Which best describes cost-effectiveness

The final speed of a baseball thrown at 48 m/s with a mass of 0.16 kg after being hit by a bat with an average force of 8300 N for 2.6 ms is 58.58 m/s.

The initial velocity of the baseball is given as 48 m/s. We have to find the final velocity of the baseball after it is hit by a bat. The mass of the baseball is given as 0.16 kg, and the force exerted by the bat is given as 8300 N for 2.6 ms. The formula for calculating the final velocity of an object is as follows:

v = u + (Ft/m)

Here, v is the final velocity of the baseball, u is the initial velocity of the baseball, F is the force exerted on the baseball, t is the time for which the force is exerted, and m is the mass of the baseball.

Now, let us substitute the given values in the above formula to find the final velocity of the baseball:

v = 48 + (8300 × 2.6 × 10^-3 / 0.16) = 58.58 m/s

Therefore, the final velocity of the baseball is 58.58 m/s.

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The velocity of the child is 3.36 m/s. Then, the distance it covered is 14 meters. The radius from the centre is then, 2.24 m.

Centripetal acceleration is the acceleration of a body moving through a circular paths. It is the rate of change of its angular velocity.

The acceleration of the child = 0.80 ms/²

time  = 4.2 s

velocity = time interval × acceleration

             = 4.2 s ×  0.80 ms/²= 3.36 m/s.

Then the distance covered  = velocity × time

= 3.36 m/s × 4.2 = 14.22 m.

This is the circumference of the circular path which is equal to 2πR.

The distance from the centre = radius of the path.

2πR = 14.22 m

R = 2.24 m

Therefore, the child will be 2.24 m far from the center of the ride.

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The term that describes weathering breaks down the rock. Weathering is the breakdown of rocks, soil, and other geological material under the influence of physical, chemical, or biological agents.

The term weathering refers to a variety of processes that wear away or weaken rocks over time. Weathering is classified into two categories: chemical and physical. Chemical weathering occurs when rock is chemically broken down by reactions with acid rain or other chemicals.

Physical weathering, on the other hand, occurs when rock is broken down into smaller pieces by water, wind, ice, or other forces that do not change the chemical composition of the rock. In conclusion, the term that describes weathering is breaking down the rock.

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a) Answer: On the equator, the Circle of Illumination divides the earth into two equal parts, with each part receiving 12 hours of daylight and 12 hours of darkness.

The equator receives an equal day and night (12 hours each) regardless of the day of the year due to the Circle of Illumination, which is a line that separates the day side of the earth from the night side of the earth. The Circle of Illumination separates the sunlit and dark sides of the earth. The earth's axis is at a 23.5-degree angle to the plane of its orbit around the sun, causing different latitudes to receive different amounts of sunlight throughout the year. On the equator, the Circle of Illumination divides the earth into two equal parts, with each part receiving 12 hours of daylight and 12 hours of darkness.

b)  Answer: The earth's axis is tilted at 23.5°, and during the December solstice, the North Pole is tilted away from the sun, causing the Arctic Circle and areas beyond it to experience a full day of daylight because the sun is above the horizon for 24 hours.

On December 22nd, between the latitudes of the Tropic of Cancer (23.5°N) and the Arctic Circle (66.5°N), 24 hours of daylight is experienced. This occurs because the earth's axis is tilted at 23.5°, and during the December solstice, the North Pole is tilted away from the sun, causing the Arctic Circle and areas beyond it to experience a full day of daylight because the sun is above the horizon for 24 hours.

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To express the tension T in the cable as a vector using the unit vectors i and j, we can break down the tension into its components in the x-direction and y-direction. T as a vector is T = T_x * i + T_y * j

Given:
a = 10.4 m (distance from point C)
b = 4 m
c = 7.7 m
T = 8.1 kN (magnitude of tension)

To find the x-component of T, we can use the cosine rule:
T_x = T * cosθ

Using the triangle formed by the load, point C, and the vertical line from point C, we can calculate the angle θ:
cosθ = b / c
θ = cos⁻¹(b / c)

Substituting the given values:
θ = cos⁻¹(4 / 7.7)

Next, we can calculate the y-component of T using the sine rule:
T_y = T * sinθ

Substituting the given values:
T_y = 8.1 kN * sin(θ)

Finally, we can express T as a vector using the unit vectors i and j:
T = T_x * i + T_y * j

To summarize:
1. Calculate θ using the cosine rule:

θ = cos⁻¹(b / c)
2. Calculate the x-component of T:

T_x = T * cosθ
3. Calculate the y-component of T:

T_y = T * sinθ
4. Express T as a vector:

T = T_x * i + T_y * j

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Answer:

The correct option is;

πR³(2/3 + (1/3)cos³θ - cosθ)

Explanation:

The volume of a segment of a sphere is given by the relation;

\(V = \pi \cdot h^2 \cdot \left (R - \dfrac{h}{3} \right)\)

We note that h = R - R·cos(θ)

Therefore by substituting the value of h in the equation of a segment of a sphere, we have;

\(V = \pi \cdot \left (R - R\cdot cos(\theta) \right ) ^2 \cdot \left (R - \dfrac{\left (R - R\cdot cos(\theta) \right )}{3} \right)\)

Which gives;

\(\dfrac{R^3\cdot \pi \cdot cos^3 (\theta) -3 \cdot R^3 \cdot\pi \cdot cos (\theta) + 2 \cdot R^3 \cdot \pi}{3}\)

\(R^3\cdot \pi \cdot \left (\dfrac{cos^3 (\theta) -3 \cdot cos (\theta) + 2 }{3} \right )\)

\(R^3\cdot \pi \cdot \left (\dfrac{cos^3 (\theta) + 2 }{3} - cos (\theta) \right )\)

\(R^3\cdot \pi \cdot \left (\dfrac{cos^3 (\theta) }{3} + \dfrac{2}{3} - cos (\theta) \right )\)

Therefore, the correct option is πR³(2/3 + (1/3)cos³θ - cosθ).

Answer:

1.) D

2.) E

3.) A

4.) B

5.)C

Explanation:

Answer:

B) A body at rest will stay at rest

Explanation:

A body in motion will stay in motion unless acted on by another force.

The mass of the car that was at rest is 4800kg.

What is mass?

Measurement of inertia, a fundamental characteristic of all matter. The resistance a body of matter offers to a change in its speed or location as a result of the application of a force is what it is in essence.

What is momentum?

As a measure of an object's kinetic energy, momentum is easily defined. Simply put, momentum is the result of mass times velocity. full response Simply said, momentum is concerned with the quantity of motion. The conserved quantity is another definition for it.

m= 3600kg

Vi= 21.0m/s

Vf = 9.0m/s

conservation of momentum

mVi= (m+M) Vf

mass of rest car M = (Vi-Vf )m/Vf

M = (21.0 m/s - 9.0m/s)* 3600 kg/ 9.0m/s

M= 4800kg

Therefore, the mass of the car that was at rest is 4800kg.

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Answer:

Rocket 2 has highest acceleration.

Explanation:

Net force,

F = mass (m) × acceleration (a)

We have,

m₁ = 4.25 kg and F = 120 N

\(a_1=\dfrac{F_1}{m_1}\\\\a_1=\dfrac{120}{4.25}\\\\a_1=28.23\ m/s^2\)

m₂ = 3.25 kg, F₂ = 120 N

\(a_2=\dfrac{F_2}{m_2}\\\\a_2=\dfrac{120}{3.25}\\\\a_2=36.92\ m/s^2\)

m₃ = 5.5 kg, F₃ = 120 N

\(a_3=\dfrac{F_3}{m_3}\\\\a_3=\dfrac{120}{5.5}\\\\a_3=21.81\ m/s^2\)

m₄ = 4.5 kg, F₄ = 120 N

\(a_4=\dfrac{F_4}{m_4}\\\\a_4=\dfrac{120}{4.5}\\\\a_4=26.66\ m/s^2\)

Hence, it can be seen that the highest acceleration is of rocket 2.

Answer:

2. Ahead of the package

Explanation:

The plane is going straight without stopping while the package is going straight down.

This indicates that about \(3.13 x 10^{10}\) electrons have been extracted from the glass rod.

(a) Electrons have been removed from the glass rod. This is because when the rod is rubbed, electrons are transferred from the glass to the material it is rubbed against. Since electrons are negatively charged, the glass rod becomes positively charged as a result of losing electrons.

(b) The number of electrons removed can be calculated using the formula Q = ne, where Q is the charge on the rod, n is the number of electrons transferred, and e is the charge of an electron. Therefore, we can rearrange the formula to find n = Q/e. Plugging in the values for Q \((+5.0 nC)\) and e \((-1.6 x 10^-19 C)\), we get:

\(n = (+5.0 x 10^-{9 C}) / (-1.6 x 10^{-19 C}) ≈ -3.13 x 10^{10\) electrons

This means that approximately \(3.13 x 10^{10}\) electrons have been removed from the glass rod.

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Answer: No

Explanation:

Whenever light travelling on a straight line encounters obstruction, it diffracts and scatter.

Scattering of light occurs when light passes through a rough path or a diffused surface.

But in case of spectral diffusion, which is the fluctuation in spectroscopy as a result of time dependent frequency shifts.

Spectral diffusion occurs in particular molecules initiated by excessive excitation energy.

Fluctuation in frequency does not mean diffraction of light or particles

Therefore, spectral diffusion does not cause light to scatter.

Answer:

shorter,higher

Explanation:

The angle of the prism (A°) if the minimum angle of deviation of a prism (δmin or δm) of refractive index (n = 1. 4) equals its refracting angle (r = A/2) is (3A - 2 × δm) / 1.4.

To find the angle of the prism (A°) given the minimum angle of deviation (δmin) and the refractive index (n), we can use the formula for the minimum angle of deviation:

δmin = A + r - (A - r) × n

Given that δmin = δm and r = A/2, we can substitute these values into the formula:

δm = A + A/2 - (A - A/2) × n

Next, simplify the equation:

δm = A + A/2 - A/2 × n

Multiply A/2 by n:

δm = A + A/2 - A × n/2

Combine like terms:

δm = 2A/2 + A/2 - A × n/2

δm = (2A + A - A × n)/2

Now, multiply both sides of the equation by 2:

2 × δm = 2A + A - A × n

Simplify further:

2 × δm = 3A - A × n

Now, isolate A on one side of the equation by moving the other terms to the other side:

2 × δm - 3A = -A × n

Divide both sides of the equation by -n:

(2 × δm - 3A) / -n = A

Finally, multiply both sides of the equation by -1 to get the positive value of A:

A = (-1) × (2 × δm - 3A) / n

Simplifying the expression:

A = (3A - 2 × δm) / n

Now, we can substitute the given values of n = 1.4 and δm to find A:

A = (3A - 2 × δm) / 1.4

This equation can be solved to find the value of A. However, it is a nonlinear equation and solving it algebraically might be challenging. You can use numerical methods or a solver to find the approximate value of A.

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By substituting the appropriate value for δmin, we can determine the angle of the prism (A°).

A = arcsin(1.4 * sin(δmin)).

To find the angle of the prism (A°) when the minimum angle of deviation (δmin) is equal to half the refracting angle (r = A/2), we can use Snell's law and the relationship between the angle of incidence (i), angle of refraction (r), and refractive index (n).

According to Snell's law, n = sin(i) / sin(r), where n is the refractive index.

Given that δmin = r, we can rewrite the equation as n = sin(i) / sin(δmin).

Since the minimum angle of deviation occurs when the angle of incidence and angle of refraction are equal, we have sin(i) = sin(δmin).

Substituting this into the previous equation, we get n = sin(δmin) / sin(δmin).

Simplifying, we find n = 1.

Since n = 1.4, we can conclude that sin(δmin) = 1.4.

To find the angle of the prism (A°), we can use the relationship sin(A) = n * sin(δmin).

Substituting the given values, we have sin(A) = 1.4 * sin(δmin).

Taking the inverse sine of both sides, we find A = arcsin(1.4 * sin(δmin)).

By substituting the appropriate value for δmin, we can determine the angle of the prism (A°). Therefore, you can use numerical methods or a solver to find the appropriate value of A.

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The equivalent dose, considering that ^99mTc emits gamma rays, is 0.10 rem. The equivalent dose is a measure of the biological effect of radiation on human tissue.

It takes into account not only the absorbed dose but also the quality factor (QF) of the radiation. The QF represents the relative biological effectiveness of different types of radiation. For gamma rays, the QF is 1, indicating that they have a similar biological effect as the reference radiation (X-rays or gamma rays). In this case, we are given that the absorbed dose is 0.10 rad. To obtain the equivalent dose, we simply multiply the absorbed dose by the quality factor:

Equivalent dose = Absorbed dose × Quality factor

Since the QF for gamma rays is 1, the calculation simplifies to:

Equivalent dose = 0.10 rad × 1 = 0.10 rem

Therefore, the equivalent dose, considering the emission of gamma rays by ^99mTc, is 0.10 rem.

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The brightness of a bulb does not change noticeably when longer copper wires are used to connect it to the battery because the resistance of the copper wires is relatively small compared to the resistance of the bulb.

According to Ohm's law, the current flowing through a conductor is proportional to the voltage applied across it and inversely proportional to its resistance.

Since the resistance of the copper wires is relatively small compared to the resistance of the bulb, most of the voltage provided by the battery is dropped across the bulb, causing it to light up with nearly the same brightness regardless of the length of the copper wires used.

The electric field in the connecting wires is not zero and the EMF (electromotive force) of the battery is also not affected by the length of the connecting wires. However, if the wires were very thin and long, they could have a significant resistance, which would cause a voltage drop across them, leading to a decrease in the voltage applied to the bulb and a reduction in its brightness.

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Answer:

C

Explanation:

Alpha decay

Potential energy is the energy an object possesses due to its position or state.

It can be thought of as stored energy that can be released or converted into other forms of energy, such as kinetic energy (energy of motion).

For example, a book sitting on a shelf has potential energy because it has the potential to fall and convert that potential energy into kinetic energy (motion). Similarly, a charged battery has potential energy because it has the potential to release electricity.

Another example of potential energy is a charged battery. A charged battery has the potential to release electricity, which is a form of energy. The more charge a battery has, the more potential energy it holds. When the battery is used to power a device, the potential energy is converted into electrical energy.

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Seasons are caused by the tilt of the Earth's axis. Winter and summer are determined by the tilt of the earth towards or away from the sun. The Earth's axial tilt changes every 41,000 years.

Earth's axial tilt is the angle between the Earth's rotational axis and the plane of its orbit around the sun. The current tilt of the Earth's axis is about 23.5 degrees relative to the plane of its orbit. This tilt is responsible for the changing seasons as the Earth orbits the sun.

The axial tilt of the Earth is not constant but changes over a cycle of about 41,000 years. This cycle is known as the obliquity cycle and is caused by gravitational interactions between the Earth and other celestial bodies such as the Moon and Jupiter.

During this cycle, the tilt of the Earth's axis varies between 22.1 and 24.5 degrees, which results in a change in the amount of solar radiation received at different latitudes. This, in turn, affects the distribution of heat on the Earth's surface and influences the climate.

The effect of this cycle on the climate is relatively small compared to other factors such as greenhouse gases and ocean currents. However, it is believed to have played a role in past climate changes, including the ice ages.

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Using the equation, B = (μoIN/2πr)

The inner radius is r = 16.2 cm,

so the field there is

B = (4π 10-7).(0.813).(535)/2π(0.162)

= 5.37 × 10-4 T

The outer radius is r = 16.2 + 5.2 = 21.4 cm.

The field there is B = (4π 10-7).(0.813).(535)/2π(0.214)

= 4.06 × 10-4 T.

A toroid having a square cross-section, 5.20cm on edge and an inner radius of 16.2cm has 535 turns and carries a current of 813mA to calculate the magnetic.

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Answer:

10N

Explanation:

ΣF = ma

ΣF = (2kg)(5m/s^2)

ΣF = 10N

Proportional scale or Proportion wheel are terms used to describe the process of preparing illustrations for expansion or reduction.

What is the proportional principle?

The relationship between two or more elements in a design and how they stack up against one another is known as proportion. When there is a proper size or quantity relationship between the elements, proportion is said to be harmonic.

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If the net torque on a rigid object whose center of mass is at rest is zero, the object could be at rest or could rotate with a constant angular velocity.
For the second question, the statement is false because the rotational kinetic energy of the entire object is not equivalent to the sum of the translational kinetic energy of each small piece of the object.

The rotational kinetic energy of a rigid body that rotates about a fixed axis is given by:

\(K_{rot} = (1/2) \times I \times \omega^2\),

where I is the moment of inertia of the body about the axis of rotation, and ω is the angular velocity of the body.

The translational kinetic energy of a small piece of the object is given by:

\(K_{trans} = (1/2) \times m \times v^2\),

where m is the mass of the small piece and v is its velocity.

While it is true that the total kinetic energy of the rigid body is the sum of the rotational and translational kinetic energies of all its small pieces, the rotational kinetic energy of the entire object is not equivalent to the sum of the translational kinetic energies of each small piece. These two types of kinetic energies are related, but not interchangeable.

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1. The probability that the gene would appear in a gamete = 7 and there are 100 people in a population with genotype tt.

Thus, all of the 100 people will contribute a talleles to the gene pool. So, the total number of alleles in the gene pool will be 200.2. The percentage of the population that is more resistant to malaria because they are heterozygous (AS) for the sickle cell gene = 49%.

This is because the frequency of the sickle cell trait in the population = 41%. Thus, the frequency of the normal (AA) genotype = (1-0.41) = 0.59.Using the Hardy-Weinberg equation: p² + 2pq + q² = 1

Where p = frequency of A allele, and q = frequency of S allelep² = frequency of AA genotype, 2pq = frequency of AS genotype, q² = frequency of SS genotype

Frequency of AS genotype = 2pq = 2 × 0.41 × 0.59 = 0.4849 or 48.49%3a. The type of genetic drift that would best describe this scenario is "bottleneck effect."

b. Assuming the frequency of the Huntington allele does not change as the population grows to 100,000, the number of individuals likely to have Huntington's disease on the island would be:

q = frequency of the Huntington allele = 0.1p = frequency of the normal allele = 0.9

Number of heterozygous individuals (2pq) = 2 × 0.1 × 0.9 × 100,000 = 18,000

Number of individuals with Huntington's disease (q²) = 0.1² × 100,000 = 1,0004a. The allele frequencies for T = 0.6628, and for t = 0.3372.

b. Observed genotype frequencies:TT = 215/391 = 0.5501Tt = 99/391 = 0.2532tt = 77/391 = 0.1967

c. The expected genotype frequencies based on Hardy-Weinberg equilibrium can be calculated using the following equations:p² + 2pq + q² = 1p + q = 1

where p is the frequency of T allele and q is the frequency of t allele.

The frequency of the T allele = (2 × 215 + 99) / (2 × 391) = 0.6766

The frequency of the t allele = 1 - 0.6766 = 0.3234

The expected genotype frequencies are:TT = p² = 0.6766² = 0.4581Tt = 2pq = 2 × 0.6766 × 0.3234 = 0.4388tt = q² = 0.3234² = 0.1031d. To determine if the observed values are significantly different from the expected values, we can use chi-square analysis.

Calculated chi-square value = Σ ((Observed - Expected)² / Expected)= (213 - 174.23)² / 174.23 + (99 - 120.56)² / 120.56 + (77 - 46.21)² / 46.21= 13.32

The degrees of freedom are (n-1) = 3-1 = 2

From chi-square distribution table, with 2 degrees of freedom at 0.05 level of significance, the critical value is 5.99Since 13.32 > 5.99, the observed values are significantly different from the expected values. Therefore, we reject the null hypothesis.

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Answer:

Explanation:

In this problem we are required to find the potential energy possessed by the television

Given data

mass of television m = 15 kg

height  added above the ground, h= 1-0.3 = 0.7 m

acceleration due to gravity g = 9.81 m/s^2

apply the formula for potential energy we have

P.E= m*g*h

P.E = 15*9.81*0.7 = 103 Joules

Answer:

neutrons

Explanation:

Neutrons are usually released when fission takes place. Fission of a nucleus may be spontaneous, that is, it may happen at random due to internal processes within the nucleus. Fission can also be induced by bombarding a nucleus with a neutron.

Answer:

Loudness of sound is determined by its amplitude.

Loudness of sound is determined by its amplitude.The intensity or loudness of a sound depends upon the extent to which the sounding body vibrates, i.e., the amplitude of vibration. A sound is louder as the amplitude of vibration is greater, and the intensity decreases as the distance from the source increases.

Answer:

The change in the object's velocity is 6.25 m/s

Explanation:

Force

According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:

F = ma      [1]

Where a is the acceleration of the object.

On the other hand, the equations of the Kinematics describe the motion of the object by the equation:

\(v_f=v_o+at\qquad\qquad[2]\)

Where:

vf is the final speed

vo is the initial speed

a is the acceleration

t is the time

It's given a constant force of F=4.5 N acts on an object of mass m=7.2 kg. The object has an acceleration we can calculate solving [1] for a:

\(a=\frac{F}{m}\)

\(a=\frac{4.5}{7.2}=0.625\)

\(a=0.625\ m/s^2\)

It's required con compute the change of velocity (or its magnitude, the speed). From [2]:

\(v_f-v_o=at\)

The expression at the left side is the change of speed Δv:

\(\Delta v=at\)

Knowing the time is t=10 s:

\(\Delta v=0.625*10\)

\(\Delta v=6.25\ m/s\)

The change in the object's velocity is 6.25 m/s