Use the work energy theorem to rank the final kinetic energy of a ball based on the initial kinetic energy Ki, the magnitude of a constant force F on the ball, the displacement of the ball, d and the angle, theta between the displacement of the ball and the net force on the ball. Rank from greatest kinetic energy (1) to least kinetic energy (4).

a) Ki=150J F=10N d=15m theta=90 degrees
b) Ki=300J F=200N d=1.5m theta=180 degrees
c) Ki=200J F=25N d=4m theta= 0 degrees
d) Ki=450J F=15N d=30m theta=150 degrees​

Comparing my diet to the food pyramid, I can see that my diet is similar in some ways and different in others.

For 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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Answer:

Base on my experience the answer is True...

Answer: True

Explanation:

Answer:

Explanation:

(a) The kinetic energy of the object at time t1 is given by:

K1 = (1/2)mv1^2

where m = 8.51 kg and v1 = (5.21î − 2.81ĵ) m/s. Substituting these values, we get:

K1 = (1/2)(8.51 kg)(5.21î − 2.81ĵ)^2 = 149.12 J

Therefore, the kinetic energy of the object at time t1 is 149.12 J.

(b) The displacement of the object during the time interval Δt = t2 − t1 is given by:

Δr = r2 − r1 = (8.00î + 4.00ĵ) m - 0î - 0ĵ = 8.00î + 4.00ĵ

The average velocity of the object during this time interval is:

vavg = Δr/Δt = (8.00î + 4.00ĵ)/(2.00 s - 0 s) = 4.00î + 2.00ĵ m/s

Using the kinematic equation:

Δv = aΔt

where Δv = v2 - v1 is the change in velocity during the time interval, we can solve for the acceleration:

a = Δv/Δt = (v2 - v1)/Δt = [(8.00î + 4.00ĵ) m/s - (5.21î − 2.81ĵ) m/s]/(2.00 s - 0 s) = 1.395î + 3.415ĵ m/s^2

The force acting on the object during the time interval Δt = t2 − t1 is given by Newton's second law:

F = ma = (8.51 kg)(1.395î + 3.415ĵ) m/s^2 = 11.83î + 29.05ĵ N

Therefore, the force acting on the object during the time interval Δt is F = 11.83î + 29.05ĵ N.

(c) The work done on the object by the force during the time interval Δt = t2 − t1 is given by:

W = F · Δr

where · denotes the dot product. Substituting the values of F and Δr, we get:

W = (11.83î + 29.05ĵ) N · (8.00î + 4.00ĵ) m = 95.52 J

Therefore, the work done on the object by the force during the time interval Δt is -95.52 J.

Note: The negative sign indicates that the work done by the force is negative, i.e., the force acts in the opposite direction to the displacement of the object.

(d) The kinetic energy of the object at time t2 is given by:

K2 = (1/2)mv2^2

where m = 8.51 kg and v2 is the velocity of the object at time t2. To find v2, we can use the kinematic equation:

v2 = v1 + aΔt

where a is the acceleration of the object during the time interval and Δt = t2 − t1. Substituting the values, we get:

v2 = (5.21î − 2.81ĵ) m/s + (1.395î + 3.415ĵ) m/s^2(2.00 s)

The statement that accurately describes the universal gravitational law is (option C) As the distance between any two bodies increases, the gravitational force between them decreases.

The universal gravitational law, also known as Newton's law of universal gravitation, is a fundamental law of physics that describes the gravitational attraction between two objects with mass. The law states that:

Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the gravitational force between two objects decreases as the distance between them increases.

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When it is time to end a reflux, first remove the heat source in the flask and then turn off the heat. Wait until the system has cooled.

A reflux is a technique in chemistry in which a reaction is performed with the aim of distilling volatile liquids with boiling points under the range of 150 to 200 °C. Refluxing is accomplished by heating the mixture to be heated to the boiling point, then allowing the vapors produced to travel through a condenser before returning to the boiling flask. The setup of reflux equipment can be seen below: For a successful refluxing, it is important to end the process by following the correct steps, which are given below

Remove the heat source in the flask Turn off the heat Wait until the system has cooled. Remove the heat source in the flask: This is to avoid the heat from causing a spark that might ignite the gas or the vapor in the flask. Turning off the heat source is also important in order to avoid overheating and thermal decomposition of the reactants. Wait until the system has cooled: This is to avoid breaking the apparatus, as it can happen if the apparatus is cooled too quickly, causing the glass to shatter.

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m=55.0 D=820 so were are looking for the velocity ? v= m\d V = 55.0*820 =45100 ...

The bug will cross the sticky region once in each cycle of its motion, where a cycle is defined as one complete round trip from the top of the bowl to the bottom and back to the top.

To find the number of cycles the bug goes through, we can use conservation of mechanical energy. At the top of the bowl, the bug has only potential energy, which is converted to kinetic energy as it slides down the bowl. At the bottom of the bowl, all of the potential energy has been converted to kinetic energy, and as the bug slides up the other side of the bowl, the kinetic energy is converted back into potential energy. At the top of the bowl again, the bug has only potential energy, and the cycle repeats.

Because there is no friction (except for the sticky patch), the total mechanical energy of the system is conserved. Therefore, the potential energy at the top of the bowl is equal to the potential energy at the bottom of the bowl, and the kinetic energy at the bottom of the bowl is equal to the kinetic energy at the top of the bowl.

We can set the potential energy at the top of the bowl to zero, and use the conservation of energy to find the potential energy at the bottom of the bowl:

mgh = (1/2)mv^2

where m is the mass of the bug, g is the acceleration due to gravity, h is the depth of the bowl, and v is the speed of the bug at the bottom of the bowl.

Solving for v, we get:

v = sqrt(2gh)

Plugging in the numbers, we get:

v = sqrt(29.810.12) = 0.775 m/s

The time it takes for the bug to slide from the top of the bowl to the bottom and back up to the top is twice the time it takes to slide from the top to the bottom:

t = 2sqrt(2h/g) = 2sqrt(2*0.12/9.81) = 0.774 s

Therefore, the frequency of the bug's motion is:

f = 1/t = 1/0.774 = 1.29 Hz

Since the bug completes one cycle in each oscillation, the bug will cross the sticky region 1.29 times per second, or approximately once every 0.78 seconds.

The magnitude of the current through the resistor R4 just after the switch is closed so the total current 0.06647 A.

(1)

The capacitor acts as short circuit just after the switch is closed.

The equivalent resistance is,

[tex]R_{eq}=R_1+R_2 || R_3+R_4\\=R_1+\frac{R_2R_3}{R_2+R_3}+R_4\\=(36)+\frac{(36)(77)}{(36)+(77)}+(120)\\[/tex]

= 180.53 Ω

Use Ohm's law to solve for total current.

V = IR

I= V/ R

[tex]=\frac{12 V} {180.53}[/tex]

= 0.06647 A

(2)

The capacitor is a break in the circuit after long time has passed since the switch was closed. The potential across capacitor is same as potential across R..

The equivalent resistance of the circuit is,

[tex]R_{eq}=R_1+ R_3+R_4[/tex]

=36Ω+77Ω+120Ω

= 233 Ω

Use Ohm's law to calculate I.

V = IR

I= V / R_eq

[tex]=\frac{12 V} {233}[/tex]

= 0.0515 A

Use Ohm's law to solve for Voltage [tex]V_3[/tex].

[tex]V_3=IR_3[/tex]

=(0.0515 A) (772)

= 3.97 V

The charge on the capacitor is,

C= Q/V

Q(∞)=CV

[tex]=(67\mu F (10^{-6} F/1 \mu F) (3.97 V)\\[/tex]

= 2.657× [tex]10^{-4} C[/tex]

(3)

The expression of charge of the capacitor while discharging is,

[tex]Q(t)=Qe^ {\frac{1}{RC}}[/tex]

The total resistance is,

[tex]R_{eq}=R_2+ R_3[/tex]

= 36 Ω + 77 Ω

= 113 Ω

The charge after 555 us is,

Q(555 us)=(2.657×10^-4 C)exp[tex](\frac{(-555 us } {(113)(67 \mu F)})[/tex]

=2.47×10 C

(4)

Use Ohm's law to solve for potential difference on the combination of R2 and R.

[tex]V_{23} = IR_{23[/tex]

[tex]=(0.06647A)\frac{(36)(77)}{(36)+(77)}\\=1.63 V[/tex]

= 1.63 V

The current [tex]I_C_{max[/tex] is,

V = IR

[tex]I_C_{max}=\frac{V_{23}} {R_{2}}[/tex]

= 1.63 V/ 36Ω

= 4.53×10^-2 A

(5)

The maximum potential by capacitor is, V = 3.97 V

Use Ohm's law to solve for current.

[tex]I_C_{max[/tex]=V/R

=3.97 V/113 Ω

=3.51×10^-2 A

Current refers to the flow of electric charge through a conductor. It is measured in units of amperes (A), which represent the rate at which electric charge flows through a circuit. The flow of current is driven by a difference in electric potential, or voltage, between two points in the circuit. There are two types of current: direct current (DC) and alternating current (AC). Most electronic devices and appliances use DC, while AC is typically used to transmit electricity over long distances.

Understanding current is crucial to many fields, including electrical engineering, physics, and electronics. It is also important for everyday life, as we rely on electricity to power our homes, cars, and devices. Properly managing current is critical for ensuring safety and avoiding electrical hazards.

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The work done when a force of 111 N is applied to move a cart a distance of 22 m is 2,442 J (joules).

To determine the work done when a force is applied to move an object, we use the formula:

work = F x d

where:

Therefore, we can calculate the work done as:

work = force x distance

work = 111 N x 22 m x 1 = 2,442 J

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The mass will come to rest at its natural length, which is also its equilibrium position.

What is spring constant?

Spring constant (k) is a measure of the stiffness of a spring or other elastic object. It is defined as the force required to stretch or compress the spring by a unit distance, usually expressed in newtons per meter (N/m) or pounds per inch (lb/in).

The distance below the natural length of the spring at which the mass will come to rest can be calculated using the energy conservation principle, which states that the initial potential energy stored in the spring will be converted into the kinetic energy of the mass as it oscillates, and then back into potential energy when the mass reaches its maximum displacement.

The potential energy stored in a spring is given by:

U = (1/2)kx²

where U is the potential energy, k is the spring constant, and x is the displacement from the natural length of the spring.

At the maximum displacement, all the potential energy is converted into kinetic energy, given by:

K = (1/2)mv²

where K is the kinetic energy and m is the mass of the object.

Using the conservation of energy, we can equate the potential energy at the maximum displacement to the kinetic energy at the resting position:

(1/2)kx² = (1/2)mv²

Rearranging, we get:

x = sqrt[(mv²)/k]

To find the velocity of the mass at the resting position, we can use the conservation of energy again to equate the potential energy at the resting position to the kinetic energy at the maximum displacement:

(1/2)kx₀² = (1/2)mv_max²

where x₀ is the displacement from the natural length of the spring at the resting position, and v_max is the  maximum velocity of the mass.

Rearranging, we get:

v_max = sqrt[(k/m)x₀²]

At the resting position, the velocity of the mass is zero, so we can use the equation of motion for simple harmonic motion to find the maximum displacement:

x_max = (v_max / w)

where w is the angular frequency of the oscillation, given by:

w = sqrt(k/m)

Substituting the expressions for v_max and w, we get:

x_max = sqrt[(k/m)x₀²] / sqrt(k/m)

Simplifying, we get:

x_max = x₀

Therefore, the maximum displacement of the mass from the natural length of the spring at the resting position is equal to the displacement from the natural length at the maximum displacement. Substituting the given values into the equation for x, we get:

x = sqrt[(22 kg x (0 m/s)²) / 11 N/m] = 0 m

Therefore, The mass will come to rest at its natural length, which is also its equilibrium position.

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Answer:

Explanation:

The heat required to completely boil a certain amount of water is given by the formula:

Q = mL

where Q is the heat required, m is the mass of the water, and L is the specific heat of vaporization of water, which is 2260 J/g.

Using the given values:

m = 1500 g

L = 2260 J/g

Substituting these values into the formula, we get:

Q = 1500 g × 2260 J/g

Q = 3,390,000 J

Therefore, 3,390,000 joules of heat transfer is required to completely boil 1500 g of water into a gas.

The beat frequency produced when a 240-hertz tuning fork and a 246-hertz tuning fork are sounded together would be 6 hertz. Option D.

The beat frequency produced when two tuning forks are sounded together is equal to the absolute value of the difference between their frequencies.

In this case, the beat frequency is:

|240 Hz - 246 Hz| = |-6 Hz| = 6 Hz

Therefore, the answer is (d) 6 hertz.

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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.

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.

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.

Forklift attachments are not integral parts of the forklift equipment but are used to hold a load or loads. Examples of forklift attachments include fork extensions, side shifters, clamps, rotators, and pallet handlers.

A forklift is a piece of heavy equipment that is primarily used to lift and move materials over short distances. It typically consists of a power-operated platform, called a pallet, that can be raised and lowered using hydraulic cylinders. The pallet is attached to a set of forks that can slide under a load, allowing it to be lifted and moved.

Forklifts are commonly used in warehouses, manufacturing facilities, and construction sites, where they can quickly and efficiently move heavy materials from one location to another. They are also used to load and unload trucks and shipping containers. Forklifts come in a variety of sizes and configurations, ranging from small, electric-powered models for indoor use, to large, diesel-powered models for outdoor applications.

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Answer:

To calculate the amount of heat absorbed by the ice, we need to use the equation:

Q = m * ΔHf

where Q is the heat absorbed by the ice, m is the mass of the ice, and ΔHf is the heat of fusion of the ice, which is 334 J/g.

First, we need to calculate the amount of heat lost by the water:

Q = m * c * ΔT

where Q is the heat lost by the water, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the temperature change of the water.

We know that the mass of the water is 100 g, c is 4.18 J/g-°C, and ΔT is 5°C, so:

Q = 100 g * 4.18 J/g-°C * 5°C

Q = 2090 J

This means that the water lost 2090 J of heat, which was absorbed by the ice. Now we can calculate the amount of heat absorbed by the ice:

Q = m * ΔHf

We know that the mass of the ice is 10 g and the heat of fusion of the ice is 334 J/g, so:

Q = 10 g * 334 J/g

Q = 3340 J

Therefore, the amount of heat absorbed by the ice is 3340 J, which is equivalent to 3.34 kJ (kilojoules). The closest answer choice is 2.09 kJ, but that is not the correct answer.

The potential difference across C4 can be found using the equation V = V4 - V3. Using the given values, V = 12.0V, C1 = 3.0 ?F, C2 = 2.0 ?F, C3 = 2.0 ?F, C4 = 1.0 ?F, and C5 = 4.0 ?F, we can solve for V4.

V4 = 12.0V + (3.0 ?F + 2.0 ?F + 2.0 ?F + 1.0 ?F) / (1.0 ?F + 4.0 ?F)
V4 = 12.0V + (8.0 ?F / 5.0 ?F)
V4 = 12.0V + 1.6V
V4 = 13.6V
Therefore, the potential difference across C4 is 13.6V - 12.0V = 1.6V.
The potential difference across C4 can be determined using the formula Q = CV. Where Q represents the charge stored in the capacitor, C represents capacitance, and V represents the potential difference across the capacitorTo determine the potential difference across C4, we can use the formula Q = CV. To determine Q, we need to determine the equivalent capacitance of the circuit.

The equivalent capacitance of capacitors in parallel is equal to the sum of their capacitance. The equivalent capacitance of capacitors in series is equal to the reciprocal of the sum of their reciprocals.C1, C2, and C3 are in series, and their equivalent capacitance is given by:C_eq1=1/((1/C1)+(1/C2)+(1/C3))=1/(1/3+1/2+1/2)=3/7 μF{C_eq1=1/((1/C1)+(1/C2)+(1/C3))=1/(1/3+1/2+1/2)=3/7μF}C_eq2 is the equivalent capacitance of C4 and C5 in parallel.C_eq2=C4+C5=1+4=5μF {C_eq2=C4+C5=1+4=5μF}

Now we can determine the equivalent capacitance of the entire circuit.C_eq=C_eq1+C_eq2=3/7+5=38/7μF{C_eq=C_eq1+C_eq2=3/7+5=38/7μF}Now, we can determine the charge stored in the circuit.Q=C_eqV=38/7*12= 65.14μC{Q=C_eqV=38/7*12=65.14μC}To determine the potential difference across C4, we can use the formula Q = CV.V=C4Q/C4= 65.14/1 = 65.14V{V=C4Q/C4=65.14/1=65.14V}Therefore, the potential difference across C4 is 65.14 V.

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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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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:

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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The work done by w is 22491 J.

The work done by Ti is 10728 J.

we have to determine the amount of work done by w. We can use the formula

W = Fd,

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

The mass of the piano is given as 255 kg, and it is lowered exactly 9 m from the second-story window to the ground.

We can calculate the force required to lower the piano using the formula

F = mg,

where m is the mass of the piano and g is the acceleration due to gravity.

Therefore, [tex]F = 255 kg x 9.8 m/s^2 = 2499 N.[/tex]

Using the formula for work, we can calculate the work done by w as follows:

W = Fd = 2499 N x 9 m = 22491 J

we have to determine the amount of work done by Ti. We are given the magnitude of two forces, 1830 N and 1295 N, and the angle between them is 60°.

We can find the resultant force using the law of cosines, which states that

[tex]c^2 = a^2 + b^2 - 2ab cos(C),[/tex]

where c is the length of the side opposite the angle C and a and b are the lengths of the other two sides.

Therefore, [tex]c = sqrt(a^2 + b^2 - 2abcos(C)) = sqrt((1830 N)^2 + (1295 N)^2 - 2(1830 N)(1295 N)cos(60°)) = 2159 N.[/tex]

The angle between the resultant force and the horizontal is 45°, so we can calculate the work done by Ti using the formula

W = Fd cos(theta),

where theta is the angle between the force and the direction of motion.

Therefore, W = 2159 N x 7 m x cos(45°) = 10728 J.

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The US city that regularly experiences the worst levels of photochemical smog that is enhanced by thermal inversions is Los Angeles.

Photochemical smog is a type of smog that is formed when pollutants in the air react with sunlight. It can cause health problems such as respiratory issues, eye irritation, and headaches.Thermal inversion occurs when a layer of warm air traps pollutants near the ground, preventing them from dispersing.

This can exacerbate the effects of photochemical smog.Los Angeles is known for its high levels of air pollution, including photochemical smog.

The combination of heavy traffic, industrial activity, and the surrounding mountains that trap pollutants in the area can contribute to the city's poor air quality. Additionally, the city's warm, sunny climate can create conditions that enhance the effects of photochemical smog.

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Answer:

see attachment

Explanation:

The maximum number of electrons in any shell is given by formula 2n² , where n is the number of shell .So in first shell , 2(1)² = 2 electrons would be accommodated.

Similarly in second shell , 2(2)² = 8 electrons would be accommodated .

Similarly we can find out the maximum number of electrons in 3rd , 4th and 5th shell .

The maximum number of electrons in valance shell is 8 .

Also, atomic numbers of ,

and we are done!

Answer:

it's b

Explanation:

no shade, direct sunlight

Answer:

it is A

Explanation:

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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Answer:

Explanation:

Adding other substances to the water besides salt, such as sugar or baking soda, would introduce confounding variables into the experiment. Other factors that could introduce confounding variables include using different volumes of water, using different amounts of salt, and heating the water at different rates. To minimize confounding variables, it is important to keep all variables constant except for the one being tested, which in this case is the effect of salt on the boiling point of water.

If this Doppler shift is due to the Sun rotating (try drawing a diagram), then  2km/s is the rotational speed of the Sun at its equator.

According to relation; of doppler shift:-

Velocity of rotation = ((observed wavelength / rest wavelength ) -1) x speed of Light

Here Observed wavelength = 486-0.0033 = 485.9967.m

and, Rest wavelength- 486 nm.

So, velocity=

((485.9967/486) - 1) x 299792.458 m/s

So, velocity = -2.035 km/s or Just 2km/s.

Doppler shift has important applications in astronomy, where it is used to determine the motion of celestial objects, such as stars and galaxies, and to measure their distance from Earth. It results in a change in the frequency of the observed waves, as perceived by the observer.

When the source of waves is moving towards the observer, the waves are compressed, and their frequency appears to be higher than their actual frequency. This is called a blue shift. Conversely, when the source is moving away from the observer, the waves are stretched, and their frequency appears to be lower than their actual frequency. This is called a red shift. It is also used in radar technology, where it is used to determine the speed and direction of moving objects, such as airplanes and vehicles.

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Complete Question:-

An astronomer observing the spectrum of the Sun finds that the Hydrogen-ß spectral line (λ = 486 nm) on the solar equator at one edge of the Sun's disk is blueshifted by 0.0033 nm compared to the same line at the center of the Sun's disk and is redshifted by the same amount on the equator at the other side of the Sun's disk. If this Doppler shift is due to the Sun rotating (try drawing a diagram), then what is the rotational speed of the Sun at its equator?

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

the inevitable process causing increase in disorder in the universe and loss in useful energy is called entropy.