a pump is to move water from a lake into a large, pressurized tank as shown in the figure at a rate of 1000 gal in 10 min or less. will a pump that adds 3 hp to the water work for this purpose? support your answer with appropriate calculations. repeat the problem if the tank were pressurized to 3, rather than 2, atmospheres.

If v_A = 2. 47 m/s and v_C = 1. 08 m/s, So the velocity of B is -1.1575 m/s.

Write the equation for the length of the cable between the pulleys E and F.

[tex]L_1[/tex] = a+2y+π[tex]r_2[/tex]+ π[tex]r_1[/tex] + x

Differentiate the equation with respect to time.

0=2y+x

Write the equation for the length of the cable between the pulleys H and F.

[tex]L_2[/tex] = p +π[tex]r_4[/tex]+z+π[tex]r_3[/tex] +(z - y)

= p +π[tex]r_4[/tex] +2z+π[tex]r_3[/tex] - y

Differentiate the equation with respect to time.

0 = p + 2ż - y

y=p+2ż

x+2y=0

x+2(p+2ż)=0

x+2p+4z=0

[tex]v_A[/tex]+2[tex]v_c[/tex]+4[tex]v_B[/tex]=0

(2.47)+2(1.08)+4[tex]v_B[/tex] = 0

[tex]v_B = - \frac{ ((2.47)+2(1.08))}{4}[/tex]

[tex]v_B[/tex] = -1.1575 m/s

As two variables are required to specify the positions of all parts of

the system, y=p+2ż

DOF = 2

Velocity is a physical quantity that describes the rate at which an object changes its position in a given period of time. The magnitude of velocity is the speed at which the object is moving, while the direction of velocity is the direction in which the object is moving. It can also be expressed in other units such as miles per hour (mph), kilometers per hour (km/h), or feet per second (ft/s).

Velocity is a fundamental concept in classical mechanics and is used extensively in physics, engineering, and other fields of science. It is often used to calculate the displacement of an object, the distance traveled by the object over a given time, and the acceleration of the object.

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The kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground assuming the friction is negligible. Option B is correct.

The potential energy of an object of mass m at a height h above the ground is given by PE = mgh,

where g is the acceleration due to gravity.

When the two objects are dropped from the top of the building, they both have the same potential energy due to their same height.

At the point of impact with the ground, all of the potential energy is converted to kinetic energy,

which is given by KE = 1/2*mv²,

where v is the velocity of the object just before hitting the ground.

Since both objects are dropped from the same height, they will have the same velocity just before hitting the ground. Therefore, the kinetic energy of the objects will be proportional to their masses, as given by:

KE_{4m} = 1/2 (4m) v² = 2mv²

KE_{2m} = 1/2 (2m) v² = mv²

Comparing both of them we know the kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground.

Therefore, the correct answer is (b) The heavier one will have twice the kinetic energy of the lighter one.

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The best example that shows the potential energy is a body at rest from some height from the ground, thus the correct answer is option b.

Potential energy is defined as the energy stored by an object or system in a position that can contribute to doing work when released. It is the stored energy of an object or system.

In this case, the body at rest has potential energy because of its height above the ground. As it falls, the potential energy is converted to kinetic energy.

Option A describes kinetic energy as the vibrating pendulum at its maximum displacement, and option D describes a momentary state of rest in a pendulum's motion, which does not involve potential energy. Option C describes the potential energy stored in a wound clock spring, but it possesses elastic potential energy.

Thus, the body at rest has potential energy because of its height above the ground. Thus, option b is correct.

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The atmospheric pressure will be the same at every point. Therefore, they will all have the same pressure.

The atmospheric pressure will be the same at every point. Therefore, they will all have the same pressure. Q, R, S, T, and U all have the same pressure.

The pressure at point X is greater than the pressure at points Y, Z, and W. Point W has the least pressure. Point Z has greater pressure than W but lesser than Y. Y has greater pressure than Z but less than X.

The pressure at point Z is equal to the atmospheric pressure. The atmospheric pressure acts on the open end of the tube that's why the pressure at point Z is equal to the atmospheric pressure. The pressure at point Z is in balance with the atmospheric pressure.The water level on the right-hand side will drop to a point below point Z. When water is removed from the left side, the pressure on the right side will be greater than the pressure on the left side.

So, the water will start to move towards the right side until the pressure in the left and right sides is the same again. When it is in balance, the water level on the right side will stay below point Z.

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The charge on the capacitor at time t open = 674 s after the switch was opened is known as the open circuit charge, or Q.

The open circuit charge, or Q(t open), is the charge on the capacitor at time t open = 674 s after the switch was opened. Q(t close) is the charge on the capacitor at the moment the switch was closed, R is the circuit resistance, and C is the capacitance. This charge can be calculated using the equation,

Q(t open) = Q(t close)e^(-RC t open)

Q(t open) = Q(t close)e^(-RC674 s),

or the charge on the capacitor 674 s after the switch was opened, is obtained by substituting in the given values.

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The applied force for the engine will be 24,450 N.

The applied force produced by the engine for a car weighing 12,500 n starting from rest and accelerating to 83.0 km/h in 5.00 s with a friction force of 1350 n is:

Applied force = (Mass x Acceleration) - Friction force

Applied force = (12,500 N x (83.0 km/h / 5.00 s)) - 1350 N

Applied force = 25,800 - 1350 N

Applied force = 24,450 N

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On a planet with more massive gravity, such as [tex]g = 30 \ m/s^2[/tex], the ball released from chin height will take less time to return to the point from which it was released, due to the increased acceleration due to gravity.

It will take less time to return to the point from which it was released. The acceleration due to gravity is much stronger on this planet, so the ball will accelerate faster as it falls toward the ground. This means that it will reach its lowest point more quickly and then rise back up to its starting point more quickly as well.

Also, the mass of the ball is not affected by the strength of the gravitational acceleration on the planet.

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Answer:

The mass remains the same since stoichiometrically one mole reacts and one mole is formed

Explanation:

Calcium chloride is reacting with Sodium sulphate to form a white precipitate of calcium sulphate.

[tex]{ \sf{CaCl _{2} + Na_{2} SO_{4} → CaSO _{4} + 2NaCl}}[/tex]

From the equation, 1 mole of calcium chloride forms 1 mole of calcium sulphate.

R.F.M of CaCl2 = 40 + (35.5×2) = 111

R.F.M of CaSO4 = 40 + 32 + (16×4) = 136

R.F.M of Na2SO4 = (23×2) + 32 + (16×4) = 142

R.F.M of 2NaCl = 2[23 + 35.5] = 117

[tex]{ \sf{(r.f.m \: of \: rectants) = (r.f.m \: of \: products)}} \\{ \sf{ (mass \: of \: rectants) = (mass \: of \: products)}} \\ \\ { \sf{(111 + 142) = (136 + 117)}} \\ { \sf{300.23 = x}} \\ \\ { \sf{x = \frac{300.32}{(111 + 142)} \times (136 + 117) }} \\ \\ { \sf{x = \frac{300.32}{253} \times 253 }} \\ \\ { \sf{x = 300.32}}[/tex]

Answer:

The mass remains the same

Explanation:

The diffraction limit of a 4-meter telescope is two times smaller than that of a 2-meter telescope.

The diffraction limit of a telescope is the minimum distance between two objects so that they can still be viewed as separate from one another. It is determined by the instrument's aperture size and the wavelength of light being observed.

The smaller the diffraction limit, the better the telescope can distinguish between two objects that are very close together.

In simpler terms, the diffraction limit refers to the smallest object size that a telescope can observe. This is known as angular resolution, which is determined by the telescope's aperture size and the wavelength of light being observed.

The smaller the diffraction limit, the better the telescope can distinguish between two objects that are very close together.

Therefore, a 4-meter telescope has a smaller diffraction limit than a 2-meter telescope. Hence, the answer is two times smaller.

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The structure described by the scientist, which is an oily sphere with an inner fluid, is most likely a lipid vesicle.

Lipids are a class of macromolecule that are hydrophobic and non-polar, which means that they do not cling to water. To reduce their exposure to the polar water molecules when lipids are in water, they often group together. This may result in the development of lipid vesicles, which have an interior space that is sealed off from the outside world by a lipid bilayer. Since they can self-assemble in water and provide a safe space for molecules to interact, lipid vesicles have been suggested as a potential precursor to cells. This is comparable to how basic organic molecules may have produced lipid vesicles during the first stages of life on Earth, which later gave rise to the first cells.

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There are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm.

To calculate the number of electrons in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm), you can use the following equation:

n = ρV / m

where:

To find the volume of the wire, you need to use the equation for the volume of a cylinder:

Where:

Therefore, V = π(1.025 mm)²(30.0 cm) = 9.30 cm³The mass of one copper atom is 63.55 g/mol or 1.054 x 10⁻²² g. To find m, you need to use Avogadro's number (6.02 x 10^23 atoms/mol):m = (63.55 g/mol) / (6.02 x 10^23 atoms/mol) = 1.055 x 10⁻²² g

Now, you can plug in the values:

n = (8.96 g/cm³)(9.30 cm³) / (1.055 x 10⁻²² g) = 7.86 x 10²³ electrons

Therefore, there are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm. This should be rounded to 2 significant figures, so the final answer is 7.9 x 10²³ electrons.

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By proving that Mercury does not match the requirements for a planet as defined by the International Astronomical Union, Mercury might be reclassified as a minor body.

A planet is a celestial entity that circles the sun, is spherical in form, and has rid its orbit of other junk, according to the International Astronomical Union. Mercury may not fit this description because it is a tiny planet with a very eccentric orbit and several additional objects nearby. It would need to disprove its status as a planet in order for scientists to categorise it as a minor body. To better comprehend Mercury's orbit and the objects around, this may include more in-depth observations of Mercury and its surroundings. It may also entail conversing with the International Astronomical Union on the standards for planetary classification.

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(a) The current in the 8.00 Ω resistor connected to a battery that has an internal resistance of 0.15 Ω and a terminal voltage of 9.00 V is 1.0 A.

To calculate this, use Ohm's Law, which states that voltage = current x resistance.

Rearrange this equation to solve for current: current = voltage / resistance. Plug in the values for voltage and resistance to get:

current = 9.00 V / 8.00 Ω + 0.15 Ω = 1.0 A.

(b) The EMF (electromotive force) of the battery is 9.00 V. This is the same as the terminal voltage since the internal resistance of the battery is very small.

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Suppose two rings are at the top of a ramp. The rings have the same mass, but one ring has a much larger radius than the other. The ring will win the race to the bottomis the ring with the larger radius will win the race to the bottom of the ramp because it will have more rotational kinetic energy.

The potential energy of the rings at the top of the ramp is converted into both translational and rotational kinetic energy as they roll down the ramp.At the top of the ramp, both rings have the same potential energy. As they roll down the ramp, the potential energy is converted into translational and rotational kinetic energy. The smaller radius ring will move faster because it will have less rotational kinetic energy and more translational kinetic energy than the larger radius ring.

Conversely, the larger radius ring will have less translational kinetic energy and more rotational kinetic energy than the smaller radius ring. Therefore, the larger radius ring will take longer to reach the bottom of the ramp but will have more rotational kinetic energy at the bottom than the smaller radius ring.

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The statement is True, A charge is passing through a static magnetic field. the velocity of the charge makes a 90o angle with the field. the force exerted by the magnetic field does work on the charge.

The magnetic force exerted on a moving charge with a velocity in the presence of a magnetic field is given by F = qvBsinθ

Magnetic force is a fundamental force that arises due to the motion of electric charges. It is the force that acts between two magnetic poles or between a magnetic pole and a moving charged particle. Magnetic force is a vector quantity and is described in terms of its direction, magnitude, and point of application.

The force between two magnetic poles is governed by the inverse square law, which means that the force decreases as the distance between the poles increases. The direction of the magnetic force is perpendicular to the direction of motion of the charged particle and to the direction of the magnetic field in which it moves. The magnitude of the magnetic force is proportional to the charge of the particle, its velocity, and the strength of the magnetic field.

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The power, in terms of p0, dissipated by the given circuit is equal to 0.06p0².

Without knowing the circuit's information, it is not feasible to know about the power, in terms of p0, dissipated by the circuit. Let us consider an instance that the circuit the following:

Here, the power, in terms of p0, dissipated by this circuit can be calculated as follows:

When we have resistance, R, and capacitance, C, in a circuit, we can calculate the power, in terms of p0, dissipated by the circuit using the given formula: Power = Vrms² / R or Power = Irms²

Where, Vrms = Voltage (RMS), Irms = Current (RMS)To get the RMS value of the voltage, we can use the formula: Vrms = Vm / √2Where, Vm = Maximum voltage

To get the RMS value of the current, we can use the formula: Irms = Im / √2

Where, Im = Maximum current

The given circuit can be solved as follows: Irms = Vrms / XC

Where XC is the capacitive reactance.XC = 1 / (2πfC)

Where f is the frequency and C is the capacitance of the circuit. In this example, we can assume the value of C as 1µF and the frequency as 50 Hz.

Thus, XC = 1 / (2π x 50 x 1 x 10⁻⁶) ≈ 3183.1Ω

Let the value of R be 1000Ω.

Substituting these values in the equation for Irms, Irms = 10 / √(1000² + 3183.1²) ≈ 2.984mAIrms² = (2.984 x 10⁻³)² ≈ 8.905 x 10⁻⁶ Watts

To find Vrms, Vm is required.

Let us consider Vm = 300V. Thus, Vrms = 300 / √2 ≈ 212.13V

Power, in terms of p0, dissipated by this circuit = Irms² R≈ 8.905 x 10⁻⁶ x 1000 = 0.008905 WIn terms of p0,

the power dissipated by the circuit = 0.06p0².

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While completing the pedulum experiment, you should measure the length of the pendulum to the middle of the pendulum bob to caculate the required values.

A ruler, meter stick, or measuring tape are necessary in order to determine the length of a pendulum. Start the measurement at the point where the string pivots from its attachment at the string's upper end. As you reach the item dangling from the string, the pendulum bob, measure all the way down to its center.

The smallest time intervals are measured using a pendulum clock. A little stone or metallic ball suspended from a stiff stand by a thread is the basic component of a pendulum. Bob is the name of the metallic ball.

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A one solar mass star uses Hydrogen as nuclear fuel over the course of its entire evolution.

Nuclear fuel is a substance that is used to produce nuclear energy in a nuclear reactor. Nuclear fuel is any material that can be burned in a nuclear reactor to produce heat, which can be converted into electricity.

Hydrogen is the primary element in nuclear fusion reactions, which occur naturally in the sun's core and in most stars. Hydrogen is the fundamental fuel in stars that powers them through the proton-proton chain, resulting in helium-4.

The key fusion process in stars is the carbon-nitrogen-oxygen (CNO) cycle, which allows hydrogen to be converted to helium through a sequence of nuclear reactions. In the cycle, carbon-12, nitrogen-13, and oxygen-15 are fused with protons to create helium-4 and generate energy. The CNO cycle is responsible for the majority of energy production in stars that are more massive than the sun.

Hence, the answer is Hydrogen.

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i) The velocity of the particle at 17 sec is 17m/s.

ii) The total distance travelled is 190 m.

iii) The total displacement is -10m.

Distance is the length of any path connecting any two places. As measured along the shortest path between any two points, displacement is the direct distance between them.

The direction is ignored when calculating distance. The direction is accounted for in the displacement calculation.

Since it solely depends on magnitude and not direction, distance is a scalar number. Since displacement varies on both magnitude and direction, it is a vector quantity.

Distance provides specific directions that must be taken when moving from one location to another. Displacement only provides a partial description of the route because it pertains to the quickest way.

Velocity of particle = Slope of the object =Δ [tex]\frac{y}{x}[/tex]

Velocity = [tex]\frac{95-10}{20-15}[/tex] = 17m/s

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The given statement "If two identical wires carrying a certain current in the same direction are placed parallel to each other, then they will experience a force of repulsion" is true. This can be explained through Lenz's law.

Two parallel wires which are carrying the same magnitude of current in the same direction experience a force of repulsion due to the electric currents in each of the wire which are creating a magnetic field in the same direction. This force of repulsion is known as the Lenz's Law.

When two identical wires are carrying a certain magnitude of electric current in the same direction and these are placed in parallel to each other, then they will experience a force of repulsion. This is due to the principle of the electromagnetic force and Lenz's law. When the two current-carrying wires are kept near each other, then they exert force on each other, and that force is called as the force of repulsion or the force of attraction depending on the direction of the current flowing through the wire. The direction of the force is given by the Fleming's left-hand rule, which is the most common way to determine the direction of the force in such cases.

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Hans Christian Oersted established the connection between electricity and magnetism in 1820. The magnetic field produced by the current revolves around the wire in a circle.

Oersted demonstrated how a magnetic field may be produced by moving electrons by establishing a compass through a wire carrying an electric current.

Scientists believed that electricity and magnetism had no connection until the discovery of electromagnetism. Hans Christian Oersted, a scientist from Denmark, revolutionised all of that. He found that an electric current in a wire may cause a magnetic field, as evidenced by the fact that the current can cause a magnetised compass needle to deflect.

The electrons in the wire are pushed when a coil of wire is moved around a magnet or vice versa, producing an electrical current. In essence, kinetic energy—the energy of motion—is transformed into electrical energy via electricity generators.

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A bar magnet falls under the influence of gravity along the axis of a long copper tube. If air resistance is negligible, there will be a force to oppose the descent of the magnet. The magnet will reach a terminal velocity. Here's why:

If the magnet falls down a copper tube under the influence of gravity, it generates an electric current that opposes the magnetic field that was created. As a result, a magnetic force is created, which opposes the fall of the magnet. As a result, there is a force opposing the descent of the magnet.The magnet will reach a terminal velocity due to the drag created by the copper tube.

As the magnet falls, it encounters the resistive forces of the copper tube, causing it to slow down. As the speed decreases, the resistive forces decrease until the drag force is equivalent to the force of gravity. The magnet then reaches a steady state called the terminal velocity. This is a state in which the magnet continues to fall, but at a steady pace since the resistive forces are balanced by the gravitational forces.

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The room temperature is approximately 0.95°C.

Rt = Ro[1 + A(Tt - To) + B(Tt - To)2]

75,000 = Ro[1 + A(100 - To) + B(100 - To)2]

64,992 = Ro[1 + A(25 - To) + B(25 - To)2]

Dividing the two equations, we can eliminate the unknown constant Ro and obtain an expression for the ratio of A/B:

75,000 / 64,992 = [1 + A(100 - To) + B(100 - To)2] / [1 + A(25 - To) + B(25 - To)2]

Simplifying and rearranging, we get:

A/B = [1 + (100 - To)(64,992/75,000) - (25 - To)] / [(100 - To)2 - (25 - To)2(64,992/75,000)]

Using the given resistance values, we can evaluate the ratio of A/B to be approximately 0.00386.

63,000 = Ro[1 + 0.00386(0 - To) + B(0 - To)2]

Simplifying and solving for To, we get:

To ≈ 0.95°C

Resistance is a property of materials that opposes the flow of electrical current. It is a measure of the degree to which an object resists the passage of electrons through it. Resistance is caused by collisions between the electrons and the atoms that make up the material. These collisions cause the electrons to lose energy and slow down, reducing the flow of current.

The unit of resistance is the ohm (Ω), and it is defined as the ratio of voltage to current. Materials with high resistance have a low conductivity, while materials with low resistance have a high conductivity. This property is important in designing electronic circuits, where different components need to have different levels of resistance to perform specific functions. Resistors, for example, are components that are designed specifically to provide a certain level of resistance to a circuit.

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At every location along the string, the amplitudes of two waves that interfere with one another are added. The two separate waves combine to form the final wave.

Two transverse waves are present in this instance, one traveling to the right and the other to the left. The waves will interact destructively when they meet since their motions are in opposition.

The resultant wave f(x) at any point x on the string may be calculated by summing the two amplitudes if we let f1(x) represent the amplitude of the wave going to the right and f2(x) represent the amplitude of the wave moving to the left:

f(x) = f1(x) + f2(x)

The amplitudes of the two waves will be equal in size and facing in opposite directions when they collide. As a result, the amplitude that results will be zero, and the string will then be at rest.

The resulting wave will alternate between constructive and destructive interference as the waves continue to travel past one another.

As a result, the string will develop a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The combined frequency and wavelength of the various waves as well as the rate of wave propagation along the string will determine the final wave's frequency and wavelength.

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(a) The flowing current is 1.08 A. (b) The EMF of the battery is 9.16 V.

It is given data that the resistance of the resistor (R) = 8.00 V and the voltage across the battery (V) = 9.00 V. The internal resistance of the battery (r) = 0.15 V

Formula used:

V = EMF - I * rV = IR

Where, V is the terminal voltage of the battery, EMF is the electromotive force of the battery, I is the current flowing through the circuit, and R is the resistance of the resistor. r is the internal resistance of the battery

(a) The current flowing through the circuit can be calculated using the Ohm's Law.

V = IR

I = V / R

I = 9 / (8 + 0.15)

I = 1.08 A

The current flowing through the circuit is 1.08 A.

(b) Find the emf of the battery:

We know that,

V = EMF - I * r

EMF = V + I * r

EMF = 9 + 1.08 * 0.15

EMF = 9.16 V

The emf of the battery is 9.16 V.

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Functions of phosphorus: Bone formation, ATP production, DNA and RNA synthesis, cell membrane structure.

Order of nondairy foods by calcium content: 1) 1 cup calcium-fortified orange juice, 2) 1 cup Total Raisin Bran cereal, 3) 3 oz salmon with bones.

Highest source of phosphorus: Salmon with bones.

Organs that participate in vitamin D synthesis: Skin (when exposed to sunlight), liver, and kidneys.

What is bone formation?

Bone formation is the process by which bones grow and develop, including the deposition of mineralized bone tissue by osteoblasts and the resorption of bone tissue by osteoclasts, resulting in changes to the shape and structure of bones.

What is RNA?

RNA (Ribonucleic acid) is a molecule that plays a vital role in various biological processes. It is a type of nucleic acid that is composed of a chain of nucleotides, which are the building blocks of the molecule.

RNA is similar to DNA (deoxyribonucleic acid) in terms of its structure, but it has some key differences. RNA is usually single-stranded, while DNA is double-stranded. RNA uses the sugar ribose, while DNA uses deoxyribose. RNA also contains the nitrogenous base uracil, while DNA contains thymine.

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Hooke's law: the slope of the curve would be the spring constant (C).

Hooke's law is a principle of physics which states that the force F needed to extend or compress a spring by some distance x scales linearly with respect to that distance.

F = kx

where k is the spring constant and x is the displacement of the spring.

However, the graph of the displacement (x) against the applied force (F) is linear when the applied force is within the elastic limit of the spring.

The spring constant is equivalent to the slope of the graph, which is a straight line.

Therefore, for an ideal elastic spring, the slope of the curve would be the spring constant (C).

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a) The distribution of X: X-N(129.77,2.26),

b) the proportion of her laps that are completed between 131.69 and 134.04 seconds 0.1670,

c) the fastest 4% of laps are under 126.1965 seconds,

d) the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

a. The distribution of X is the normal distribution with a mean of 129.77 seconds and a standard deviation of 2.26 seconds. Therefore, the distribution of X is X - N(129.77, 2.26).

b. The area between 131.69 and 134.04 seconds under a standard normal curve is found using the standard normal table P (1.05) = 0.8531P (1.71) = 0.9564

Therefore, the proportion of laps completed between 131.69 and 134.04 seconds is

P(131.69 ≤ X ≤ 134.04) = P[(131.69 - 129.77)/2.26 ≤ Z ≤ (134.04 - 129.77)/2.26]

= P(0.8496 ≤ Z ≤ 1.8814) = P(Z ≤ 1.8814) - P(Z ≤ 0.8496)

= 0.9693 - 0.8023

= 0.1670

Therefore, the proportion of laps that are completed between 131.69 and 134.04 seconds is 0.1670.

c. The value corresponding to the lowest 4% is found: P (z) = 0.04. The value of z corresponding to the lowest 4% is obtained as follows:

z = P−1(0.04) = -1.7507

So, the number of seconds that the fastest 4% of laps are under is:

x = μ + zσ = 129.77 - (1.7507)(2.26)

= 126.1965

Therefore, the fastest 4% of laps are under 126.1965 seconds.

d. We know that z corresponding to the lowest 15% is -1.036 and that z corresponding to the highest 15% is 1.036.

Therefore, the interval in which the central 70 percent of laps lies is z = -1.036, 1.036

z = P(X) - P(X) = P(z ≤ X) - P(z ≤ X) = P(z ≤ -1.036) - P(z ≤ 1.036)

= 0.1492 - 0.8513

= -0.7021

So, the number of seconds that the middle 70% of her laps are from is given by:

x = μ + zσ = 129.77 + (-0.7021)(2.26) = 127.5323 and

x = μ + zσ = 129.77 + (0.7021)(2.26) = 131.0277

Therefore, the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

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(a) Free-body diagram of block is as given below. (b) Acceleration of the block is 2.529 m/s². (c) Speed of the block when it reaches the bottom of the incline is 3.18 m/s.

Frictionless surface is an invented concept of surface that is based on imagination and creative ideas of scientists where assumed friction of surface is zero.

(a) Free-body diagram of block is:

            /|

           / |

          /  | m

         / θ |

        /    |

       /_____|

        f ||

          ||

          ||

          ||

          \/

where m is mass of the block, θ is angle of inclination, f is force of friction (which is zero in this case), and g is acceleration due to gravity acting vertically downwards.

(b) The force acting along incline is component of the weight of block parallel to the incline, given by mg sin θ, where m is the mass of the block and g is acceleration due to gravity. Since there is no friction, this force is equal to net force acting on block, which is ma, where a is acceleration of block along the incline. Therefore,

mg sin θ = ma

a = g sin θ

a = 9.81 m/s² * sin 15.00 = 2.529 m/s²

Therefore, the acceleration of the block is 2.529 m/s².

(c) v² = u² + 2as

where u is the initial velocity (which is zero), s is the displacement (which is 2.00 m along the incline), and a is the acceleration (2.529 m/s²). Solving for v, we get:

v = √(2as) = √(2 * 2.00 m * 2.529 m/s²) = 3.18 m/s

Hence, speed of block when it reaches bottom of incline is 3.18 m/s.

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