil was discovered in Mexico and the North Sea. d. Sport Utility Vehicles and minivans became popular. e. Natural oil reserves became depleted
13. If the supply of gasoline rises, a substitute that may increase in demand could be electric or hybrid vehicles.
14. Here is how each of the following events may have affected the world price of oil using basic supply and demand analysis:
a. Tax credits offered for expenditures on home insulation would likely decrease the demand for oil as people would use less energy to heat their homes. This would lead to a decrease in the price of oil.
b. The completion of the Alaskan oil pipeline would increase the supply of oil, leading to a decrease in the price of oil.
c. The discovery of oil in Mexico and the North Sea would increase the supply of oil, leading to a decrease in the price of oil.
d. The popularity of Sport Utility Vehicles and minivans would increase the demand for oil as these vehicles typically consume more gasoline than smaller cars. This would lead to an increase in the price of oil.
e. The depletion of natural oil reserves would decrease the supply of oil, leading to an increase in the price of oil.
Four point masses 2kg, 4kg, 6kg and 8kg are placed at the corners of Square ABCD of 2cm long respectively. Find the Position of centre of mass of the system from the corner A.
Four point masses 2kg, 4kg, 6kg and 8kg are placed at the corners of Square ABCD of 2cm long respectively. the Position of center of mass of the system from the corner A. is (1 , 1.4 ) cm.
Considering A as it origin
center of mass along X axis
[tex]X = \frac{M_{a}r_{a} + M_{b}r_{b} + M_{c}r_{c} + M_{d}r_{d} }{M_{a} + M_{b} + M_{c}+ M_{d}}[/tex]
X = 2×0+4×2+6×2+8×0 ÷ (2+4+6+8)
X = 20 ÷ 20 = 1 cm
[tex]Y = \frac{M_{a}r_{a} + M_{b}r_{b} + M_{c}r_{c} + M_{d}r_{d} }{M_{a} + M_{b} + M_{c}+ M_{d}}[/tex]
Y = 2×0+4×0+6×2+8×2 ÷ (2+4+6+8)
Y = 28 ÷ 20 = 1.4 =cm
The position of the center of the mass from the corner A which is the origin is (1 , 1.4 ) cm.
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describe what the weather would be like as a warm front passes, then describe what would occur as a cold front passes.
The air becomes humid during warm front passes and a cold front means a transition where warm air is being replaced by the cold air.What do you mean by weather?
The weather means the atmosphere at a particular place and time with respect to temperature, pressure, cloudiness, wind, etc.
A warm front means when the air is very warm and humid as compared to before.
A cold front is when the air is very colder and drier than the air above it. More than 15 degrees temperature can drop down when a cold front passes.
A cold front will probably bring winds, thunderstorms, and rain.Therefore, the cold front moves faster than the warm front.Learn more about the Weather here:
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what is scientific learning
Answer:
the learning which is gained through observation and experimentation
(•) How many electrins represent a Change of -70 mic?
The number of electrons represent a Change of -70 μC is 4.3 × 10¹⁴.
Electric charge is the physical property of matter that experiences force when it is placed in electric field. F = qE where q is amount of charge, E = electric field and F = is force experienced by the charge. there are two types of charges, positive charge and negative charge which are generally carried by proton and electron resp. like charges repel each other and unlike charges attract each other. the flow charges is called as current. Elementary charge is amount of charge a electron is having, whose value is 1.602 x 10⁻¹⁹ C
The value of elementary charge that is charge on 1 electron is 1.6× 10⁻¹⁹ C
-70 μC = N × 1.6× 10⁻¹⁹ C
N = -70 μC / 1.6× 10⁻¹⁹ C
N = -70 μC / 1.6× 10⁻¹⁹ C
N = 4.3 × 10¹⁴ electrons
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What is the acceleration of a 650 kg racing camel that has a forward net force of 897N
Answer:
a = 0.724 m/s2
Explanation:
Known:
m = 650 kg
F = 897 N
a = ?
Use this formula:
F = ma
a = F/m
a = 650/897
a = 0.724 m/s2
5. A child wanting to make a cordial ice block, places 200g of cordial at 25°C in the freezer. If the freezer can remove energy at the rate of 250 joules per second, what time will it take for the cordial to freeze? (Assume the specific latent heat and specific heat capacity of cordial are the same as water.)
The time taken for the cordial to freeze is 267.2 s.
What is the time taken for the cordial to freeze?The amount of heat energy (Q) required to freeze the cordial can be calculated using the following formula:
Q = ml
where;
m is the massl is the latent heat of fusion of iceQ = 334 J/g x 200 g
Q = 66,800 J
The time taken for the cordial to freeze is calculated as;
t = Q/W
where;
W is the rate of energy removal or powert is timet = (66,800 J) / (250 J/s)
t = 267.2 s
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Q8 (10pts)
You are working with cartesian unit vectors and ŷ in the plane of the board. Your friend is introducing a
new unit vector  = 0.52 + qŷ, but isn't sure what value q should have. Solve for q and make a
recommendation for what value they could use. If you determine more than one possible value for g,
mention this in your recommendation.
The length one vectors i, j, and k, which stand for conventional measure vectors in three different dimensions, contribute along the positive x, y, and z axes, respectively.
What are the Cartesian plane's unit vectors?Unit vectors i and j, which run along the x-axis and y-axis, respectively, define the Cartesian coordinate system. The radial unit vector r, which indicates the direction away from the origin, and the unit vector t, which is orthogonal (perpendicular) to the radial direction, together create the polar coordinate system.
Can a unit vector be created by adding two unit vectors?The size of the discrepancy is three if the product of two vectors with units is a unit vector. steps to determine the size of Consider a and b, two unit vectors whose total is a unit vector c.
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16. Other things constant, what do you expect will happen in the next 50 years to the relative demand for each of the following. a. Nursing homes. Demand b. Baby high chairs. Demand Price Price
The thing that I expect will happen in th the below is each of the following.
Nursing Homes: Demand for nursing homes is likely to increase in the next 50 years due to the aging population. Baby High Chairs: Demand for baby high chairs may increase or decrease depending on demographic and lifestyle trends. What is the justification?With regards to Nursing Homes as the population ages, there will certainly be a greater demand for nursing homes during the next 50 years. The need for long-term care facilities is anticipated to increase as people live longer. More patients might need specialized care that can only be offered in a nursing home setting as medical technology advances. However, future changes to healthcare and governmental policy may also have an impact on the demand for nursing homes.
Baby High Chairs depending on demographic and lifestyle trends, demand for baby high chairs may rise or fall. Baby high chairs may become less popular if birth rates keep falling or if parents choose more adaptable seating solutions. However, if more parents opt to
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What is the critical angle between polycarbonate (n1 = 1.58) and quartz (n2 = 1.41)?
24 degrees
46 degrees
63 degrees
75 degrees
Answer:
Approximately [tex]63.2^{\circ}[/tex].
Explanation:
The refractive index [tex]n[/tex] gives the ratio between the speed of light in vacuum and the speed of light in the given material. A larger refractive index means slower speed of light in the medium. In this question, the speed of light is slower in polycarbonate than in quartz.
When light travels from a material of low light speed to a material of higher light speed, the angle of refraction [tex]\theta_{r}[/tex] will exceed the angle of incidence [tex]\theta_{i}[/tex] (both with respect to the normal.)
The critical angle at this interface is the [tex]\theta_{i}[/tex] for which [tex]\theta_{r} = 90^{\circ}[/tex]. Note that since [tex]\theta_{i}\![/tex] cannot exceed [tex]90^{\circ}[/tex], [tex]\theta_{i} < \theta{r}[/tex] and light must be entering a faster medium from a slower medium. In this question, light would be entering quartz ([tex]n = 1.41[/tex], faster) from polycarbonate ([tex]n = 1.58[/tex], slower.)
By Snell's Law:
[tex]n_{i}\, \sin(\theta_{i}) = n_{r}\, \sin(\theta_{r})[/tex],
Where:
[tex]n_{i}[/tex] is the refractive index of the medium from which light enters, [tex]n_{r}[/tex] is the refractive index of the medium light enters into,[tex]\theta_{i}[/tex] is the angle of incidence at which light enters the interface (with respect to the normal), and[tex]\theta_{r}[/tex] is the angle of refraction at which light leaves the interface (also with respect to the normal.)Set [tex]n_{i} = 1.58[/tex] (polycarbonate), [tex]n_{r} = 1.41[/tex] (quartz), and [tex]\theta_{r} = 90^{\circ}[/tex]. Rearrange the equation and solve for [tex]\theta_{i}[/tex]:
[tex]\begin{aligned}\sin(\theta_{i}) &= \frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \end{aligned}[/tex].
[tex]\begin{aligned}\theta_{i} &= \arcsin\left (\frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \right) \\ &= \arcsin \left(\frac{1.41\, \sin(90^{\circ})}{1.58}\right) \\ &\approx 63.2^{\circ}\end{aligned}[/tex].
Would two observers standing on opposite sides of the truck hear the same pitch at the same time? Explain.
No, two observers standing on opposite sides of the truck would not hear the same pitch at the same time.
Why are sound wavelengths different?This is due to the fact that the sound waves produced by the truck's horn would move at a specific pace that would be constant for both viewers. The distance between the horn and each viewer, however, fluctuates as the truck passes the two people, resulting in a variation in the amount of time it takes for the sound waves to reach each person.
The Doppler effect, which comes from this change in time, changes how the sound waves are perceived in terms of pitch. To be more precise, the observer in front of the truck would hear a higher pitch (shorter wavelength) and the observer behind the truck would hear a lower pitch (longer wavelength).
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The short-term effects of marijuana can include __________.
Answer:
Explanation:
Increased heart rate
A vehicle is being planned that is driven by a flywheel engine. It has to run for at least 30 minutes and develop a steady power of 500 W.
Answer:
To meet the requirements of running for at least 30 minutes and developing a steady power of 500W, the flywheel engine needs to have sufficient energy storage capacity and be capable of delivering a steady power output.
Assuming that the flywheel engine is 100% efficient (i.e., no energy losses due to friction, air resistance, or other factors), the energy storage capacity required can be calculated as follows:
Energy storage capacity = Power x Time
= 500W x 30min
= 15,000 watt-minutes or 250 watt-hours
This means that the flywheel engine needs to be capable of storing at least 250 watt-hours of mechanical energy.
5) Find the electric current of this circuit:
( ) 5 A
( ) 8.5 A
( ) 3 A
( ) 10 A
The electric current in the circuit below is 3 A And the right option is C. 3A.
What is electric current?
Electric current is the rate of flow of charge in a circuit.
To calculate the electric current in the circuit below, we use the formula:
Formula:
I = V/R'.....................Equation 1Where:
I = Electric currentV = VoltageR' = Effective resistanceFrom the question,
Given:
V = 285 VR' = (20//20)+25+25+15R' = (20/2)+25+25+15+20R' = 10+25+25+15R' = 95 ohmsSubstitute these values into equation 1
I = 285/95I = 3 AHence, the right option is C. 3A
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A small block with mass 0.0400 kg
is moving in the xy
-plane. The net force on the block is described by the potential-energy function U(x,y)=(5.50J/m2)x2−(3.70J/m3)y3
.
Part A
What is the magnitude of the acceleration of the block when it is at the point x
= 0.40 m
, y
= 0.50 m
?
Express your answer with the appropriate units.
Part B
What is the direction of the acceleration of the block when it is at the point x
= 0.40 m
, y
= 0.50 m
?
Express your answer in degrees.
The magnitude of acceleration at the given point is 8.04 m/s², and the direction of acceleration at the given point is 38.5° below the negative x-axis.
To find the magnitude of acceleration at the given point, we need to calculate the force acting on the block using the potential-energy function and then use Newton's second law, F=ma, to find the acceleration.
The force acting on the block can be found by taking the negative gradient of the potential-energy function;
F = -∇U = (-∂U/∂x)i + (-∂U/∂y)j
where i and j are unit vectors in the x and y directions, respectively.
Taking the partial derivatives of U(x,y) with respect to x and y, we get;
∂U/∂x = 11.0 J/m² × x
∂U/∂y = -11.1 J/m³ × y₂
Plugging in the values x=0.40 m and y=0.50 m, we get;
∂U/∂x = 1.76 J/m
∂U/∂y = -1.39 J/m
Therefore, the force acting on the block at (0.40 m, 0.50 m) is;
F = (-1.76 J/m)i + (-1.39 J/m)j
Using Newton's second law, F=ma, we can find the magnitude of acceleration:
a = F/m = ([tex]F_{x}[/tex][tex]F_{y}[/tex]/m₂ + [tex]F_{y}[/tex]₂/m₂)1/2
= [(1.76 J/m)2 + (-1.39 J/m)2]/0.0400 kg
= 8.04 m/s2
Therefore, the magnitude of acceleration at the given point is 8.04 m/s².
To find the direction of acceleration at the given point, we need to find the angle between the force vector and the positive x-axis.
The angle θ can be found using the formula;
θ = tan-1([tex]F_{y}[/tex] /[tex]F_{x}[/tex])
Plugging in the values of [tex]F_{x}[/tex] and [tex]F_{y}[/tex] at (0.40 m, 0.50 m), we get;
θ = tan-1(-1.39 J/m / 1.76 J/m)
= -38.5°
Since the force vector is in the third quadrant (i.e., both [tex]F_{x}[/tex] and [tex]F_{y}[/tex] are negative), the angle θ is negative. Therefore, the direction of acceleration at the given point is 38.5° below the negative x-axis.
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The length of the Achilles tendon increases 0.500 cm when the force exerted on it by the muscle increases from 3230 N to 4787 N.
How much work is done by the muscle in stretching the tendon?
The work done by the muscle in stretching the Achilles tendon is 20.04 joules.
To calculate the work done by the muscle in stretching the Achilles tendon, we can use the formula:
Work = Force × Distance
We know that the force exerted on the tendon by the muscle increased from 3230 N to 4787 N, causing the tendon to stretch by 0.500 cm.
converting the distance from centimeters to meters:
Distance = 0.500 cm = 0.005 m
Now we can calculate the work done by the muscle:
Work = Force × Distance
Work = (4787 N + 3230 N)/2 × 0.005 m
Work = 4008.5 N × 0.005 m
Work = 20.04 J
Therefore, the work done by the muscle in stretching the Achilles tendon is 20.04 joules.
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From a sack of fruit containing 3 Apples ,2 Bananas , and 3 oranges , a random sample of 4 pieces of fruit is selected. Suppose X is the number of apples and Y is the number of bananas in the sample.
(a) Find the joint probability distribution of X and Y.
(b) Find P[(X,Y)A], where A is the region that is given
The joint probability distribution of X and Y is 2/70 and 3/70.
The value of P[(X,Y)A], where A is the region that is given is 1/2.
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The value of P[(X,Y)A], where A is the region that is given is:
= 0 + 2/70 + 3/70 + 3/70 + 18/70 + 9/70
= 35 / 70
= 1/2.
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