Answer:
To be accurate, it must be able to give consistent measurements
of a quantity
Explanation:
The angular momentum of a rotating two-dimensional rigid body about its center of mass G is ______. a. m V_G b. I_G V_G c. m omega d. I_G omega
The angular momentum of a rotating two-dimensional rigid body about its center of mass G is I_Gω. Hence, the correct answer is (d) I_Gω.
Angular momentum is defined as the amount of rotational motion that a body has when rotating about an axis, which is given by L = Iω. Here, I is the moment of inertia and ω is the angular velocity. The moment of inertia is a measure of the object's resistance to rotational motion. It depends on the object's mass and its distribution about the axis of rotation.
The moment of inertia is different for different axes of rotation, but if an object is rotating about its center of mass, then the moment of inertia is minimum, which is denoted by I_G. Therefore, the angular momentum of a rotating two-dimensional rigid body about its center of mass G is given by I_Gω, as stated in option (d).
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What type of relationship exists between the comma teasel and all of the other plant
Answer:
Parasitic Relationship
A symbiotic relationship that is mutualism exists between the comma teasel and all of the other plants.
What is a Symbiotic relationship?Symbiosis or symbiotic relationship is any type of close and long-term biological interaction which is present between two different biological organisms, be it mutualistic relationship, commensalistic relationship, or parasitic relationship. The organisms, each termed as a symbiont, must be of different species.
The comma teasel and all of the other plants share a relationship where, the comma teasel pollinates flowers of different plant species. Pollination is important for the reproduction in plants and in return, the plants provide nectar to the organism.
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A car traveling due north at 60 km/hr increased its velocity to 80 m/s due south in 20 seconds. Draw i) speed against time graph, ii) acceleration against time graph.
The slope of the graph is acceleration of the car with a value of 3.2 m/s².
The given parameters;
initial velocity of the car, u = 60 km/hrfinal velocity of the car, v = 80 m/stime of motion of the car, t = 20 sThe initial velocity of the car in m/s is calculated as follows;
\(60 \ \frac{km}{hr} \times \frac{1 \ hr}{3600 \ s} \times \frac{1000 \ m}{1 \ km} = 16.67 \ m/s\)
The acceleration of the car is calculated as follows;
\(a = \frac{v- u}{t} \\\\a = \frac{80 - 16.67 }{20} \\\\a = 3.2 \ m/s^2\)
The graph of the velocity against time and acceleration against time is in the image uploaded.
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how often do industrial oxygen cylinders need to be tested
Answer:
5 years\(\)
What would african americans do once they could vote?
African Americans would have the power to elect representatives who would fight for their rights and interests. They would be able to participate in local, state, and national politics, bringing their unique perspectives and concerns to the table.
African Americans would also have a greater say in issues affecting their communities, such as education, healthcare, and criminal justice reform. With the ability to vote, African Americans would gain a stronger voice and greater influence in shaping the policies and laws that govern their lives. However, the right to vote alone does not guarantee equality or justice, and there would still be significant challenges and obstacles to overcome in the fight for racial equality. It would take ongoing activism and advocacy to ensure that the voting rights of African Americans are protected and that their voices are heard.
African Americans also participated in political campaigns and formed political organizations to raise awareness about issues affecting their communities. By engaging in the democratic process, they worked to dismantle systemic racism and contribute to a more inclusive society. Their increased involvement in politics helped to advance the civil rights movement and shape the political landscape of the United States.
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A water strider bug is supported on the surface of a pond by surface tension acting along the interface between the water and the bug’s legs. Assume the bug weighs 10−4 N and the surface tension force acts vertically upward. Determine the minimum length of the interface needed to support the bug
Answer:
minimum interface length = 1.36 mm
Explanation:
given data
weight of the bug = \(10^{-4}\) N
solution
we will apply here Surface Tension formula that is
Surface Tension ,σ = Force ÷ length ........................1
and we consider here surface tension for water is 7.34 × \(10^{-2}\) N/m
so that here minimum interface length needed to support the bug is
minimum interface length = Force ÷ σ
minimum interface length = \(10^{-4}\) ÷ 7.34 × \(10^{-2}\)
minimum interface length = 1.36 mm
If mass of an empty 7.0 mL pycnometer is 10.2g and the mass of the same pycnometer with an unknown liquid is 21.8g. Determine the density of the unknown liquid to ONE DECIMAL PLACE in g/mL.
The formula for calculating density is expressed as
Density = mass/volume
From the information given,
mass of empty pycnometer = 10.2
mass of the same pycnometer with an unknown liquid is 21.8.
Mass of unkown liquid = 21.8 - 10.2 = 11.6
volume of unknown liquid = 7
Thus,
Density = 11.6/7
Density = 1.7 g/ml
please help urgent have you ever seen the old “Pull the tablecloth out from under the dishes” trick? Use Newton’s 1st Law to explain the following:
a. In this trick, are the dishes “objects in motion,” or “objects at rest?”
b. If the dishes end up staying on the table, was an UNBALANCED FORCE applied to them? How do you know?
Answer:
I kinda dont remember the 1st law so search it up on
and it should tell u , but if u need any help from the
A brick, milk, and ice cubes are all examples of matter.
true because
brick: solid
milk: liquid
ice cube: solid
What is electric current
Answer:
Electric current is electric charge in motion. It can take the form of a sudden discharge of static electricity, such as a lightning bolt or a spark between your finger and a ground light switch plate. ... Most electric charge is carried by the electrons and protons within an atom.
Explanation:
because it is
You are writing a procedure to characterize 90Sr/90Y contamination in a legacy facility. Gas proportional probes that measure 10cm x 15cm will be used to scan floors and walls. The 150 cm2 area probe will be moved along its 10cm axis. What scan speed must be maintained in order to meet a total contamination (fixed plus removable) MDA of 1000 dpm/100cm2 ? Assume that the detector efficiency is 0.35 cpm/dpm and the probe background is 500 cpm. State any other assumptions and show all calculations.
Characterizing 90Sr/90Y contamination in a legacy facility requires a procedure that can meet a total contamination (fixed plus removable) MDA of 1000 dpm/100cm2.
The procedure uses gas proportional probes that measure 10cm x 15cm, which will scan the floors and walls of the facility. The 150 cm2 area probe will be moved along its 10cm axis. This question aims to find the scan speed that must be maintained to meet the specified MDA.
Assumptions: The detector efficiency is 0.35 cpm/dpm, and the probe background is 500 cpm.
The MDA can be determined using the following equation:MDA = (2.71 × B × t × E) / Awhere, B = background count rate, t = counting time, E = detector efficiency, and A = area of the surveyed surface.Substituting the given values, we get:1000
= (2.71 × 500 × t × 0.35) / 100Simplifying this equation, we get:t
= (100 × 1000) / (2.71 × 500 × 0.35)
The time required to survey an area of 150 cm2 with a 10 cm axis is 42.96 seconds.
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Find the volume of the following shape.
7 km
5 km
1.9 km
3 km
3 km
Round to the nearest hundredth.
The volume of the triangular shape is 10.35 km³.
In geometry, volume is the amount of space enclosed by a three-dimensional object. It is measured in cubic units, such as cubic meters or cubic centimeters. The volume of a regular object can be calculated using a formula, while the volume of an irregular object can be calculated by dividing it into smaller regular objects and adding up their volumes.
For example, the volume of a cube with a side length of 1 meter is 1 cubic meter. The volume of a sphere with a radius of 1 meter is 4/3π cubic meters. The volume of a cylinder with a radius of 1 meter and height of 2 meters is 2π cubic meters.
The formula gives the volume of a triangular shape:
V = 1/2 * b * h * t
where:
b is the base of the triangle
h is the height of the triangle
t is the thickness of the triangle
In this case, we have:
b = 7 km
h = 1.9 km
t = 3 km
So now, the volume of the triangular shape is:
V = 1/2 * 7 km * 1.9 km * 3 km = 10.35 km³
Therefore, the volume of the triangular shale is 10.35 km³.
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A 3kg ball moving at 8 m/s strikes a 2kg ball at rest,if the collision is elastic,what is the speed of the lighter ball if the heavier ball moves at 2m/s in the opposite direction
Answer:
Speed of lighter ball is 4 m/s.
Explanation:
Applying the principle of conservation of linear momentum,
momentum before collision = momentum after collision.
\(m_{1}\)\(u_{1}\) + \(m_{2}\) \(u_{2}\) = \(m_{1}\)\(v_{1}\) - \(m_{2}\)\(v_{2}\)
\(m_{1}\) = 3 kg, \(u_{1}\) = 8 m/s, \(m_{2}\) = 2 kg, \(u_{2}\) = 0 m/s ( since it is at rest), \(v_{1}\) = 2 m/s, \(v_{2}\) = ?
(3 x 8) + (2 x 0) = (8 x 2) - (2 x \(v_{2}\))
24 + 0 = 16 - 2\(v_{2}\)
2\(v_{2}\) = 16 - 24
2\(v_{2}\) = -8
\(v_{2}\) = \(\frac{-8}{2}\)
= -4 m/s
This implies that the light ball moves at the speed of 4 m/s in the opposite direction of the heavier ball after collision.
I just need to know how to get the answer
F=150N.
A high wind velocity is defined as quickness of motion or operation; swiftness; or speed.
The speed at which a body's position changes over time in a given direction is known as mechanics. the velocity of activity or reaction; the rate at which something occurs.
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. The displacement that an object or particle experiences with respect to time are expressed vectorially as velocity
(1400-1250)
150 N
F=150N
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If the density of water is 1 gram/cm3, this means that the mass of 100 cm3
of water should be *
Answer:
m = 100[gram]
Explanation:
In order to solve this problem, we must remember the definition of the density of matter, which is the relationship between mass and volume. The density can be calculated by means of the following formula.
\(Ro=m/V\)
where:
Ro = density = 1 [gramm/cm³]
m = mass [gramm]
V = volume = 100 [cm³]
Now replacing:
\(m=Ro*V\\m=(1\frac{grm}{cm^{3} } )*100cm^{3} \\m=100[gram]\)
What is the Zenith angle at 45 degrees North during the Spring Equinox?
2. Calculate the Zenith angle, Solar elevation angle, and beam spreading at a site located at 45 Degrees North on the Autumnal eqinox on September 22nd.
3. At what latitude does daylight hours have the least variability?
4. true or false: The greater the solar angle (from 0 degrees to 90 degrees), the less spread out the solar beam is and the more concentrated solar radiation will be at that point.
The Zenith angle at 45 degrees North during the Spring Equinox is 45 degrees.
The Zenith angle is measured as the angle between the vertical line (directly overhead) and the line connecting the observer to the Sun. During the Spring Equinox, when the Sun is directly above the Equator, the Zenith angle at any latitude is equal to the latitude itself.
To calculate the Zenith angle, Solar elevation angle, and beam spreading at a site located at 45 degrees North on the Autumnal equinox (September 22nd), additional information is needed, such as the time of day and the observer's exact location (longitude). These factors affect the position of the Sun in the sky. The Zenith angle is the angle between the vertical line and the line connecting the observer to the Sun. The Solar elevation angle is the complement of the Zenith angle (90 degrees minus the Zenith angle). Beam spreading refers to the divergence of the solar beam as it travels through the atmosphere, which is influenced by factors such as atmospheric conditions and the Sun's position.
The latitude at which daylight hours have the least variability is the Equator (0 degrees latitude). At the Equator, the length of daylight hours remains relatively constant throughout the year, with minimal variation. In contrast, as you move farther away from the Equator towards the poles, the variability in daylight hours becomes more pronounced, with significant changes between the seasons.
False. The spread of the solar beam, known as beam spreading, is actually greater at higher solar angles (closer to 90 degrees) compared to lower solar angles (closer to 0 degrees). At higher solar angles, the solar beam covers a larger area due to the greater incidence angle, resulting in a larger spread of solar radiation. As the solar angle decreases and approaches 0 degrees, the solar beam becomes more concentrated and focused on a smaller area, leading to a higher intensity of solar radiation at that point.
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A climbing chain pulls a roller coaster with a force of 29,738N to the top of the roller coaster 102m high. How many joules of work has it done
Answer:
3,033,276 J
Explanation:
The work can be calculated as
W = Fd
Where F is the force and d is the distance.
Replacing F by 29,738 N and d by 102 m, we get:
W = (29,738 N)(102 m)
W = 3,033,276 J
Then, it has done 3,033,276 J
Two Kilograms of an Ideal gas with constant specific heats begin a process at 300 kPa and 50° C. The gas is first expanded at constant pressure until its volume doubles. Then it is heated at constant volume until its pressure doubles. Properties of the gas are R 0.75 kJ/kg. K and Cp=2.5 kJ/kg. K. a. Draw the process in a P-V diagram. b. Calculate the work done by the gas during the entire process c. Calculate change in internal energy of the gas during the entire process.
a) The P-V diagram for the process is shown below:
C
|
| B (2V, 300 kPa)
| |
P | |
| |
| |
| |
| |
| |
| |
|_ |________
V (m³)
A (V, 300 kPa)
b) The total work done is 600 KJ.
c) The change in internal energy of the gas during the entire process is 61.85 kJ.
a. The process can be divided into two steps:
Step 1: Expansion at constant pressure (process AB in the diagram)
Step 2: Heating at constant volume (process BC in the diagram)
b. The work done by the gas during the entire process can be calculated by the area under the P-V curve:
W = W_AB + W_BC
W_AB = P(V_B - V_A) = (300 kPa)(2V - V) = 600 kJ
W_BC = 0 (constant volume process)
W = 600 kJ
c. The change in internal energy of the gas during the entire process can be calculated using the first law of thermodynamics:
ΔU = Q - W
ΔU = Q_AB + Q_BC - W
Q_AB = mCpΔT = (2 kg)(2.5 kJ/kg.K)(50 K) = 250 kJ
Q_BC = mCvΔT = (2 kg)(0.75 kJ/kg.K)(273 K) = 410.85 kJ
ΔU = (250 kJ + 410.85 kJ) - 600 kJ = 61.85 kJ
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How harmful are the emissions from cosmetics, hygiene, and cleaning products?
Claim
Evidence 1
Evidence 2
Evidence 3
Reasoning
The packaging used in the beauty sector is less functional and more ornate. The packaging waste generated by the cosmetics industry accounts for around 70% of all waste, or 20 billion units annually.
Thus, Lipstick, shampoo, and body wash are discarded after being used up. There is very little recycling. Currently, the oceans get 8 million tonnes of plastic annually and cosmetics.
Since plastic is not biodegradable, it will never decay. Instead, it disintegrates and fragments into miniscule sizes via a process called "photodegradation." and cosmetics.
The length of this procedure varies based on the type of plastic used, from 100 to 500 years. The more hazardous and challenging it is to clean up, the smaller the plastic becomes.
Thus, The packaging used in the beauty sector is less functional and more ornate. The packaging waste generated by the cosmetics industry accounts for around 70% of all waste, or 20 billion units annually.
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A 51 cm diameter wheel accelerates uniformly about its center from 150 rpm to 290 rpm in 4.0 s. (A)Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.1 s after it has started accelerating.
Radial component of the linear acceleration = 99.47 m/s^2
Explanations:The diameter of the wheel, d = 51 cm
The radius, r = d/2 = 51/2 = 25.5 cm
r = 25.5/100 = 0.255 m
r = 0.255 m
\(\begin{gathered} N_{i\text{ }}=\text{ 150 rpm} \\ w_i=\text{ 150}\times\frac{2\pi}{60} \\ w_i=\text{ }15.71\text{ rad/s} \end{gathered}\)\(\begin{gathered} N_f=\text{ 290 rpm} \\ w_f=\text{ 290}\times\frac{2\pi}{60} \\ w_f=\text{ }30.37\text{ rad/s} \end{gathered}\)\(\begin{gathered} w_f=w_i+\alpha t \\ 30.37=15.71+4\alpha \\ 4\alpha=30.37-15.71 \\ 4\alpha=\text{ }14.66 \\ \alpha=\frac{14.66}{4} \\ \alpha\text{ = }3.67rad/s^2 \end{gathered}\)At t = 1.1, first calculate the new angular velocity
\(\begin{gathered} w=w_1+\alpha t \\ w\text{ = 15.71+3.67(1.1)} \\ w\text{ = 15.71+}4.04 \\ w\text{ = }19.75\text{ rad/s} \end{gathered}\)The radial component of the linear acceleration is given as:
\(\begin{gathered} a_r=w^2r \\ a_r=19.75^2\times0.255 \\ a_r=\text{ }99.47\text{ m/}s^2 \end{gathered}\)A calorie is defined as the amount of energy needed to raise the temperature of one gram of water one degree centigrade.
True
False
A calorie is defined as the amount of energy needed to raise the temperature of one gram of water one degree centigrade is True.
A calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are widely used. A staple calorie, food calorie, or kilogram calorie was originally defined as the amount of heat required to raise the temperature of 1 kilogram of water by 1 degree Celsius (or 1 Kelvin). [1] [3] A small calorie or gram calorie is defined as the amount of heat required to cause the same increase in 1 gram of water, so 1 large calorie equals 1000 small calories.
In nutrition and food science, the term calorie and the symbol cal most often refer to large units. It is often used in publications and on package labels to describe the energy value per serving or weight of food, recommended caloric intake, metabolic rate, etc. Some authors recommend spelling calorie and symbol cal (both uppercase C).However, to avoid confusion, this convention is often ignored.
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electric field lines point in the opposite direction WHAT charges would move if they were in the field
Answer:
Negative
Explanation:
hope i helped
A hydraulic lift is used to raise an automobile of mass 1520 kg. The radius of the shaft of the lift is 8.00 cm and that of the piston is 1.00 cm. How much force must be applied to the piston to raise the automobile?
To raise the automobile with a hydraulic lift, a force of approximately 19,000 N must be applied to the piston.
In a hydraulic lift, the principle of Pascal's law is applied, which states that pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container. By utilizing this principle, a smaller force applied to a smaller piston can generate a larger force on a larger piston.
In this scenario, the force needed to lift the automobile can be calculated using the formula:
\(\frac{F_{1}}{A_{1}} =\frac{F_{2}}{A_{2}}\)
where \(F_{1}\) is the force applied to the piston, \(A_{1}\) is the area of the piston, \(F_{2}\) is the force generated on the larger piston (required to lift the automobile), and \(A_{2}\) is the area of the larger piston.
Given the radius of the shaft (small piston) as 0.08 m and the radius of the piston as 0.01 m, we can calculate the forces applied and generated as follows:
\(A_{1} = \pi (0.08)^2\\A_{2}= \pi (0.01)^2\)
\(\frac{F_{1}}{A_{1}} =\frac{F_{2}}{A_{2}}\)
Simplifying the equation and substituting the values, we can solve for \(F_{2}\):
\(F_{2}=\frac{F_{1}A_{2}}{A_{1}}\)
Plugging in the values, we find:
\(F_{2}=\frac{F_{1} \pi (0.01)^2 }{ \pi (0.08)^2} \\F_{2}= \frac{F_{1}\times 0.0001}{0.0064} \\F_{2}= 0.015625 \times F_{1}\)
Given that the mass of the automobile is 1520 kg and the acceleration due to gravity is \(9.8 \hspace m/s^{2}\), we can equate \(F_{2}\) to the weight of the automobile:
\(F_{2}= mg\\0.015625\times F_{1}= 1520\times 9.8\)
Solving for \(F_{1}\), we find:
\(F_{1}\approx \frac{1520\times 9.8}{0.015624} \\F_{1} \approx 19072 \hspace N\)
Therefore, a force of approximately 19,000 N must be applied to the piston in order to raise the automobile using the hydraulic lift.
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What does vitamin c do for our body?
Answer:
necessary for the growth, development and repair of all body tissues. it's involved in many body functions, including formation of collagen, absorption of iron, the proper functioning of the immune system, wound healing, and the maintenance of cartilage, bones, and teeth.
Explanation:
Answer:
Vitamin C act as antioxidant which protect our cell from damaging caused by radicals.
Suppose a spring weh sping constant 3 N/m is horizonal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 0.8 Ha (Cycles pet second). What is the mass? Assume there is no friction
Mass = heip (units)
The mass of the object attached to the spring is approximately 0.119 kg.
To determine the mass of the attached object using the spring, we can utilize Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement of the spring from its equilibrium position.
The frequency of the spring's motion (f) can be related to the mass (m) and the spring constant (k) using the equation:
f = (1 / (2π)) * √(k / m)
Rearranging this equation, we can solve for the mass:
m = (k / (4π² * f²))
Given:
Spring constant (k) = 3 N/m
Frequency (f) = 0.8 Hz
Substituting these values into the equation, we get:
m = (3 N/m) / (4π² * (0.8 Hz)²)
Calculating this expression:
m ≈ 0.119 kg
Therefore, the mass of the object attached to the spring is approximately 0.119 kg.
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The mass attached to the spring is approximately 0.238 kg.
To find the mass attached to the spring, we can use the formula for the angular frequency (ω) of a mass-spring system:
ω = √(k / m),
where ω is the angular frequency, k is the spring constant, and m is the mass.
Given:
k = 3 N/m (spring constant),
f = 0.8 Hz (frequency).
First, let's convert the frequency from Hz to radians per second (rad/s):
ω = 2πf = 2π(0.8) ≈ 5.03 rad/s.
Now, we can solve the formula for m:
ω = √(k / m),
m = k / ω^2,
m = 3 N/m / (5.03 rad/s)^2.
Calculating the value:
m ≈ 3 N/m / (5.03 rad/s)^2 ≈ 0.238 kg.
Therefore, the mass attached to the spring is approximately 0.238 kg.
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which statement describes the energy transformation that occurs when a person eats a sandwich to gain for a long hike
The statement that best describes the energy transformation that occurs when a person eats a sandwich to gain for a long hike is: Potential energy is transformed into kinetic energy.
The correct answer is option D.
When a person eats a sandwich to gain energy for a long hike, the energy transformation involves the conversion of chemical potential energy stored in the food into kinetic energy that the person can utilize for physical activity.
The sandwich, as a source of nutrients, contains stored chemical potential energy derived from the sun through the process of photosynthesis. When the person consumes the sandwich, the body breaks down the complex molecules present in the food, such as carbohydrates, proteins, and fats, through the process of digestion. This breakdown releases stored chemical energy in the form of molecules like glucose.
Once these molecules are absorbed into the bloodstream, they are transported to the body's cells, including muscle cells. Through the process of cellular respiration, the glucose molecules are further broken down in the presence of oxygen to release energy in the form of adenosine triphosphate (ATP), the primary energy currency of cells.
ATP provides the energy required for muscle contraction, allowing the person to engage in physical activity such as hiking. As the person moves, the potential energy stored in the food is converted into kinetic energy, enabling the muscles to generate mechanical work and propel the body forward.
In summary, the correct option is B as the energy transformation that occurs when a person eats a sandwich to gain energy for a long hike involves the conversion of potential energy stored in the food (chemical potential energy) into kinetic energy that is utilized by the body's muscles for movement and physical activity.
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The question probable may be:
Which statement describes the energy transformation that occurs when a person eats a sandwich to gain energy for a long hike?
A. Thermal energy is transformed into kinetic energy.
B. Kinetic energy is transformed into potential energy.
C. Thermal energy is transformed into potential energy.
D. Potential energy is transformed into kinetic energy.
Please explain how you got the answer :(
Answer:
36.5 kJ
Explanation:
Energy by machine = energy to machine × efficiency
E = 52.1 kJ × 0.70
E = 36.5 kJ
Please help me, I am following along diligently. V(t) = t^2 -9t+18, with distance, s measured in meters, left or right of 0, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t=0 sec is 1 meter right of 0, that is s(0)= 1Part I: Average velocity over the interval 0 to 8 secondsPart II: The instantaneous velocity and speed at time 5 secsPart III: The time intervals when the particle is moving rightPart IV: The time intervals when the particle is going faster, and slowing downPart V: Total distance the particle has traveled between 0 and 8 seconds
Given that the velocity at any time t is
\(v(t)=t^2-9t+18\)Also, the time interval is from t = 0 to t = 8 seconds
The position at time t = 0 s is s(0) = 1 m towards right of zero.
The initial time is t = 0 s, so the initial velocity will be
\(\begin{gathered} v_i(t=0)=0^2-9\times0+18\text{ } \\ v_i(0)\text{ = 18 m/s} \end{gathered}\)The final time is t = 8 s, so the final velocity will be
\(\begin{gathered} v_f(t=8)=8^2-9\times8+18 \\ v_f(8)\text{ = 64-72+18} \\ =\text{ 10 m/s} \end{gathered}\)The average velocity will be
\(\begin{gathered} v_{av}=\frac{v_i+v_f}{2} \\ =\frac{18+10}{2} \\ =14\text{ m/s} \end{gathered}\)Thus, the average velocity is 14 m/s.
Part II:
The instantaneous velocity at time t =5 s will be
\(\begin{gathered} v(t=5)=5^2-9\times5+18 \\ =25-45+18 \\ =-2\text{ m/s} \end{gathered}\)The instantaneous speed is the magnitude of instantaneous velocity.
Thus, the instantaneous speed will be 2 m/s.
Part III:
The particle will move towards the right when v(t) > 0
The time intervals will be
\(\begin{gathered} t^2-9t+18>0 \\ t^2-6t-3t+18>0 \\ t(t-6)-3(t-6)>0 \\ (t-6)(t-3)>0 \\ t-6>0\text{ or t>6} \\ t-3>0\text{ ot t>3} \end{gathered}\)Thus, time intervals are t > 3 and t > 6 when the particle is moving towards the right.
Part IV :
The particle will move faster if the acceleration, a(t) > 0
The particle will slow down if the acceleration, a(t) < 0
So, first, we need to find the acceleration, it can be calculated as
\(\begin{gathered} a(t)=\text{ }\frac{d(v(t))}{dt} \\ =\frac{d(t^2-9t+18)}{dt} \\ =2t-9 \end{gathered}\)For the particle moving faster,
\(\begin{gathered} a(t)>0 \\ 2t-9>0 \\ 2t-9+9>9+0 \\ 2t>9 \\ \frac{2t}{2}>\frac{9}{2} \\ t>\frac{9}{2} \\ t>4.5\text{ s} \end{gathered}\)For particle slowing down,
\(\begin{gathered} a(t)<0 \\ 2t-9<0 \\ 2t-9+9<9+0_{} \\ 2t<9 \\ \frac{2t}{2}<\frac{9}{2} \\ t<4.5\text{ s} \end{gathered}\)The total distance can be calculated as
\(\begin{gathered} s(t)=\int ^8_0v(t)dt \\ =\text{ }\int ^8_0(t^2-9t+18)\mathrm{d}t \\ =\lbrack\frac{t^3}{3}\rbrack^8_0-9\lbrack\frac{t^2}{2}\rbrack^8_0+18\lbrack t^{}\rbrack^8_0 \\ =\frac{1}{3}\lbrack512-0\rbrack-9\lbrack64-0\rbrack+18\lbrack8-0\rbrack \\ =\text{ 170.67-576+144} \\ =-261.33\text{ m} \end{gathered}\)Here, the negative symbol indicates it is towards the left from zero.
What is the independent variable
Answer:
independent variables are variables in mathematical modeling, statistical modeling and experimental science
The region of magnetic influence around either pole of a magnet is called the magnetic field. The magnetic field line points out from the south magnetic pole and in from the north magnetic pole. This statement is:
Answer:
This statement is not true
Explanation:
Because The normal magnetic field line points out from the north magnetic pole and in from the south magnetic pole.
Answer:
false
Explanation:
hope this helps :)