You find some limestone rock in southern Indiana and notice that it has fossil trilobites in it. Later you find the same fossil trilobites in a limestone in Colorado. From this you determine that the two rock types were deposited during the same time period using what concept or principle?

The equilibrant force is 45 N, acting in the direction opposite to the net force.

The equilibrant force is the force that is required to balance all other forces acting on an object in a specific situation. To find the equilibrant force for the given forces, you need to determine the net force acting on the object.

The net force can be found by adding the individual forces acting on the object:

Net force = 53 N + 28 N - 12 N - 24 N = 45 N

Equilibrant force = - 45 N = 45 N, acting in the opposite direction of the net force.

In this case, the equilibrant force is 45 N, acting in the direction opposite to the net force.

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Answer:

Speed of  cannonball just before it hits the ground is  90.77 m/s

Explanation:

Complete Question

A small cannon is placed on top of a fortification. the cannonball leaves the muzzle of the cannon with a speed of 85 m/s at an angle of 25°c above the horizontal. just before the cannonball hits the ground, the vertical component of velocity is 48 m/s downward. what is the speed of the cannonball just before it hits the ground? ignore air resistance.

Solution

Given  

Speed = 85 m/s

The angle = 25 degrees

When it will hit the ground, then vertical velocity = 48 m/s

However, in the projectile motion, the horizontal component will not change  

Vr = V cos (theta) = 85 * cos25

Speed of  cannonball just before it hits the ground is  

V’ = Sqrt (48^2 + (85 * cos 25)^2) = 90.77 m/s

Answer:

The address fulfills the requirement in Article II, Section 3, Clause 1 of the U.S. Constitution for the President to periodically "give to the Congress Information of the State of the Union, and recommend to their Consideration such measures as he shall judge necessary and expedient."

Explanation:

Answer:

I think it's A. Commander in Chief

Explanation:

Answer:

Explanation:

Field characteristics

The strength of the field at the Earth's surface ranges from less than 30 microteslas (0.3 gauss) in an area including most of South America and South Africa to over 60 microteslas (0.6 gauss) around the magnetic poles in northern Canada and south of Australia, and in part of Siberia.

The equivalent resistance between points A and B in the diagram is 22 Ω

We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:

1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃

1/Rₜ = 1/6 + 1/6 + 1/6

1/Rₜ = 3/6

1/Rₜ = 1/2

Rₜ = 2 Ω

Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:

R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁

R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

R = 22Ω

Thus, we can conclude that the equivalent resistance is 22 Ω

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Answer:

Population 1 indicates growth while Population 2 indicates a declining population

Explanation:

Here, using the given rate of change of the population, we want to determine which of the two is growing and which is declining

From the rate of change of both, we can determine this. Looking at the differential equation for the first one, we can see that it is of positive value. Looking at the differential equation for the second one. we can see it is of negative value

While a positive change rate indicates growth, a negative change rate will indicate otherwise

Hence, we can conclude that the one with a negative rate change will indicate a declining population

Answer:

the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

Explanation:

You can write the KVL equations:

Top left loop:

  I2(4) +(I2 +I3)(2) +I1(1) = 10

Bottom left loop:

  (I1-I2)(4) +(I1-I2-I3)(2) +I1(1) = 10

Right loop:

  (I2+I3)(2) +(I2+I3-I1)(2) = 5

In matrix form, the equations are ...

  \(\left[\begin{array}{ccc}1&6&2\\7&-6&-2\\-2&4&4\end{array}\right]\cdot\left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}10\\10\\5\end{array}\right]\)

These equations have the solution ...

  \(\left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}2.500\\0.625\\1.875\end{array}\right]\)

This means the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

_____

This can be worked almost in your head by using the superposition theorem. When the 5V source is shorted, the 10V source is supplying (I1) to a circuit that is the 4 Ω and 2 Ω resistors in parallel with their counterparts, and that 2+1 Ω combination in series with 1 Ω for a total of a 4Ω load on the 10 V source. That is, I1 due to the 10V source is 2.5 A, and it is nominally split in half through the upper and lower branches of the circuit. There is no current flowing through the (shorted) 5 V source branch.

When the 10V source is shorted, the 5V source is supplying a 4 +4 Ω branch in parallel with a 2 +2 Ω branch, a total load of 8/3 Ω. This makes the current from that source (I3) be 5/(8/3) = 15/8 = 1.875 A. There is zero current from this source through the 1 Ω resistor.

Nominally, the current from the 5V source splits 2/3 through the 2 Ω branch and 1/3 through the 4 Ω branch.

Using superposition, I2 = I1/2 -I3/3 = (2.5 A/2) -(1/3)(15/8 A) = 0.625 A. This is the same answer as above, without any matrix math.

  (I1, I2, I3) = (2.5 A, 0.625 A, 1.875 A)

__

It helps to be familiar with the formulas for resistors in series and parallel.

The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)

The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.

To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).

The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).

In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).

Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.

If co > co_critical, the system is considered overdamped (Option E).

If co = co_critical, the system is considered critically damped (Option D).

If co < co_critical, the system is considered underdamped (Option C).

Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.

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Therefore, the magnitude of the displacement vector is approximately 162.9 m. The magnitude of the displacement vector is approximately 162.9 m, and its direction is approximately 48.1 degrees with respect to the negative x-axis.

(a) Magnitude of the displacement vector:

The magnitude of the displacement vector can be found using the Pythagorean theorem:

|d| = √(dx²+ dy²)

Given the x-vector component magnitude is 107 m and the y-vector component magnitude is 125 m:

|d| = √((107 m)² + (125 m)²)

|d| = 162.9 m

Therefore, the magnitude of the displacement vector is approximately 162.9 m.

(b) Direction of the displacement vector:

The direction of the displacement vector can be found using trigonometric functions. We can use the arctan function to calculate the angle θ between the negative x-axis and the displacement vector:

θ = tan⁻¹(dy / dx)

Given the x-vector component points along the negative x-axis and the y-vector component points along the negative y-axis:

dx = -107 m

dy = -125 m

θ = tan⁻¹((-125 m) / (-107 m))

θ = tan⁻¹(1.1682)

θ = 48.1 degrees

The angle θ represents the positive angle with respect to the negative x-axis. Therefore, the direction of the displacement vector is approximately 48.1 degrees with respect to the negative x-axis.

Hence, the magnitude of the displacement vector is approximately 162.9 m, and its direction is approximately 48.1 degrees with respect to the negative x-axis.

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The mass of the boat is 8000 Kg.

It is given that,

Length of a boat = 4 m

Width of  a boat = 2 m

Height up to which water is displaced or its water line = 1 m

Volume of water displaced by the boat:-

Volume =  Length x Breadth x Height

V = 4 x 2 x 1 = 8 m³

Buoyant force is the upward force exerted on an object when it is immersed in a fluid fully or partly. It is also called Upthrust.

Buoyant force acting on the boat:-

Fb = ρ g V

m g = ρ g V

m = ρ V

ρ is the density of water which is equal to 1000 Kg/m³

mass = ρ V

mass =1000 x 8

mass = 8000 Kg

Hence, mass of the boat is equal to 8000 Kg

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The units of the derived quantities are matched as;

Derived units are units of measurement derived from the seven base units specified by the International System of Units (SI).

The following are some derived quantities and their corresponding derived units.

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Answer:

Explanation:

magnetic field B = (3 i + 8 x 2 j )x 10⁻³ T

= (3 i + 16 j )x 10⁻³ T

L = - i ( unit length of conductor )

Force F = I ( L x B ) , I is current

= 5 [ - i x ( 3i + 16 j ) 10⁻³]

= 5 ( - 16 k ) x 10⁻³

F = - 80 x 10⁻³ k

Answer:

Explanation:

His displacement is 0 because he ended up exactly where he started.

Answer: The change in momentum is +20 kg.m/s

Explanation:

To calculate the final velocity of object, we use the first equation of motion:

\(v=u+at\)

where,

v = final velocity

u = initial velocity = 0 m/s

a = acceleration = \(10m/s^2\)

t = time = 0.5 s

Putting values in above equation, we get:

\(v=0+(10\times 0.5)\\\\v=5m/s\)

Momentum is defined as the product of the mass and velocity of an object. It is given by the equation:

\(p=mv\)

where,

p = momentum

m = mass of object = 2 kg

Let the upward velocity be positive and the downward velocity be negative

When the object is dropped, the velocity is downward

v = -5m/s

Initial momentum = \(2kg\times (-5m/s)=-10kg.m/s\)

When the object is bounced back, the velocity is upward

v = +5m/s

Final momentum = \(2kg\times (+5m/s)=10kg.m/s\)

Change in momentum = Final - Inital

Change in momentum = [10 - (-10)] = +20 kg.m/s

Hence, the change in momentum is +20 kg.m/s

The most amount of work is done in  Slowing down from 200 km/hr to 180 km/hr.

A force must be applied in order for work to be completed, and there must also be motion or displacement in the force's direction. The amount of force multiplied by the distance moved in the force's direction is known as the work done by a force acting on an item. Work has no direction and only magnitude. Work is a scalar quantity as a result.

Let the mass of the car be m.

Then work done in slowing down from 70 km/hr to rest = 1/2×m×70² = 4900m/2.

work done in slowing down from 100 km/hr to 70 km/hr =  1/2×m×(100² - 70²) = 5100 m/2.

work done in slowing down  from 200 km/hr to 180 km/hr = 1/2×m×(180² - 100²) = 22400m/2.

Hence, the most amount of work is done in  Slowing down from 200 km/hr to 180 km/hr.

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Answer:

b: density decreases

e: volume increases

Explanation:

When the water changes to ice, there won't be a loss of water, so the mass will be the same. However the ice will occupy more space, so the volume will increase. Then, since density is the mass divided by the volume, if the volume increase and the mass stays the same, the density decreases.

So, the answers are:

b: density decreases

e: volume increases

The language of the given pushdown automaton (PDA) can be described as follows:

The PDA has a stack alphabet consisting of symbols 'a', 'b', 'z', '6', '1', '۸', '2', '9', '0', 'x', 'y'. 'z' represents the stack end symbol.

The transitions of the pushdown automaton (PDA) are as follows:

Thus, the language accepted by this PDA is characterized by a sequence of 'a's followed by a sequence of 'b's, where the number of 'b's is three times the number of 'a's, and each 'b' is followed by a corresponding sequence of '90', '91', '92', 'a', 'b', 'b', 'b', '1', 'b', 'b', '1', and ending with '1'.

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Answer:

The expansion and contraction of materials can also cause problems. For example, bridges expand in the summer heat and need special joints to stop them bending out of shape.A bimetallic strip has two metal strips glued together. One of these metals expands more for each degree temperature rise than that other.

(a) The emf induced in the wire is 0.112 V.

(b) The direction of the current will into the page.

(c) The polarity of A will be positive and L will be negative.

(d)  The current flowing through the wire is 0.224 A.

The emf induced in the wire is calculated as follows;

EMF = BLv

EMF = (8 x 10⁻²) x 0.2 x 7

EMF = 0.112 V

Since, the magnetic field is out of the page, the current will follow counter clockwise and will point into the page.

The current is flowing counter currently, hence the polarity of A will be positive and L will be negative.

V = IR

I = V/R

I = (0.112)/0.5

I = 0.224 A

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Fission reactors are an important energy source, but environmental costs and issues are associated with their production. The most significant issue is the production of nuclear waste, which poses a serious threat to the environment and public health.

Nuclear waste is radioactive and can remain hazardous for thousands of years, making it difficult to safely dispose of. Moreover, it can contaminate water, soil, and air if disposed of improperly. Another issue is the high consumption of water required to cool the reactor, which can have a negative impact on aquatic life in rivers and lakes. Furthermore, the production and mining of uranium, which is the fuel for fission reactors, can lead to soil erosion and contamination. Additionally, uranium mining requires large amounts of energy, contributing to greenhouse gas emissions and other forms of pollution. In conclusion, producing energy through fission reactors results in several environmental costs and issues. While nuclear power is a clean source of energy compared to fossil fuels, its production and waste disposal methods pose serious environmental risks.

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The optimum condenser aperture setting for most specimens is a condenser aperture that fills the objective aperture.

This allows for maximum resolution and contrast when viewing specimens. It is important to note that some specimens may require a slightly different setting, but filling the objective aperture is a good starting point. Keeping the condenser aperture fully closed or 70% open can result in decreased resolution and contrast, while filling 70% of the objective or having it 70% closed may not provide enough light for the specimen to be seen clearly. Overall, it is best to adjust the condenser aperture to match the objective aperture for the most optimal results. This setting ensures that the maximum amount of light is utilized, providing sufficient contrast and resolution for the specimen being observed. When the condenser aperture is properly adjusted, it will enhance the overall image quality and allow for a better examination of the specimen.

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The maximum height of the ball is approximately 6.096 m and the work done by gravity is -4.95 J.

Given information,

m = 0.071 kg

V₀ = 11 m/s

(a) Finding the maximum height:

The initial kinetic energy of the ball is converted into potential energy at its maximum height.

Initial kinetic energy = Potential energy at maximum height

(1/2)mv₀² = mgh

(1/2)(0.071 kg)(11 m/s)² = (0.071 kg)(9.8 m/s)h

h = (0.5)(11²)/(9.8) ≈ 6.096 m

Part (b) Calculating the work done by gravity:

The work done by gravity during the ball's flight to its maximum height is equal to the change in potential energy. Since the gravitational potential energy is defined as zero at the initial height, the work done by gravity is equal to the negative of the potential energy at the maximum height.

Wg = -mgh

Wg = -0.071 × 9.8 × 6.096

Wg ≈ -4.95 J

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Electromagnetic waves give off energy. The electromagnetic spectrum shows us that the shorter the wavelength, the higher the frequency, and the greater the energy the wave carries.

Electromagnetic waves are an energized form of oscillating electric on magnetic fields travelling in a cosmic distance. Across the electromagnetic spectrum is an extensive range of frequencies that encompass the entirety of electromagnetic radiation, including lower frequency radios waves to elevated frequency gamma rays.

The wavelength of an electromagnetic wave is the consecution of two successive crests or troughs in the wave's measurement, while its frequency is counted by the total amount of oscillations passing through a mark per second, determined via Hertz (Hz).

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Answer:

ididate is a good one and

Answer:

#6 is 14 miles in 7 mins

Explanation:

you need to get the unit rate (how many miles per min) then multiply from there so you take 10/5 (because there 5 mins) and get 2 miles per min, then you take 2 an multiply it by 7 (because you want to know how far she went in 7 min) and you get 14

Answer:: 14miles in 7 mins

Answer:

Similitudes y diferencias entre los músculos de los peces y los de los animales terrestres.

Explicación:

Los músculos de los peces se diferencian del músculo de los animales terrestres porque los peces tienen músculos rojos, rosados y blancos. También tienen tejido muscular de pescado que se compone de músculo estriado al igual que el músculo de los animales terrestres. La mayor parte del tejido muscular de los peces es de color blanco, pero muchos peces también tienen una cierta cantidad de tejido oscuro de color marrón o rojizo. El músculo oscuro se encuentra justo debajo de la piel a lo largo del costado del cuerpo.

Answer:

horse rider

Explanation:

it will help in the future  and its fun