the maximum clock frequency, given a critical path of 10 ns, is f = _____ mhz ?

Answer:

105,000km or about 65,244mi

Explanation:

If the space shuttle orbits around it 1.4 times every hour then the speed of the space shuttle in km/hour would be 595330.8 Km/hour, and its speed in meters would be 165369.67 m/s.

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object.

Average speed = total distance /Total time

As given in the problem If the circumference of a space shuttle's orbit around Earth is 42,522 km and the space shuttle orbits around it 1.4 times every hour, then we have to find the speed of the space shuttle in km/hour

The total distance covered by the space shuttle in an hour = 42,522×1.4

                                                                                                 = 595330.8 Km

The speed of the space shuttle in meters/second = 595330.8 × 1000/3600

                                                                                   = 165369.67 m/s

Thus, the speed of the space shuttle would be 595330.8 Km/hour, and its speed in meters would be 165369.67 m/s.

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Answer:

We can use Coulomb's law to solve this problem:

F = k * q1 * q2 / r^2

where F is the force between the two charges, k is Coulomb's constant (k = 9 x 10^9 N m^2 / C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.

We know the force F, the distance r, and the magnitude of one of the charges q1. We can rearrange the equation to solve for the magnitude of the other charge q2:

q2 = F * r^2 / (k * q1)

Substituting the values we have:

q2 = (250 N) * (0.15 m)^2 / (9 x 10^9 N m^2 / C^2 * 6.5 x 10^-5 C)

Simplifying:

q2 = 8.65 x 10^5 C

Therefore, the magnitude of the other charge is 8.65 x 10^5 C.

Answer:-50 J

Explanation:

Answer: -50 N

Explanation:

Answer:What they did not count on is the immense distance to the stars, which made the shift so small it was not able to be detected until the 1830s. The first scientist to do so was Friedrich Bessel in 1838. The method that is used to measure distances to nearby stars is called trigonometric parallax, or sometimes, triangulation.

Explanation:

(a) The  work done by Emily in dragging the box is 1,332 J.

(b) In the absence of friction, the change in kinetic energy is 1,322 J.

(c) The work done by frictional force is 600 J.

(d) In the presence of frictional force, the change in kinetic energy is 732 J.

The work done by Emily in dragging the box is the product of the applied force in horizontal direction and the displacement of the box.

W = fd cosθ

W = 222 x 12 x cos(60)

W = 1,332 J

In the absence of friction, energy will be conserved.

change in kinetic energy = work done on the box

ΔK.E = 1,332 J

W = fd

W = 50 x 12

W = 600 J

ΔK.E = 1,332 J - 600 J

ΔK.E = 732 J

Thus, the  work done by Emily in dragging the box is 1,332 J.

In the absence of friction, the change in kinetic energy is 1,322 J.

The work done by frictional force is 600 J.

In the presence of frictional force, the change in kinetic energy is 732 J.

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Answer:

E_loss  = 690000 [J]

Explanation:

The principle of conservation of Energy tells us that energy is converted from Kinetic to mechanical when the body moves from the highest point to the point where the velocity is maximum. That is, all potential energy is transformed into kinetic energy.

\(E_{pot}=E_{kin}\)

Now we must determine the kinetic energy at the end, when the roller coaster is at the point where the reference point of power energy is zero.

\(E_{kin}=\frac{1}{2} *m*v^{2}\)

where:

m = mass = 800 [kg]

v = 45 [m/s]

Now replacing:

\(E_{kin}=0.5*800*(45)^{2}\\E_{kin}=810000[J]\)

Now by means of the difference of the energy at the beginning minus the final energy, it determines the amount of energy that is lost by the effects of friction and heat.

\(E_{loss}=1500000-810000\\E_{loss}=690000[J]\)

Gravitational force between two masses m, and m, is represented as F = Gm₂ m₂ / r^2 where r = xi+yj + zkG, m, m₂ are nonzero constants and let's assume that I = 0

a) Calculation:For F = Gm₂ m₂ / r^2.

Using r = xi+yj + zk and let r^2 = x^2 + y^2 + z^2∴ F = Gm₂ m₂ / (x^2 + y^2 + z^2), Where G, m, m₂ are nonzero constants. Divergence of F = ∇ · F= 1/r^2(d/dx(r^2Fx) + d/dy(r^2Fy) + d/dz(r^2Fz))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)^(3/2)) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)^(3/2)) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)^(3/2)))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2))= 1/r^2(Gm₂ m₂ [2x(x^2+y^2+z^2)-3x^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2y(x^2+y^2+z^2)-3y^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2z(x^2+y^2+z^2)-3z^2]/(x^2+y^2+z^2)^(5/2))= 1/r^2(Gm₂ m₂ [(2x^2+2y^2+2z^2-3x^2)/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3y^2]/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3z^2]/(x^2+y^2+z^2)^(3/2)])= 1/r^2(Gm₂ m₂ [x^2+y^2+z^2]/(x^2+y^2+z^2)^(3/2))= 0.

Curl of F = ∇ × F= i(d/dy(Fz) - d/dz(Fy)) - j(d/dx(Fz) - d/dz(Fx)) + k(d/dx(Fy) - d/dy(Fx))= i(d/dy(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ y/(x^2+y^2+z^2))) - j(d/dx(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ x/(x^2+y^2+z^2))) + k(d/dx(Gm₂ m₂ y/(x^2+y^2+z^2)) - d/dy(Gm₂ m₂ x/(x^2+y^2+z^2)))= i(Gm₂ m₂ [-2xz]/(x^2+y^2+z^2)^(5/2)) - j(Gm₂ m₂ [-2yz]/(x^2+y^2+z^2)^(5/2)) + k(Gm₂ m₂ [(x^2+y^2-2z^2)]/(x^2+y^2+z^2)^(5/2))

b) Calculation:The line integral of F along a curve C can be evaluated by the following formula∫C F.dr = ∫∫ ( ∇ x F) ds, Where r is the position vector of the curve, s is the scalar parameter representing the curve, and the integral is evaluated from the initial point to the final point.

Using the curl of F obtained in part a) and for the surface with ∂S as C∫C F.dr = ∫∫ ( ∇ x F) ds= ∫∫ curl(F) ds= ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds...[1]

Let's consider the surface S as a plane perpendicular to the z-axis of the form ax+by+c=0 and the curve C as the intersection of the plane and the cylinder x^2 + y^2 = a^2.

Let's choose the unit normal to the surface S as k (along the z-axis).

The curl of F is a vector field perpendicular to the plane and along the direction of k.

Thus the integral can be written as∫C F.dr = ∫∫ ( ∇ x F) . k ds= ∫∫ (x^2+y^2-2z^2) ds...[2]

Now let's evaluate the integral over the given plane ax+by+c=0. We can write x = t, y = (c-at)/b and z = 0, where t is the scalar parameter along the line of intersection of the plane and the cylinder (x^2 + y^2 = a^2).

Since the curve C is on the cylinder of radius a, we have x^2+y^2 = a^2 ⇒ t^2+(c-at)^2/b^2 = a^2On solving for t, we have t = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2].

Substituting t in x and y, we get the curve C in the x-y plane as a function of the scalar parameter s asx = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2]y = (c-at)/b= (c-(bc±ab √(a^2-b^2-c^2))/[a^2+b^2])/b.

Now we can evaluate the integral over the curve C, which is along the intersection of the plane and the cylinder.

Integral over C (x^2+y^2-2z^2) ds= ∫t₁^t₂ [(t^2 + [(c-at)^2]/b^2 - 2(0)^2)^(1/2)] dt= ∫t₁^t₂ [(a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2]^(1/2) dt.

Now we can choose the value of t₁ and t₂ such that the square root in the integrand is minimized (so that the integral is path-independent).

This can be done by choosing the value of t that gives the minimum value of (a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2 over the range of t from t₁ to t₂.

On differentiation with respect to t and equating to 0, we get the value of t = bc/(a^2+b^2).

Substituting this value of t in the integrand, we get the minimum value of the square root in the integrand to be |c| √(a^2+b^2)/|b|.

Thus the integral over C is given by∫C F.dr = ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds= ∫∫ (x^2+y^2-2z^2) ds= ∫t₁^t₂ |c| √(a^2+b^2)/|b| dt= |c| √(a^2+b^2)/|b| (t₂-t₁).

Now we can see that the integral is path-independent as it depends only on the end points t₁ and t₂ and not on the path taken to reach them.

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Answer:

Dietz

Explanation:

He is the guy you must justt be smart and know stuff.

According to the special theory of relativity, the speed of light is always 300000 km/s. Thus, the exact measure from  the side of the observer will result in  the same speed for light from the car.

The special theory of relativity proposed by Einstein states that the speed of light is constant. The apparent changes of the motion of all the objects are measured with respect to a frame of reference.

The speed of light in air is 300000 km/s. The car is moving in  sped of 0.02 km/s. For an observer, the speed coming from the car with the given speed will be small.

However, original speed of the light coming from the car is the same as in the air that is 300000 km/s.

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Answer:

A. Piccolo

B. The flute would usually have the highest pitch, but because the piccolo is half the size of a flute, it's higher pitched. The piccolo in C has a range from D5 – C8 which is pretty high pitched. This means that the piccolo's range is an octave above that of the flute.

C. The human ear naturally picks out higher notes, so when piccolos play extremely high, we can hear them more easily than the other instruments in a band or orchestra.

D. I'm sorry but I don't know this one.

Answer:

a)  3.0  10⁴ m / s, b) 3.7 10¹ m, c) 0.750 kg, d) 4 10¹² m²,  e)  75 m, f) 60 m²

g) 5.207 10³ m², e) 4.847 10⁷ s

Explanation:

The international system (SI) of measurements has as fundamental units the meter for length, the second for time and kilogram for mass.

Let's reduce the different magnitudes to the SI system

a) 30 km / h (1000m / 1 km) (1 h / 3600 s) = 3.0 10⁴ m / s

b) 37 Dm (10 m / 1 Dm) = 3.7 10¹ m

c) 750 g (1 kg / 10,000 g) = 0.750 kg

d) 4 10⁶ km² (1000 m / 1km) ² = 4 10¹² m²

e) 7500 cm (1 m / 100 cm) = 75 m

f) 600000 cm² (1m / 10² cm) ² = 60 m²

g) 520700000 mm³ (1 m / 10³ mm) ³ = 5.20700000 109/10 ^ 6

  = 5.207 10³ m²

e) 3.4 years (l65 days / 1 yr) (24 h / 1 day) (3600 s / 1h) = 4.847 10⁷ s

Answer:

7 N

Explanation:

Work = Force * distance

35J = Force * 5 meters               Divide by 5

35/5 = Force

7 Newtons = Force

Answer:

By opening the door, Elijah is using the chemical energy, which he obtained from eating food to do work. Thus, he is converting chemical energy to mechanical energy.

Stretching the spring by opening the screen door convert the potential energy which is stored in the spring to kinetic energy.

Overall there is conversion of chemical energy to potential energy.

By letting the door go, Elijah is using chemical energy. By snapping shut, the door is converting potential energy to kinetic energy. The overall energy change is conversion of chemical energy to kinetic energy.

Explanation:

With a temperature change of 31°C, the mercury column's height changes by 0.0106 cm.

As the temperature rises, the mercury will expand in the capillary tube, increasing its volume. V = VT = (1.8*10-4 (oC)-1)(0.100 cm3)(20 oC) = 3.6*10-4 cm3 = 0.36 mm3, or the formula V = VT.

\(A1 * h1 = A2 * h2\)

\(A1 = πr1^2 = π(0.005 cm/2)^2 = 7.85 × 10^-5 cm^2\)

The cross-sectional area of the bulb is:

\(A2 = πr2^2 = π(0.31 cm/2)^2 = 0.0755 cm^2\)

\(ΔV = V0 * β * ΔT\)

\(V0 = A1 * h1\)

\(h2 = (A1/A2) * h1 + (ΔV/A2)\)

\(h2 = (7.85 × 10^-5 cm^2)/(0.0755 cm^2) * h1 + (0.000182 (°C)^-1 * 31°C *\) 7.85 × \(10^-5 cm^2)/(0.0755 cm^2)\)

\(h2 = 0.0106 h1 + 0.00000122 cm\)

\(Δh = h2 - h1 = 0.0106 h1 + 0.00000122 cm - h1 = 0.0106 cm\)

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Answer:

The weight and the mass of an object are related because the weight of an object is a measure of the force exerted on the object by gravity, or the force needed to support it. w=mg

A wave is a disturbance that travels from one point to another in a medium. This disturbance can also be referred to as variation in energy. Light consists of energy derived from oscillating magnetic and electric fields. As light moves, it carries this energy from the source to another location. Also, waves have frequency and wavelength. Given these characteristics of light, we can conclude that

light is a kind of wave

In the given figure, four long straight wires perpendicular to the page form a square with an edge length of "a."

The arrangement described can be visualized as four long straight wires positioned perpendicular to the page, intersecting at their centers to form a square. Each wire can be thought of as an infinitely long line, with their cross-sections creating the square shape. The wires are oriented such that they are perpendicular to the page, meaning they extend in a direction perpendicular to the two-dimensional plane of the page.

The square formed by the wires has an edge length of "a," which implies that each side of the square has a length of "a." The wires intersect at the center of the square, dividing it into four equal sections. The configuration of the wires allows for a symmetrical arrangement, with each wire positioned at a 90-degree angle to its adjacent wires.

This setup involving perpendicular wires forming a square can have various applications in physics, engineering, and circuit design, as it provides a simple and symmetrical arrangement for the interaction of electric currents, magnetic fields, and other related phenomena.

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As you stand near a railroad track, the train passes by at a speed of 30.1 m/s while sounding its horn at a frequency of 219 Hz. The frequency you hear as the train approaches you is different from the frequency you hear while it recedes. Let's see how.

Speed of sound in air (v) = 342 m/s

Train's speed (u) = 30.1 m/s

Frequency of the horn (f) = 219 Hz.1.

The frequency heard when the train approaches the observer is given by:

f' = (v ± u)f/v

Where, +ve sign is taken if the observer and the source are approaching each other.-ve sign is taken if the observer and the source are receding from each other.

In this case, the observer is standing near a railroad track, so the train is approaching the observer. Thus, we will take the +ve sign.

Substituting the given values, we get:

f' = (342 + 30.1) Hz/342 Hz × 219 Hz= 250.1 Hz

Therefore, the frequency heard when the train approaches you is 250.1 Hz.

The frequency heard when the train recedes from the observer is given by:

f'' = (v - u)f/v

Here, the observer is standing near a railroad track, so the train is receding from the observer.

Thus, we will take the -ve sign.

Substituting the given values, we get:

f'' = (342 - 30.1) Hz/342 Hz × 219 Hz= 187.4 Hz

Therefore, the frequency heard when the train recedes from you is 187.4 Hz.

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Answer:

30.3 m

Explanation:

vf = final velocity = 0 at the apex

vo = original velocity = 24.39 m/s

a = - 9.81 m/s^2

vf = vo + at

0 = 24.39  -9.81 t   shows t= 2.486 s

df = final height

df = vo t  + 1/2 a t^2

   = 24.39( 2.486) + 1/2 ( -9.81)(2.486^2) = 30.3 m

Answer:

Only one parent is needed, and it is faster than sexual reproduction.

Explanation:

Sorry I'm not the best at explaining it but that's the answer.

asexual reproduction provides an advantage to the organisms that live on a rotting log by generating huge number of creatures in a very short amount of time

Asexual reproduction refers to a type of reproduction where a child is born to a single parent. The newly created people are clones of their parents since they have the same genetic makeup and physical characteristics.

Both multicellular and unicellular species can reproduce asexually. There will be no gamete fusion involved in this procedure, and the number of chromosomes will remain the same. With the exception of specific situations where there is a possibility that a rare mutation will occur, it will inherit the same genes as the parent.

The benefits of asexual reproduction are as follows:

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To determine the number of moles of F2 remaining after 3 mol of S have reacted, we need to consider the balanced chemical equation for the reaction between F2 and S. However, as the equation is not provided, we cannot provide an exact answer.

Assuming a simple stoichiometric ratio, let's consider the balanced equation:

F2 + S -> SF2

Based on this equation, for every 1 mol of S, 1 mol of F2 is required to react. Therefore, if 3 mol of S have reacted, we would expect 3 mol of F2 to have also reacted, assuming the reaction has gone to completion.

Since the initial mixture contained 9 mol of F2, and 3 mol of F2 have reacted along with the 3 mol of S, the remaining number of moles of F2 would be 9 - 3 = 6 mol.

Again, it's important to note that this is a simplified assumption based on a stoichiometric ratio, and the actual balanced equation may differ, which would affect the final result.

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The solar system shows the planets in their orbits around the sun in this order: Mercury, Venus, Earth with Moon, Mars, Jupiter, Saturn. Fixed stars are around the outside of the orbit of Saturn.

Explanation:

Aristarchus of Samos was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center. So I had to choose the choice that was most similar to that.

Answer: 35

Explanation:

Given the following :

M = 0.5 kg

Power of heater = 100W

From the graph ;

Time (t) = 7seconds

Change in temperature(Dt) = t2 - t1

Where t2 = 70°C, t1 = 30°C

Dt = (70 - 30)°C = 40°C

Recall Q = iVt

IV = power

Q = mcDt

c = specific heat capacity of liquid

mcDt = ivt

mcDt = power × t

0.5 × c × 40°C = 100 × 7

20°C × c = 700 J

c = 700 J/ 20°C

c = 35 J / kg°C

Answer:

TRUE

Explanation:

Answer:

3.2 hours

Explanation:

400÷125=3.2

3.2 or 3 hours and 12 minutes.

Answer:

The untrue option is C: "More arrowheads on lines mean a brighter light"

Explanation:

Ray diagrams are used to show how the light behaves with things like mirrors or lenses. Where we only study how the direction of the light changes when it interacts with these objects.

The "light" is represented with arrows, where again, the only thing we care is the direction of the light, so the first statement is true, the arrowheads show the direction of the light, and only that.

The intensity of the light, in this context, has no effect on how light behaves, so there is not a necessity of representing the intensity of the light, thus, more arrowheads on lines do not mean a brighter light. It may only be used to represent changes in direction of the light.

Finally, we know that light travels in straight pats (the pats can be curved in some cases, like with large gravitational fields, but this is not the case of a ray diagram) so the lines that represent the light should always be straight, thus option B is also true.

The untrue option is C: "More arrowheads on lines mean a brighter light"

The age limit to drink beer is 17 or 18 and up

Explanation:

\( \sin(60) = \frac{ \sqrt{3} }{2} \\ \\ \sin(60 ) {}^{2} = ( \frac{ \sqrt{3} }{2} ) {}^{2} \\ \\ \sin(60 ) {}^{2} = \frac{3}{4} \)