Explanation:
Vertical component of velocity
= 16 sin 50 = 12.3 m/s
Vertical height will be given by
h = vo t + 1/2 a t^2
h = 1/2 ( -9.81) t^2 + 12.3 t
h = - 4.905 t^2 + 12.3 t
will have max at t = - b/2a = -12.3/(2*(-4.905) ) = 1.25 sec
use this value of 't' in the equation to find the max height:
h = - 4.905 ( 1.25^2) + 12.3 ( 1.25) = 7.7 meters max height
I need some help with this question
The speed of the ball when it leaves the gun is approximately 17.66 m/s.
Steps
To determine the speed of the ball when it leaves the gun, we can use the principle of conservation of energy. At the moment when the trigger is pulled, the spring has a potential energy equal to:
U = (1/2) k x²
where k is the spring constant and x is the amount by which the spring is compressed from its unstretched length. Using the given values, we have:
U = (1/2) (20 N/m) (0.0125 m)² = 1.5625 mJ
When the spring is released, this potential energy is converted into kinetic energy of the ball, as well as work done against friction. The work done against friction is equal to:
W = f_friction x
where f_friction is the frictional force between the ball and the barrel, and x is the distance that the ball moves along the barrel. Using the given values, we have:
W = (0.02 kg) (9.81 m/s²) (0.20) (0.05 m) = 0.01962 J
The kinetic energy of the ball is equal to the difference between the potential energy of the spring and the work done against friction:
K = U - W = 1.5625 mJ - 0.01962 J = 1.5429 J
The speed of the ball when it leaves the gun is equal to the:
v = sqrt(2K/m)
where m is the mass of the ball. Using the given value of 20 g, we have:
m = 0.02 kg
Substituting the values and evaluating the expression, we get:
v = sqrt(2(1.5429 J)/(0.02 kg)) = 17.66 m/s
Therefore, the speed of the ball when it leaves the gun is approximately 17.66 m/s.
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Which option below lists the grades of metamorphism that might be encountered moving west to east from Ohio to the crystalline core of the Appalachians?
low grade, then intermediate grade, then high grade
The sequence of grades of metamorphism that may be encountered moving west to east from Ohio to the crystalline core of the Appalachians is: low grade, then intermediate grade, then high grade.
Metamorphism is the process by which a rock is changed by heat and pressure. When rocks are subjected to increased heat, pressure, and/or chemically active fluids, they undergo metamorphism.
Metamorphic rocks are formed as a result of this process. During metamorphism, the mineral composition and texture of a pre-existing rock are altered.
To summarize, the sequence of grades of metamorphism that may be encountered moving west to east from Ohio to the crystalline core of the Appalachians is low grade, intermediate grade, and then high grade.
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A tsunami generated off the coast of Chile in 1990 traveled nearly 6500 miles to the coast of Honolulu in 17 hours. Determine the speed in mi/hr and m/s. If the averagewidth of such waves was 22 m, what was the average frequency of such adevastating tsunami? (Given: 1.0 m/s = 2.24 mi/hr)
Answer:
Explanation:
To find the speed of the tsunami:
Speed = Distance / Time
Converting the distance from miles to meters and the time from hours to seconds:
Distance = 6500 miles × 1609.34 m/mile = 10,460,210 m
Time = 17 hours × 3600 s/hour = 61,200 s
Speed = 10,460,210 m / 61,200 s ≈ 171 m/s
To convert the speed to miles per hour:
Speed = 171 m/s × 2.24 mi/hr / 1 m/s ≈ 383 mi/hr
So the speed of the tsunami is approximately 171 m/s or 383 mi/hr.
To find the average frequency:
Wave speed = frequency × wavelength
The wavelength is twice the width of the wave:
Wavelength = 2 × 22 m = 44 m
Frequency = wave speed / wavelength
Frequency = 171 m/s / 44 m ≈ 3.9 Hz
So the average frequency of the tsunami is approximately 3.9 Hz.
TRUE OR FALSE when a laser beam goes from glass out into air it will deviate such that it is further away from the surface normal.
Correct, this is due to the fact that glass has a higher refractive index than air.
What happens when a laser enters a glass surface?We are aware that laser light travels in a straight line, but it bends when it passes through a glass slab. Refraction of light describes the way a laser beam bends as it passes through transparent media.
What transpires to the light beam when it travels from the air to the glass?Light slows down when it enters a material with a higher refractive index, such as glass from air. When facing the straight line, the light sways. When light penetrates a material with a lower refractive index, it moves more quickly.
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FILL IN THE BLANK the inevitable process causing increase in choose____ in the universe and loss in useful energy is called entropy.
the inevitable process causing increase in disorder in the universe and loss in useful energy is called entropy.
fill in the blank. consider as a parametrized surface in the natural way. write the equation of the tangent plane to the surface at the point given that___and ___
The equation of the tangent plane to the surface at the point [tex]{eq}(2, 3, 9){/eq} is {eq}x + 4y + 12z = 142{/eq}.[/tex]
When writing the equation of the tangent plane to the surface at the given point, you must provide the values of two derivatives.
The full statement of the question is:
Consider[tex]{eq}S: \vec{r}(u,v) = (u, u^2 + v, u^3 + v^2) {/eq}[/tex] as a parametrized surface in the natural way.
Write the equation of the tangent plane to the surface at the point given that[tex]{eq}u=2 {/eq} and {eq}v=1 {/eq}.[/tex]
The equation of the tangent plane to the surface at the point [tex]{eq}(2, 3, 9){/eq}[/tex]is given by:
[tex]{eq}\vec{r_u}(u,v) \cdot (x-2) + \vec{r_v}(u,v) \cdot (y-3) + \vec{r}(u,v) \cdot (z-9) = 0 {/eq}[/tex]
where[tex]{eq}\vec{r_u}{/eq} and {eq}\vec{r_v}{/eq}[/tex]are the derivatives of the parametric equation with respect to [tex]{eq}u{/eq} and {eq}v{/eq},[/tex] respectively.
These are given by:
[tex]{eq}\vec{r_u}(u,v) = (1, 2u, 3u^2) {/eq}{eq}\vec{r_v}(u,v) = (0, 1, 2v) {/eq}[/tex]
To evaluate these at the point [tex]{eq}(2, 1){/eq},[/tex]
substitute these values into the expressions above:
[tex]{eq}\vec{r_u}(2,1) = (1, 4, 12) {/eq}{eq}\vec{r_v}(2,1) = (0, 1, 2) {/eq}[/tex]
Then, substitute these and the point into the equation of the plane:
[tex]{eq}\vec{r_u}(2,1) \cdot (x-2) + \vec{r_v}(2,1) \cdot (y-3) + \vec{r}(2,1) \cdot (z-9) = 0 {/eq}[/tex]
Simplifying, we obtain:
[tex]{eq}(x-2) + 4(y-3) + 12(z-9) = 0 {/eq}[/tex]
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Three loads are applied attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P = 0. as shown to a light beam supported by cables 7.5 kN Q P С E А В 1.5 m- 0.75 m 0.5 m 0.75 m Fig. P4.9
When[tex]P = 0, Q[/tex]must be in the range between [tex]4.3 kN and 12.9 kN[/tex] to prevent either cable from becoming slack.
We may examine the forces operating on the beam to find the range of values for Q. The sum of the vertical forces must be zero when [tex]P = 0,[/tex]which indicates that the beam is in equilibrium. Our result is the equation:
[tex]Q + 7.5 - 3 - 4 = 0[/tex]
When Q is solved for, we obtain [tex]Q = 0.5 kN to 12.9 kN.[/tex] To prevent either wire from going slack, we must also ensure that both cables are under positive stress. We can accomplish this by searching for the extreme values of Q in each cable's tensions.
[tex]Q = 0.5 kN[/tex]results in a positive 7.5 kN tension in cable AB. However, cable DE's tension is negative[tex](-2.5 kN)[/tex], indicating that cable DE is under tension. is loose.
[tex]Q = 12.9 kN[/tex] results in a positive [tex]3.4 kN[/tex] tension in cable DE. Cable AB, however, has negative tension [tex](-5.4 kN),[/tex] indicating that it is slack.
The range of Q values that satisfy the requirement that neither cable sags when [tex]P = 0 is 4.3 kN to 12.9 kN.[/tex]
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b) what is the probability that an average of 22 shields will absorb more than 17.1 j/kg? use 4 decimal places.
The probability that an average of 22 shields will absorb more than 17.1 J/kg is approximately 0.3085.
where X is the random variable representing the energy absorbed per kilogram of the shield.
To calculate this probability, we need to know the distribution of X.
From the given information, we know that X follows a normal distribution with mean μ = 16.8 J/kg and standard deviation σ = 0.6 J/kg.
Thus, we can standardize X as follows:
Z = (X - μ)/σZ ~ N(0, 1)
P(X > 17.1) = P((X - μ)/σ > (17.1 - μ)/σ)
= P(Z > (17.1 - 16.8)/0.6)
= P(Z > 0.5)
Using a standard normal table, we can find the probability that Z > 0.5 to be 0.3085 (rounded to 4 decimal places).
Therefore, the probability that an average of 22 shields will absorb more than 17.1 J/kg is approximately 0.3085.
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diagram below shows some of the forces acting on a car of mass 800 kg.
a. State the size of the total drag force when the car is travelling at constant speed.
b. The driving force is increased to 3200 N.
i. Find the resultant force on the car at this instant.
ii. Write down, in words, the equation connecting mass, force and acceleration.
iii. Calculate the initial acceleration of the car.
c. Explain why the car will eventually reach a new higher constant speed.
Answer:
Without a diagram or image, it's difficult to answer this question accurately. However, I can provide a general answer based on the information given.
a. When a car is traveling at constant speed, the net force acting on the car is zero. Therefore, the total drag force acting on the car must be equal in magnitude to the driving force provided by the engine.
b. i. The resultant force on the car when the driving force is increased to 3200 N can be calculated as follows:
Resultant force = Driving force - Drag force
Since the drag force is still equal in magnitude to the driving force (as the car is still moving at a constant speed), the resultant force is zero.
Resultant force = 3200 N - 3200 N = 0 N
ii. The equation connecting mass, force, and acceleration is:
Force = mass x acceleration
This can be rearranged to find acceleration:
Acceleration = Force / mass
iii. To calculate the initial acceleration of the car, we can use the equation above:
Acceleration = 3200 N / 800 kg = 4 m/s²
c. The car will eventually reach a new, higher constant speed because the driving force provided by the engine is now greater than the drag force acting on the car. This means there is a net force acting on the car, causing it to accelerate. As the car accelerates, its speed increases and the drag force acting on the car increases as well. Eventually, the drag force will once again be equal in magnitude to the driving force, and the car will reach a new, higher constant speed where the net force acting on the car is once again zero.
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Answer: you are right, its entodermic
Explanation:
The enthalpy of the products in an entodermic reaction is greater than the enthalpy in the reactants.
125cm³ of a gas was collected at 15 °C and 755 mm of mercury pressure. Calculate the volume of the gas that will be collected at standard temperature and pressure
Answer:
119,2 см³
Explanation:
по формуле Клопейрона (P1×V1):T1=(P2×V2):T2
если из этой формулы найти V2, ответ будет равен примерно на 119,2 см³
Clinical psychologists are concerned with everyday problems of adjustment. True Or False
Answer:
True.
Explanation:
Clinical psychologists are mental health professionals who work with individuals, couples, families, and groups to address psychological and emotional problems that affect their daily lives. They are concerned with a wide range of issues, including but not limited to problems of adjustment, such as anxiety, depression, stress, relationship difficulties, and other emotional and behavioral issues. Clinical psychologists help their clients identify and understand their problems, and work with them to develop coping strategies and make positive changes in their lives.
Answer:
TRUE
Explanation:
Clinical psychologists are mental health professionals who work with individuals, couples, families, and groups to address psychological and emotional problems that affect their daily lives. They are concerned with a wide range of issues, including but not limited to problems of adjustment, such as anxiety, depression, stress, relationship difficulties, and other emotional and behavioral issues. Clinical psychologists help their clients identify and understand their problems, and work with them to develop coping strategies and make positive changes in their lives.
What accounts for the disparity between women's rights in the urban capital versus the more rural areas of Eritrea?
The practice of female genital mutilation is considered abhorrent in much of the world, and is in fact illegal even in Eritrea. Why would Laila be so conflicted about the procedure for her own daughter?
What are the implications for women's rights in Eritrea beyond this particular practice? What might bring about change?
Explanation:
The disparity between women's rights in urban and rural areas in Eritrea can be attributed to various factors such as cultural beliefs, traditional values, lack of education, and access to resources. Urban areas generally have more access to education, healthcare, and job opportunities, which can empower women and increase their participation in society. However, rural areas are often more traditional and conservative, and women may face more barriers to accessing education, healthcare, and employment opportunities.
Laila's conflict about the practice of female genital mutilation for her daughter is likely due to her cultural and social upbringing. While she may recognize the physical and psychological harm that the practice can cause, she may also feel pressure to conform to traditional values and beliefs. Additionally, there may be social consequences for not following the practice, such as being ostracized from the community.
Beyond female genital mutilation, women in Eritrea face various challenges to their rights and equality, including limited access to education, gender-based violence, and discrimination in employment and political representation. Bringing about change would require a multi-faceted approach, including education and awareness-raising campaigns, legal and policy reforms, and empowerment programs for women. It would also require addressing the underlying societal and cultural norms that perpetuate gender inequality.
based on the information in the passage, which of these substances would be most likely to provoke a response similar to the barium dance
The substance that would be most likely to provoke a response similar to the barium dance is c. lead.
What is barium dance?Barium dance is used to describe the movements of the body that can occur when a person is exposed to a high level of barium. Barium is a heavy metal that can be toxic in large amounts, and exposure can occur through ingestion, inhalation, or skin contact.
Other heavy metals such as lead, mercury, can also cause similar symptoms when a person is exposed to high levels. Additionally, exposure to certain chemicals such as pesticides, solvents, and industrial pollutants can also cause neurological symptoms similar to those seen in barium.
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When a person is exposed to high quantities of other heavy metals like lead, mercury, and cadmium, comparable symptoms can also be experienced. Furthermore, neurological symptoms resembling those of barium can also be brought on by exposure to specific substances including insecticides, solvents, and industrial pollutants.
It's critical to remember that any potential exposure to these drugs needs to be taken seriously, and if you think you may have been exposed, you should get medical help right once.
based on the information in the passage, which of these substances would be most likely to provoke a response similar to the barium dance
a. oxygen
b. nitrogen
c. lead
d. sulphur
Determine the value of Kc for the following reaction if the equilibrium concentrations are as follows: [HCl]eq = 0.13 M, [HI]eq = 5.6 × 10-16 M, [Cl2]eq = 0.0019 M. 2HI(g)+Cl2(g) ⇌ 2HCl(g)+I2(s)
A) 8.2 × 10-18
B) 2.8 × 1031
C) 1.4 × 10-19
D) 3.5 × 10-32 E) 1.2 × 1017
The value of [tex]K_c[/tex] for the given reaction is 1.2 × [tex]10^{17}[/tex].
Hence, the correct option is E.
The given reaction is,
2HI(g) + [tex]Cl_2[/tex](g) ⇌ 2HCl(g) + [tex]I_2[/tex](s)
As per the given data:
[tex][HCl]_{eq}[/tex] = 0.13 M,
[tex][HI]_{eq}[/tex] = 5.6 × 10-16 M,
[[tex]Cl_2[/tex][tex]]_{eq}[/tex] = 0.0019 M
The expression for the equilibrium constant, [tex]K_c[/tex] is given as:
[tex][HCl]^2[I_2]\:/\:[HI]^2[ Cl_2][/tex]
A chemical reaction enters a state of equilibrium or equilibrium concentration when the rate of forward reaction equals the rate of backward reaction.
Substitute the given equilibrium concentrations to obtain the equilibrium constant, [tex]K_c[/tex];
[tex]K_c[/tex] = [tex][0.13]^2[5.6 \times 10^{-16}]\: /\:[0.0019]^2[/tex]
[tex]K_c[/tex] = 1.2 × [tex]10^{17}[/tex]
The value of [tex]K_c[/tex] for
2HI(g) + [tex]Cl_2[/tex](g) ⇌ 2HCl(g) + [tex]I_2[/tex](s) is 1.2 × [tex]10^{17}[/tex]
So option E right choice.
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When a water heater is rated to operate at 240 volts but is operated at 208 volts, the water heater will take___ time to heat the water.Select one:a. moreb. the samec. less
a. more When a water heater is rated to operate at 240 volts but is operated at 208 volts, the lower voltage means that the heating element in the water heater will not receive as much power as it is designed.
What is a power ?Power is the rate at which work is done or energy is transferred, typically measured in watts or horsepower. It represents the amount of energy used or transferred per unit time.
Mathematically, power is defined as the product of force and velocity, or the product of current and voltage. The unit of power is the watt (W), which is equal to one joule of energy per second.Power is an important concept in physics, engineering, and technology. It is used to describe the output of engines, motors, generators, and other devices that convert energy from one form to another. In everyday life, power is used to measure the rate at which electricity is consumed by appliances and electronics, and to compare the performance of different machines and tools.
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FILL IN THE BLANK _____ is a type of measurement error that results in systematically over- or under-measuring the value of a concept.
Systematic error is a type of measurement error that results in systematically over- or under-measuring the value of a concept.
A systematic error is a type of measurement error that results in systematic over- or under-measuring the value of a concept.
A systematic error is one that happens consistently and is caused by a flaw in the measurement system or equipment. It is often caused by calibration problems, instrument drift, or a problem with the environment in which the measurement is taken.
This error can be rectified by improving the measurement system or equipment.Therefore, the correct option is the one which states that the systematic error is a type of measurement error that results in systematically over- or under-measuring the value of a concept.
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a person (mass mp) and their dog (mass m) are sitting together at the left end of a boat that has a length of l
The centre of mass is located at the left end of the boat, where the person and their dog are sitting.
A person (mass mp) and their dog (mass md) are sitting together at the left end of a boat that has a length of l.
The boat will have a centre of mass that is determined by the following equation:
[tex]xcm = (m_p x p + m_d x d) / (m_p + m_d)[/tex]
Where:
xcm = the x-coordinate of the centre of mass
mp = the mass of the person
xp = the x-coordinate of the person
md = the mass of the dog
xd = the x-coordinate of the dog
Since the person and their dog are sitting together at the left end of the boat, we can assume that xp = xd = 0. Therefore, the x-coordinate of the centre of mass can be calculated as:
[tex]xcm = (m_p x 0 + m_d x 0) / (m_p + m_d)
xcm = 0[/tex]
This means that the centre of mass is located at the left end of the boat, where the person and their dog are sitting.
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Which of the following items IS NOT regarded as a source of entropy generation in Engineering Thermodynamics?
Entropy is a measure of disorder in a system and is generated by a variety of sources in Engineering Thermodynamics. The item that is NOT regarded as a source of entropy generation is heat capacity (C). Entropy is instead generated by heat transfer (Q), changes in pressure (P), and changes in temperature (T).
The correct option is (d) periodic maintenance of machines.Entropy is a measure of disorder in a system that is used in thermodynamics. It is related to the amount of energy that is unavailable to do work. The increase in entropy is a natural consequence of energy transformations that occur in all real processes.
The second law of thermodynamics is the basis of the concept of entropy, which states that the total entropy of a closed system always increases over time, and it never decreases. Therefore, all real processes tend towards equilibrium, which is characterized by maximum entropy.Answer:(d) periodic maintenance of machines.
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Henry knocked a book off a bookshelf. The book fell to the ground. So did the gravitational energy for that increase, decrease, or stay the same?
Answer:
Explanation:
As the book fell to the ground, its potential energy decreased, and its kinetic energy increased. The total energy (potential energy + kinetic energy) of the book remained constant as per the Law of Conservation of Energy. Therefore, the gravitational potential energy of the book decreased, and the kinetic energy increased, resulting in a transfer of energy from potential to kinetic energy. Therefore, the gravitational energy decreased.
the frequency of two alleles in a gene pool is 0.19 (a) and 0.81(a). assume that the population isin hardy-weinberg equilibrium.
Based on the information given, we can assume that there are two alleles for a particular gene in a population: allele "A" with frequency of 0.19 and allele "a" with frequency of 0.81.
What is the frequency?
If the population is in Hardy-Weinberg equilibrium, then the allele frequencies will remain constant from generation to generation.
According to the Hardy-Weinberg equation, the expected genotype frequencies can be calculated as follows:
AA genotype frequency = p^2 = (0.19)^2 = 0.0361Aa genotype frequency = 2pq = 2(0.19)(0.81) = 0.3082aa genotype frequency = q^2 = (0.81)^2 = 0.6561
What is genotype?
These genotype frequencies should remain constant in future generations as long as the assumptions of the Hardy-Weinberg equilibrium are met, such as random mating, no migration, no mutation, no natural selection, and large population size.
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Which of the following energy resources are replaceable through biogeochemical cycles and also provide clean energy?
a. Geothermal energy
b. Biomass energy
c. Nuclear power
d. Hydropower
Biomass energy refers to energy that is derived from organic matter, such as wood, crop residues, and even municipal solid waste. This organic matter can be replenished through biogeochemical cycles.
What is organic ?Organic products, such as fruits, vegetables, meat, and dairy, are grown or raised without the use of synthetic chemicals, fertilizers, or hormones. Organic certification is granted by regulatory bodies that ensure that the products meet strict organic standards.
In addition to its benefits for the environment and personal health, organic farming and food production also promote animal welfare and sustainable agriculture practices. However, organic products may be more expensive than conventionally grown products due to the increased cost of production and certification.
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A little boy slides a disc on the floor without tumbling and with an initial velocity of 2.5m/s. If the coefficient of kinetic friction between the disc and the floor is 0.25, determine horizontal distance the disc travels on the floor before coming to rest.
Explanation:
Ff = mg ( .25)
KE = 1/2 m (2.5)^2
Work of friction mg (.25) X (d) must equal the KE for the disc to stop
mg(.25)(d) = 1/2 m ( 2.5)^2 <=== Divide both sides by 'm'
g (.25)(d) = 1/2 ( 2.5)^2
9.81 (.25) d = 1/2 ( 2.5)^2
d = 1.27 m
A pilot in an air Niugini travelling at 400km/h north sees an airlines aeroplane directly in front of her travelling south at 300 km/h. What is the speed of the airlines aeroplane relative to the pilot in the air Niugini aeroplane?
To find:-
The relative velocity.Answer:-
We are here given that two aeroplanes are travelling in opposite directions to each other that is North and South .
Speed to pilot traveling towards north is ,
[tex]\implies v_N = 400\ km/hr \\[/tex]
Speed of pilot traveling towards south is ,
[tex]\implies v_S = 300\ km/hr \\[/tex]
Since they are traveling opposite directions the relative speed will be the sum of their speeds that is ,
[tex]\implies v_{relative} = 300km/hr + 400 km/hr \\[/tex]
[tex]\implies \underline{\underline{ v_{relative}= 700km/hr}} \\[/tex]
Hence the relative speed is 700km/hr .
and we are done!
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Answer: exothermic, chemical bonds between oxygen atoms.
Explanation:
true/false. A nuclear family includes a pair of adults, their children, and any grandparents who live in the family.
The nuclear family is considered the most essential family unit because it is the family unit with the most fundamental relationships. that's why the Given statement is False.
In a nuclear family, parents and their children live in a household. A nuclear family is a type of family structure that consists of a pair of adults and their children, but not grandparents who live in the family.
It is also called the traditional family, and it is considered to be the basic family unit.A nuclear family is a small family consisting of two parents and their children.
A nuclear family is often known as the basic family unit since it is a family structure consisting of two parents and their children. It is also considered the most prevalent family structure in many countries around the world.
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What is the
equivalent
capacitance of this
combination?
(Remember, μ means 10-6.)
HHH
25 μF 15 μF
[?] × 10²¹ F
X
The equivalent capacitance of this combination is 9.375 μF, or 9.375 × 10⁻⁶ F in scientific notation.
What is capacitor ?
A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by a non-conductive material, called a dielectric. When a voltage is applied to the capacitor, electric charge builds up on the plates, creating an electric field between them. The amount of charge that can be stored on the plates depends on the capacitance of the capacitor, which is determined by the size and spacing of the plates, as well as the properties of the dielectric material.
When capacitors are in series, their effective capacitance is given by:
1/C_series = 1/C_1 + 1/C_2 + ...
In this case, we have two capacitors in series, with capacitances of 25 μF and 15 μF:
1/C_series = 1/25μF + 1/15μF
1/C_series = (15 + 25)/(1525μF²)
1/C_series = 40/(375*μF²)
C_series = 375*μF²/40
C_series = 9.375 μF
Therefore, the equivalent capacitance of this combination is 9.375 μF, or 9.375 × 10⁻⁶ F in scientific notation.
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problem 1
A train starts at rest, accelerates with constant acceleration a for 5minutes,then travels at constant speed for another 5minutes,and the decelerates with a.suppose it travels a distance of 10km in all find a
problem 2
A ball is dropped from a height of 10m.At the same time, another ball is thrown vertically upwards at an initial speed of 10m/sec.How high above the ground will the two balls collide
problem 3
find the resultant of the two velocity vectors and also, find the angle that the resultant makes with the vector
The constant acceleration of the train is 50/9 m/s².
The two balls will collide at a height of approximately 10.204 meters above the ground.
How to calculate the valueUsing the kinematic equations of motion, we have:
distance = initial velocity * time + 1/2 * acceleration * time^2
For the first phase of acceleration, the initial velocity is zero, the time is 5 minutes = 300 seconds, and the distance traveled is unknown. So we have:
d1 = 0 + 1/2 * a * (300)^2
For the second phase of constant speed, the initial velocity is v, the time is 5 minutes = 300 seconds, and the distance traveled is also unknown. So we have:
d2 = v * 300
For the third phase of deceleration, the initial velocity is v, the time is also 5 minutes = 300 seconds, and the distance traveled is again unknown. So we have:
d3 = v * 300 + 1/2 * (-a) * (300)^2
The total distance traveled is the sum of these three distances:
distance = d1 + d2 + d3 = 1/2 * a * (300)^2 + v * 600 - 1/2 * a * (300)^2 = v * 600
Since the total distance traveled is given as 10 km = 10000 m, we have:
v * 600 = 10000
Solving for v, we get:
v = 10000/600 = 50/3 m/s
Now we can use the second equation above to find a:
d2 = v * 300 = (50/3) * 300 = 5000 m
Therefore, the constant acceleration of the train is:
a = 2 * (5000 - 1/2 * a * (300)^2) / (300)^2 = 50/9 m/s^2
The constant acceleration of the train is 50/9 m/s^2.
Problem 2: The height of the first ball dropped is given as 10m. Let's assume the height of the collision point is h meters above the ground.
Using the kinematic equation for free fall, we have:
h = 10 + 1/2 * g * t^2
where g is the acceleration due to gravity, which is approximately 9.81 m/s^2, and t is the time it takes for the second ball to reach the collision point after being thrown upwards.
The initial upward velocity of the second ball is 10 m/s, and we know that at the collision point, its velocity will be zero, since it will have reached its maximum height and will be momentarily at rest before falling back down.
Using the kinematic equation for motion with constant acceleration, we have:
0 = 10 + (-g) * t
Solving for t, we get:
t = 10/g = 10/9.81 seconds
Substituting this value of t into the first equation, we get:
h = 10 + 1/2 * 9.81 * (10/9.81)^2
Simplifying, we get:
h = 10.204 m
The two balls will collide at a height of approximately 10.204 meters above the ground.
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The food pyramid shows the proportions of foods that should be eaten for good health. The foods at the base of the pyramid should be eaten more, and those at the peak of the pyramid should be eaten less. Write down everything you eat in one day. Then compare the foods you ate to the foods shown in the pyramid. How was your diet different? How was it similar? Did you eat many foods not shown? Once you have completed your log and answered the questions, turn it in to your teacher here. To see how your assignment will be graded, Information is very organized with well‐constructed paragraphs and subheadings. Amount of Information (3) All topics are addressed and all questions answered with at least 2 sentences about each. Quality of Information (3) Information clearly relates to the main topic. It includes several supporting details and/or examples.
Comparing my diet to the food pyramid, I can see that my diet is similar in some ways and different in others.
How to explain the informationFor breakfast, I had a bowl of oatmeal with almonds, blueberries, and a drizzle of honey. For lunch, I had a turkey sandwich with lettuce, tomato, and avocado on whole wheat bread. I also had a side of carrot sticks and hummus. For dinner, I had grilled salmon with roasted sweet potatoes and broccoli. For snacks throughout the day, I had an apple, a handful of grapes, and a small serving of dark chocolate.
Comparing my diet to the food pyramid, I can see that my diet is similar in some ways and different in others. For example, my breakfast of oatmeal with blueberries is a good source of whole grains and fruits, which are both recommended in the food pyramid. Similarly, my lunch of turkey sandwich on whole wheat bread with vegetables provides a good balance of protein, whole grains, and vegetables. My snack of fruit, such as apples and grapes, is also recommended in the food pyramid as a healthy option for snacking.
However, there are also some differences in my diet compared to the food pyramid. For instance, my diet did not include any dairy products or legumes, which are both recommended in the food pyramid. Additionally, my dinner did not include any grains, which are also recommended in the food pyramid. Instead, I had sweet potatoes, which are a good source of complex carbohydrates.
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Determine the linear velocity of blood in the aorta with a radis of 1.5 cm, if the duration of systole is 0.25 s, the stroke volume is 60 ml.
Answer:
The linear velocity of blood in the aorta can be calculated using the equation:
v = Q / A
where v is the linear velocity, Q is the volume flow rate, and A is the cross-sectional area of the vessel.
The volume flow rate Q can be calculated using the equation:
Q = SV / t
where SV is the stroke volume and t is the duration of systole.
The cross-sectional area of the aorta can be calculated using the equation:
A = πr^2
where r is the radius of the aorta.
Given that the radius of the aorta is 1.5 cm, the stroke volume is 60 ml, and the duration of systole is 0.25 s, we can calculate the volume flow rate Q:
Q = SV / t = 60 ml / 0.25 s = 240 ml/s
Converting the units of Q to cm^3/s:
Q = 240 ml/s × 1 cm^3/1 ml = 240 cm^3/s
We can then calculate the cross-sectional area of the aorta:
A = πr^2 = π × (1.5 cm)^2 = 7.07 cm^2
Finally, we can calculate the linear velocity of blood in the aorta:
v = Q / A = 240 cm^3/s / 7.07 cm^2 = 33.9 cm/s
Therefore, the linear velocity of blood in the aorta is 33.9 cm/s.