You see a bolt of lightning and then hear thunder 6 seconds later. About how many miles away was the lightning
Answer:
1.2 miles away
Explanan:
Seconds/five= Miles away
6/5=1.2
A 21.1 kg person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The bottom of the ladder rests on a floor with a rough surface where the coefficient of static friction is 0.14 . The angle between the horizontal and the ladder is θ . The person wants to climb up the ladder a distance of 0.88 m along the ladder from the ladder’s foot. What is the minimum angle θmin (between the horizontal and the ladder) so that the person can reach a distance of 0.88 m without having the ladder slip? The acceleration of gravity is 9.8 m/s 2 . Answer in units of ◦
The minimum angle so that the person can reach a distance of 0.88 m without having the ladder slip is 8⁰.
What is the weight of the person?The weight of the person is calculated by applying the following formula.
W = mg
where;
m is the mass of the persong is acceleration due to gravityW = ( 21.1 kg x 9.8 m/s² )
W = 206.78 N
The force of friction is calculated as;
Ff = μW
where;
μ is coefficient of frictionFf = 0.14 x 206.78
Ff = 28.95 N
If the person must not fall, the clockwise moment must be equal to anticlockwise moment.
28.95 x 0.88 x cosθ = 206.78 x 0.88 x sinθ
28.95 x cosθ = 206.78 x sinθ
28.95 / 206.78 = sinθ / coθ
28.95 / 206.78 = tanθ
θ = arc tan ( 28.95 / 206.78 )
θ = 8⁰
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What statement about energy transfer in a wave is true?
Answer:
Energy moves between the particle of the medium.
Explanation:
the gauge pressure of a pneumatic cylinder reads 50lb/in^2. assume standard atmospheric pressure(14.7 psi). absolute pressure is 64.7 before and after. what is the volume in the cylinder after the gas is compressed
The new volume of the cylinder after the gas is compressed is 7.03 cubic inches.
Measure atmospheric pressure.
The pressure the atmosphere is exerting at a certain location is known as atmospheric pressure. Normal measurement is done at 14.7 psi, or sea level.
Atmospheric pressure = 14.7 psi
Figure out the gauge pressure.
Gauge pressure = 50 lb/in2
The absolute pressure should be calculated.
Absolute pressure = 64.7 psi
Determine the cylinder's new volume.
New volume = (Absolute pressure - Atmospheric pressure) / Gauge pressure
New volume = (64.7 - 14.7) / 50
New volume = 7.03 cubic inches
Hence, the cylinder's new volume is 7.03 cubic inches.
Complete Question:
What is the volume of the cylinder after the gas is compressed if the gauge pressure of the pneumatic cylinder reads 50lb/in^2 and the absolute pressure is 64.7psi before and after?
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In the Pacific, the seafloor on one side of the youngest crust gets very old, but the seafloor on the other side is much younger. How do you think the location of the youngest aged seafloor in the Pacific Ocean contributes to a more complicated age pattern in the ocean (hint: think about the distance of the youngest seafloor from the nearest continents on both sides of the ocean)?
There is less room for older crust to exist in the eastern Pacific since the youngest seabed in the Pacific Ocean is not found in the basin's center.
Before coming into contact with continents, the ocean basin stretches for a much greater extent. When compared to the seafloor on the other side of the youngest crust in the Pacific, the former side matures more quickly. Since the Pacific Ocean's youngest seabed extends across a considerably larger area before colliding with continents, we think this causes the age pattern to be more complex. The eastern Pacific Ocean basin bottom is destroyed by subduction beneath the continents before it has a chance to age noticeably. On the western side of the youngest seafloor ages, however, the ocean basin reaches the continents from a slightly greater distance.
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❤️❤️❤️PLEASE HELP ME WITH THIS QUESTION TWO PARTS❤️❤️❤️
Answer:
yes
Explanation:
Which of the following is the best example of motion?
A. Waving your arms
B. Tossing and turning in your bed
C. Walking from home to school
D. Your dog wagging his tail
Answer:
Maybe A. waving your arms?
Identity ten devices that use cells or batteries. What types of cells or batteries are used in each device? Are the cells or batteries used the best choice?
Ten devices that use batteries are: smartphones, laptops, flashlights, digital cameras, portable speakers, electric toothbrushes , remote controls, electric shavers, handheld game consoles, and electronic toys
What are the batteries?
Here are ten devices that use cells or batteries:
Smartphones - most smartphones use rechargeable lithium-ion batteries.Laptops - laptops use rechargeable lithium-ion batteriesDigital cameras - digital cameras use rechargeable lithium-ion batteries or disposable alkaline batteriesElectric toothbrushes - electric toothbrushes typically use rechargeable nickel-metal hydride (NiMH) batteriesFlashlights - flashlights often use disposable alkaline batteries, although some models use rechargeable lithium-ion batteriesRemote controls - remote controls typically use disposable alkaline batteriesPortable speakers - portable speakers usually use rechargeable lithium-ion batteriesCalculators - calculators often use button cell batteries, such as the CR2032 lithium batteryWatches - watches use a variety of batteries, including button cell batteries like the SR626SW silver oxide battery or the CR2032 lithium batteryToys - many toys use disposable alkaline batteriesWhether or not the cells or batteries used in these devices are the best choice depends on various factors such as the device's power requirements, energy efficiency, cost, and environmental impact.
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When ___ attacks the surface of a metal, it becomes tarnished.
Answer:corrosion (i believe)
Explanation:
Answer
Mix baking soda and salt with hot water and cover everything with it. The proportions are not crucial, but about 1 tablespoon of salt and 1 tablespoon of baking soda to 3 dl water should do the trick. Lightly tarnished objects should clean up in a few minutes, and you just rinse them of and dry them.
Explanation:
what was the history of a trebuchet
Answer:
The trebuchet was invented in France and was first reported to be used in 1124AD in the siege of Tyre (in present-day Lebanon) during the Crusades. As it was much more powerful than a catapult, a trebuchet became the siege weapon of choice.
Explanation:
Most people think that the trebuchet is a medieval weapon, but actually, it has its origins in ancient China. The ancient Chinese trebuchet could throw huge boulders up to 250 pounds, a distance of 200 feet. In addition, it was lightweight and mobile which was crucial as it could be moved around the battlefield with ease. The thing I love about the chinese trebuchet is that it pushes the boundaries of ancient engineering to create a ballistics revolution - a flexible, portable, killing machine.
A cyclist accelerates from 0 m/s to 10 m/s in 3 seconds. What is his acceleration?
Answer:
3.33 m/s^2
Explanation:
\(a = \frac{v \: - \: u}{t} \)
V = final velocity ( 10m/s^2 )
U = Initial velocity ( 0m/s^2 )
t = Time taken ( 3 s )
\(a = \frac{10 - 0}{3} = 3.3333......\)
approximately = 3.33 m/s^2
6CO2 + 6H20 → C6H12O6 + 602
What type of model is shown?
a
b
computer model
conceptual model
physical model
C
mathematical model
Answer:
C. physical model
Explanation:
Sana nakatulong
why is the concept of potential difference useful
Answer:
Explanation:
the concept of potential difference is useful because it gives information about the energy available to push the current in the electric circuit.
What distance would an object need to be located in front of a converging lens for
the image to be the same size as the object?
Closer than F
Between F and 2F
Beyond 2F
At 2F
Answer:
2*F
Explanation:
If we put an object of a given size exactly at a distance 2*F from the lens, the virtual image (the image generated by the lens) will be generated at a distance 2*F from the lens and the size will be equal to the size of the real object (but the image will be inverted)
Now let's do the math.
The relation between the distance of the object to the lens O, and the distance between the image and the lens I is:
1/O + 1/I = 1/F
solving for O, we get:
1/O = 1/F - 1/I = (I - F)/(F*I)
O = F*I/(I - F)
Such that the relation between the height of the original object, H and the height of the virtual image H' is:
H/H' = -I/O
Replacing by O we get:
H/H' = -I/(F*I/(I - F))
If the sizes are equal, then H/H' = - 1 (remember that the image is inverted, thus the sign)
-1 = -I/(F*I/(I - F))
F*I/(I - F) = I
F*I = (I - F)*I
F = (I - F)
F + F = I = 2*F
The distance between the image and the lens is 2*F
O = F*I/(I - F) = F*2*F/(2*F - F) = 2*F
The object is at a distance 2*F from the lens.
(T/F) gases diffuse because of differences in partial pressures from areas of higher pressure to areas of lower pressure.
The given statement "gases diffuse because of differences in partial pressures from areas of higher pressure to areas of lower pressure." is True because in areas with higher pressure, the gas molecules are more densely packed and push against each other, creating pressure. In areas with lower pressure, the molecules have more room to move around, leading to diffusion.
This pressure is then transferred to other areas with lower pressure, causing the molecules to move and spread out. This is known as the principle of diffusion, and it explains why gases diffuse from areas of higher to lower pressure. When two areas of gas with different pressures come in contact, the molecules will mix until both areas have the same partial pressure. Diffusion is an important process that helps to maintain equilibrium in nature.
It is responsible for the circulation of air, the spread of pollutants in the environment, and the distribution of temperature in a closed environment. The principle of diffusion is also used in industrial processes such as the production of chemicals and foods. Overall, diffusion is an important process that is responsible for the mixing and circulation of gases in the atmosphere. It is caused by differences in partial pressure between areas of higher and lower pressure, and it helps to maintain equilibrium in nature.
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An electromagnetic wave has a frequency of 1.0 < 1014 Hz. What is the
wavelength of the wave? Use the equation 1 = and the speed of light as
V
f
3.0 x 108 m/s.
O A. 3.3 x 10-8 m
B. 3.0 x 1022 m
C. 3.3 x 105 m
0
D. 3.0 x 10-6 m
Answer:
D. 3.0 × 10^-6 m
Explanation:
Wavelength is found by dividing the speed of light by the frequency:
λ = c/f = (3·10^8 m/s)/(1.0·10^14 Hz) = 3.0·10^-6 m
what are two different examples of positive exeleration
Answer:Accelerating your car to get up to speed on a freeway
An airplane accelerating to take off
Accelerating out of the starting blocks at a track meet
Explanation:
if a light wave hits a smooth surface at an angle of incidence of 40 degrees the angle of reflection is
According to the law of reflection, when a light wave hits a smooth surface, the angle of reflection is equal to the angle of incidence. Therefore, if the angle of incidence is 40 degrees, the angle of reflection will also be 40 degrees.
The law of reflection states that the angle of incidence (the angle between the incident light ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected light ray and the normal to the surface). This law holds true for smooth surfaces, such as mirrors or still water.
In this case, when a light wave hits a smooth surface at an angle of incidence of 40 degrees, the angle of reflection will also be 40 degrees. The incident light ray and the reflected light ray will be on opposite sides of the normal to the surface, forming an equal angle with it.
Understanding the law of reflection is crucial in various applications, including optics, image formation, and the study of light behavior. It allows us to predict and analyze the behavior of light rays when they encounter reflective surfaces, enabling us to understand how images are formed and how light interacts with different materials.
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An elephant has a mass of 3500 kg. It is standing still.
Draw a free body diagram showing the forces acting on it.
Find it’s weight on Earth
A free-body diagram represents the forces acting on a body. Let's draw a free-body diagram showing the forces acting on an elephant: Here, the force acting downwards is the weight (W) of the elephant, which is balanced by the normal force (N) exerted by the ground.
Weight of the elephant on Earth: The weight of the elephant is equal to the force due to gravity acting on it. On Earth, the acceleration due to gravity (g) is approximately 9.81 m/s².
So, the weight of the elephant on Earth = mass × acceleration due to gravity= 3500 kg × 9.81 m/s²= 34335 N.
Therefore, the weight of the elephant on Earth is 34335 N.
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which type of scientist measures tides, currents, and waves?
The type of scientist that typically measures tides, currents, and waves is an oceanographer or a physical oceanographer.
Oceanographers study various aspects of the ocean, including its physical properties, dynamics, and processes. They use specialized instruments and techniques to measure and analyze tides, currents, and waves to understand their patterns, behavior, and impact on coastal areas and marine ecosystems. Oceanographers may use devices such as tide gauges, current meters, wave buoys, and acoustic Doppler profilers to collect data on tides, currents, and waves. They analyze these measurements to study phenomena such as tidal variations, ocean circulation patterns, wave energy, and coastal erosion. This information is crucial for understanding ocean dynamics, predicting coastal hazards, and developing strategies for coastal management and engineering.Physical oceanographers often work in collaboration with other scientists, such as marine geologists, meteorologists, and biologists, to gain a comprehensive understanding of the marine environment. Their research contributes to advancements in oceanography, climate studies, marine resource management, and coastal engineering.
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A box is being pushed across the floor at a constant velocity with an
applied force of 30N, what is the magnitude of the frictional force acting
on this box?
Answer:
Magnitude of frictional force = 30 N
Explanation:
According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:
Fn=m.a
The net force is the vector addition of each individual force. If the sum of all the forces acting on an object is zero, then the acceleration is zero. That means the object moves at a constant speed or is at rest.
When an object is pushed across a horizontal rough surface, there are two forces acting in the direction of the motion: The applied force and the frictional force.
If the applied force is greater than the frictional force, then the object moves at a constant positive acceleration. If the frictional force is greater than the applied force, then the object won't move at all (if it was at rest) or will start a deaccelerated motion (braking).
Finally, if both forces are equal, the object will move at a constant speed or remains at rest. Since the box is moving at a constant speed, we can conclude the frictional force equals the applied force:
Magnitude of frictional force = 30 N
.Part A. What is the magnitude of the current in the 30 ohm resistor in the figure? answer in Amperes
Part B. What is the direction of the current?
Part A: To calculate the magnitude of the current in the 30-ohm resistor in the figure, we need to apply Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance.
The voltage across the resistor is given as 6 volts (from the battery) and the resistance of the resistor is 30 ohms. Therefore, the magnitude of the current can be calculated as: Current (I) = Voltage (V) / Resistance (R) = 6V / 30Ω = 0.2 Amperes. So, the magnitude of the current in the 30-ohm resistor is 0.2 Amperes. Part B: To determine the direction of the current, we need to apply Kirchhoff's Current Law (KCL), which states that the algebraic sum of the currents entering and leaving any node in a circuit must be zero. In the given circuit, we can see that the current flowing through the 30-ohm resistor is leaving the node and entering into the negative terminal of the battery. Therefore, the direction of the current in the 30-ohm resistor is from left to right.
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Which location, 23 degrees or 48 degrees would experience the same earthquake at stronger intensity?Explain why.
Answer:
48 degress
Explanation:
An earthquake causes many different intensities of shaking in the area of the epicenter where it occurs. So the intensity of an earthquake will vary depending on where you are. Sometimes earthquakes are referred to by the maximum intensity they produce. In the United States, we use the Modified Mercalli Scale. Earthquake intensity is a ranking based on the observed effects of an earthquake in each particular place. Therefore, each earthquake produces a range of intensity values, ranging from highest in the epicenter area to zero at a distance from the epicenter.
A car is traveling at 50 m/s and slows down to 10 m/s in 5 seconds. What is
the car's acceleration? (Remember what is needed when an object slows
down) *
Answer:
-8m/s2
Explanation:
it decelerate. initial velocity u=50m/s and final velocity v= 10m/s and the time t= 5s
using this equation v= u+at
a= v-u/t= 10-50/5=-40/5= -8m/s2
Answer:
\( \boxed{\sf Acceleration \ (a) = -8 \ m/s^2} \)
Given:
Initial velocity (u) = 50 m/s
Final velocity (v) = 10 m/s
Time taken (t) = 5 seconds
To Find:
Acceleration (a) of the car
Explanation:
From equation of motion we have:
\( \boxed{ \bold{v = u + at}}\)
By substituting value of v, u & t in the equation we get:
\( \sf \implies 10 = 50 + 5a \\ \\ \sf \implies 5a + 50 = 10 \\ \\ \sf \implies 5a = 10 - 50 \\ \\ \sf \implies 5a = - 40 \\ \\ \sf \implies a = - \frac{40}{5} \\ \\ \sf \implies a = - 8 \: m {s}^{ - 2} \)
\( \therefore\)
Acceleration (a) of the car = -8 m/s²
The following table contains the applied forces and corresponding extension of a perfect spring. Determine the spring stiffness. Provide your answer in N/m to 4 decimal places. X (m) F (N) 0. 43 59. 34 0. 52 71. 76 0. 57 78. 66 0. 74 102. 12 0. 81 111. 78 0. 88 121. 44 0. 96 132. 48 Answer:
The spring stiffness, or spring constant, of the given perfect spring is approximately 137.9623 N/m. This means that for every meter of extension, the spring will exert a force of 137.9623 N.
This value was obtained by applying Hooke's Law and calculating the ratio of the change in force to the change in extension using two data points from the table.
To determine the spring stiffness, we need to calculate the spring constant (k) using Hooke's Law, which states that the force applied on a spring is directly proportional to the extension it undergoes.
Hooke's Law can be represented as F = kx, where F is the applied force and x is the extension of the spring.
In the given table, we have the applied forces (F) and corresponding extensions (x). We can use any two data points from the table to find the spring constant.
Let's choose the first and last data points from the table:
(x1, F1) = (0.43 m, 59.34 N) and (x2, F2) = (0.96 m, 132.48 N).
Using Hooke's Law, we can calculate the spring constant (k) as follows:
k = (F2 - F1) / (x2 - x1)
= (132.48 N - 59.34 N) / (0.96 m - 0.43 m)
= 73.14 N / 0.53 m
≈ 137.9623 N/m (rounded to 4 decimal places)
Therefore, the spring stiffness, or spring constant, is approximately 137.9623 N/m.
Hooke's Law is a fundamental concept in physics that describes the relationship between the force applied on a spring and the resulting extension it undergoes.
The formula F = kx represents this relationship, where F is the applied force, k is the spring constant, and x is the extension of the spring.
By using two data points from the table, we can calculate the spring constant by finding the ratio of the change in force to the change in extension.
This calculation allows us to quantify the stiffness of the spring.
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Chebyshev's theorem states that the proportion of values is at least 1-1/k2. what is the meaning of k?
k is the number of standard deviations greater than one that that proportion of observations will be discovered within.
What does Standard Deviation mean?A standard deviation measures the spread of data in relation to the mean.
A low standard deviation suggests that the data is concentrated around the mean, whereas a high standard deviation shows that the data is spread.
A standard deviation near 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.
The curve on top of Image 7 is more spread out and hence has a higher standard deviation, whereas the curve below is more grouped around the mean and thus has a smaller standard deviation.
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A sailor walks north on a ship at 3mph. The ship is traveling S30°E at 24mph. Find the true direction in which the sailor is walking as an angle with the positive x-axis. 4 (a) 0 = 1-4√3 1- 4√3 (b) 0 = 4 3 (c) 0 = 4√3 4√3 (d) 0 = 3 (e) None of these 6e-¹ +6e² if r <0 2e- 5e2T
The correct option is e).
To find the true direction in which the sailor is walking, we can use vector addition to add the velocity of the sailor to the velocity of the ship. Let's assume that the positive x-axis is pointing east and the positive y-axis is pointing north. Then the velocity of the sailor can be represented as a vector in the direction of the positive y-axis with a magnitude of 3 mph. The velocity of the ship can be represented as a vector in the direction S30°E with a magnitude of 24 mph.
To add these two vectors, we can resolve the vector of the ship into its x and y components. The angle between the positive x-axis and S30°E is 60 degrees, so we can find the x and y components of the ship's velocity using trigonometry:
x-component = 24 mph * cos(60°) = 12 mph
y-component = 24 mph * sin(60°) = 20.8 mph
Now we can add the x and y components of the ship's velocity to the velocity of the sailor. Since the sailor is walking north, their velocity has no x-component and only a y-component of 3 mph. Adding these vectors, we get:
resultant velocity = (12 mph + 0 mph) i + (20.8 mph + 3 mph) j
= 12 i + 23.8 j
where i and j are unit vectors in the x and y directions, respectively.
The angle between the positive x-axis and the resultant velocity can be found using trigonometry:
tan(θ) = (23.8 mph) / (12 mph)
θ = tan⁻¹(23.8/12)
θ ≈ 63.4°
So the true direction in which the sailor is walking is at an angle of approximately 63.4° with the positive x-axis.
Therefore, the answer is (e) None of these as none of the options matches with the value obtained.
The last part of the question seems incomplete and unrelated, so we cannot provide an answer without additional context.
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what frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?
The frequency heard by a passenger on the train is lower than the original frequency, given that the train is moving away from the source of the sound.
What is the frequency frecede?When a source of sound is moving relative to an observer, the perceived frequency of the sound can be affected by the Doppler effect. The Doppler effect causes a shift in frequency when there is relative motion between the source and the observer.
In this case, the train is moving at a speed of 18.0 m/s relative to the ground, in a direction opposite to the first train and receding from it. As the train moves away from the source of the sound, the perceived frequency of the sound decreases.
The exact change in frequency can be calculated using the Doppler effect equation, which takes into account the relative velocity of the source and observer.
However, since the specific frequency of the sound source is not provided in the question, it is not possible to calculate the exact frequency heard by the passenger on the train
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One strategy in a snowball fight is to throw
a snowball at a high angle over level ground.
While your opponent is watching this first
snowball, you throw a second snowball at a
low angle and time it to arrive at the same
time as the first.
Assume both snowballs are thrown with
the same initial speed 12.8 m/s. The first
snowball is thrown at an angle of 63◦
above the horizontal. At what angle should you
throw the second snowball to make it hit the
same point as the first? Note the starting and
ending heights are the same. The acceleration
of gravity is 9.8 m/s
2
.
The angle he should throw the second snowball to make it hit the same point as the first is 27⁰.
What is the range of a projectile?
The range of the projectile is the distance traveled by a projectile in the horizontal direction.
There is no acceleration in this direction since gravity only acts vertically.
The range of a projectile is given as;
R = u²sin(2θ) / g
where;
u is the initial velocity of the objectθ is the angle of projectiong is acceleration due to gravityR is the range of the projectileFor the range of a projectile the angle of projection is related in the following equation.
when the initial angle of projection = θ
new angle of projection so that it will have the same range = 90 - θ
new angle = 90 - 63⁰ = 27⁰
check;
sin(2 x 63) = sin(2 x 27) = 0.809
Thus, the angle he should throw the second snowball to make it hit the same point as the first is 27⁰.
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Find the center of mass of the region bounded by y=9-x^2 y=5/2x , and the z-axis. Center of Mass = __?
Note: You can earn partial credit on this problem.
The centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8). Formulae used to find the centre of mass are as follows:x bar = (1/M)*∫∫∫x*dV, where M is the total mass of the system y bar = (1/M)*∫∫∫y*dVwhere M is the total mass of the system z bar = (1/M)*∫∫∫z*dV, where M is the total mass of the systemThe region bounded by y=9-x^2 and y=5/2x, and the z-axis is shown in the attached figure.
The two curves intersect at (-3, 15/2) and (3, 15/2). Thus, the total mass of the region is given by M = ∫∫ρ*dA, where ρ = density. We can assume ρ = 1 since no density is given.M = ∫[5/2x, 9-x^2]∫[0, x^2+5/2x]dAy bar = (1/M)*∫∫∫y*dVTherefore,y bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]y*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]ydA...[1].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore,y bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]y*dxdy...[2].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.Substituting the values and evaluating the integral, we get y bar = (1/M)*[(9-5/2)^2/2 - (9-(15/2))^2/2]= (1/M)*(25/2)...[3].
Also, the x coordinate of the center of mass is given by,x bar = (1/M)*∫∫∫x*dVTherefore,x bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]x*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]xdA...[4].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore, x bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]xy*dxdy...[5].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.
Substituting the values and evaluating the integral, we get x bar = (1/M)*[63/8]= (1/M)*(63/8)...[6]Thus, the centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8).
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