By using the definition of path-connectedness, show that [0,3) is path-connected.

Answers

Answer 1

By using the definition of path-connectedness,  [0,3) is path-connected can be shown as f(t) is a linear function, and the interval [0,1] is mapped to [0,3) in a continuous and smooth manner.

To show that the interval [0,3) is path-connected, we need to demonstrate that for any two points in the interval, there exists a continuous path connecting them entirely within the interval.

Let's take two arbitrary points in [0,3), say a and b, where 0 ≤ a < b < 3.

Consider the following continuous function f: [0,1] → [0,3) defined as:

f(t) = (1-t)a + tb

where t is a parameter ranging from 0 to 1.

We can verify that f(0) = (1-0)a + 0b = a, which is the starting point, and f(1) = (1-1)a + 1b = b, which is the ending point.

Now, let's show that f(t) lies entirely within [0,3) for any value of t. Since a < b, we know that the function f(t) = (1-t)a + tb lies between a and b for all t ∈ [0,1]. Since a and b are in the interval [0,3), f(t) is also bounded within [0,3).

Moreover, f(t) is a linear function, and the interval [0,1] is mapped to [0,3) in a continuous and smooth manner.

Therefore, we have constructed a continuous path (via the function f) connecting any two points a and b within [0,3), satisfying the definition of path-connectedness.

Hence, we can conclude that the interval [0,3) is path-connected.

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Related Questions

Compare venus's rotation to Earth's

Answers

Firstly its axis of rotation is inclined at 177.36 degrees (compared to 23.5 degrees on Earth). This means that Venus rotates in a retrograde direction from east to west, making the Sun rise in the west and set in the east. Further to this the rotation is very slow: a sidereal day on Venus lasts 243 Earth days.

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a footballer took a penalty kick and ball moved with a velocity of 4mls, calculate the work done by the footballer if the mass of the ball was 40g​

Answers

Answer:

Work done = 80 gm/s

Explanation:

Given:

Final velocity (v) = 4 m/s

Initial velocity (u) = 0 m/s

Mass of ball (m) = 40 g

Find:

Work done.

Computation:

Using work energy rule

Work done = Change in kinetic energy

Work done = 1/2[mv-mu]

Work done = 1/2[(40)(4) - (40)(0)]

Work done = 1/2[(40)(4)]

Work done = 80 gm/s

A force of 10 N works on a ball over a distance of 5 m. The force is perpendicular to the displacement of the ball. What is the total work done by the force?​

Answers

Since the force is perpendicular to the displacement of the ball, the total work done by the force is 50 Nm.

Given the following data:

Force = 10 NewtonDistance = 5 meters

To find the total work done by the force:

The work done by an object is the product of the perpendicular force acting on the object and the distance it covers.

Mathematically, work done is given by the formula:

\(Work\;done = Force\) × \(distance\)

Substituting the given parameters into the formula, we have;

\(Work\;done = 10\) × \(5\)

Work done = 50 Nm.

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A bullet of mass 140.0 g is fired horizontally with a velocity 0.670 km/s into Block A of mass 12.1 kg as shown in Figure (a). The bullet embeds itself in the block which now moves at velocity V₁. The block then collides with Block B such that both momentum and kinetic energy is conserved. Block B moves with velocity V₂ as shown in Figure (c) after the collision. Assume there is no friction between the blocks and the table and that Block B has a mass 21.6 kg. M B A B B (a) What is V₁? Submit Answer Tries 0/40 What is V₂? Submit Answer Tries 0/40 (b) (c)

Answers

Both the velocities are V₁ = 0.670 km/s, V₂ = 0.670 km/s.

(a) The bullet embeds itself in Block A, so the total momentum before the collision is equal to the momentum of Block A after the collision. The momentum is given by the product of mass and velocity.

Mass of the bullet = 140.0 g = 0.140 kg

Velocity of the bullet = 0.670 km/s

Total momentum before collision = Mass of the bullet * Velocity of the bullet

                             = 0.140 kg * 0.670 km/s

Since momentum is conserved, this total momentum is also equal to the momentum of Block A after the collision. Therefore, V₁ = 0.670 km/s.

(b) After the collision between Block A and Block B, both momentum and kinetic energy are conserved. Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision.

Total momentum after collision = Momentum of Block A + Momentum of Block B

Using the given masses and velocities:

Total momentum after collision = (Mass of Block A * V₁) + (Mass of Block B * V₂)

Since momentum is conserved, this total momentum is equal to the total momentum before the collision.

Therefore, we can set up the equation:

(Mass of Bullet * Velocity of Bullet) = (Mass of Block A * V₁) + (Mass of Block B * V₂)

Substituting the given values:

(0.140 kg * 0.670 km/s) = (12.1 kg * V₁) + (21.6 kg * V₂)

Solving this equation will give us the value of V₂, which is the velocity of Block B after the collision.

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Imagine you inherit a farm and now have to purchase fertilizer for the farm. The farm is 340 acres and had corn planted the previous year. You must add fertilizer to the soil before you plant this year's crop. You go to the local fertilizer store and find SuperPhosphate-brand fertilizer. You read the fertilizer bag and can recognize from your high school chemistry class a molecular formula C*a_{3}*P_{2}*H_{14}*S_{2}*O_{21} (you don't understand anything else written on the bag because it is imported fertilizer from Japan). You must decide how much fertilizer to buy for application to your cornfields. If each bag contains 25 kg of fertilizer and costs $54.73, how many bags of fertilizer must you purchase, and how much will it cost you to add the necessary fertilizer to your fields ?

Answers

Total Cost is =  $107,380 if The farm is 340 acres and had corn planted  add fertilizer to the soil before you plant this years' crop.

What is called fertilizer?

A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".

Why is fertilizer important?

Without fertilizers, nature struggles to replenish the nutrients in the soil. When crops are harvested, important nutrients are removed from the soil, because they follow the crop and end up at the dinner table. If the soil is not replenished with nutrients through fertilizing, crop yields will deteriorate over time.

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(a) The current in the circuit is direct current.
What is meant by direct current?
Tick one box.

Answers

Explanation:

If the polarity of an electrical source doesn't change with time, it is called direct current.

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A glacier advances at 3.7 × 10^−6 cm/s. How far will it move in 89000 s? Answer in units of cm.^

Answers

\(v = 3.7 \times {10}^{ - 6} \: \: \frac{cm}{s} \)

\(3.7 \times {10}^{ - 6} = \frac{x}{89000} \\ \)

Multiply sides by 89000

\(3.7 \times {10}^{ - 6} \times 89 \times {10}^{3} = x \)

\(37 \times {10}^{ - 1} \times 89 \times {10}^{ - 3} =x \)

\(37 \times 89 \times {10}^{ - 4} = x \)

\(x = 3293 \times {10}^{ - 4} \: \: cm \)

And we're done.....♥️♥️♥️♥️♥️

Chen is testing the friction of three surfaces. he pushes the same ball across three different surfaces with the same force and measures the distance the ball rolls over each surfacel. the ball moved ten inches across surface 1, six inches across surface 2, and fifteen inches across surface 3. which could most likely describe the three surfaces? surface 1 is ice, surface 2 is gravel, and surface 3 is blacktop. surface 1 is gravel, surface 2 is ice, and surface 3 is blacktop. surface 1 is blacktop, surface 2 is gravel, and surface 3 is ice. surface 1 is blacktop, surface 2 is ice, and surface 3 is gravel.

Answers

Surface 1 is blacktop, Surface 2 is gravel, and Surface 3 is ice. is most likely describe the three surfaces.

What is friction?

Friction, force that resists the sliding or rolling of one solid object over another. Frictional forces, such as the traction needed to walk without slipping, may be beneficial, but they also present a great measure of opposition to motion. About 20 percent of the engine power of automobiles is consumed in overcoming frictional forces in the moving parts.

The major cause of friction between metals appears to be the forces of attraction, known as adhesion, between the contact regions of the surfaces, which are always microscopically irregular. Friction arises from shearing these “welded” junctions and from the action of the irregularities of the harder surface plowing across the softer surface.

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A 17.5-cm-diameter loop of wire is initially oriented perpendicular to a 1.3-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.15 s .

Answers

The magnitude of the average induced emf in the loop during the rotation is 3.7 V.

When a loop of wire is rotated in a magnetic field, an induced electromotive force (emf) is generated in the loop. The magnitude of this induced emf can be calculated using Faraday's law of electromagnetic induction:

ε = -N * (ΔΦ/Δt)

where ε is the induced emf, N is the number of turns in the loop, ΔΦ is the change in magnetic flux through the loop, and Δt is the time interval during which the change occurs.

In this case, the loop has a diameter of 17.5 cm, which corresponds to a radius of 8.75 cm (or 0.0875 m). The area of the loop is given by A = π * r^2, where r is the radius.

Therefore, the initial magnetic flux through the loop is Φ = B * A, where B is the magnetic field strength. Given that the magnetic field is 1.3 T, we can calculate the initial magnetic flux.

Φ = 1.3 T * π * \((0.0875 m)^2\)

Next, we need to calculate the change in magnetic flux as the loop rotates. Since the loop is initially oriented perpendicular to the magnetic field, and then it is rotated to become parallel, the change in magnetic flux is simply the difference between the final and initial magnetic fluxes.

ΔΦ = Φ_final - Φ_initial

Since the final magnetic flux is zero (as the loop becomes parallel to the field direction), the change in magnetic flux is -Φ_initial.

Finally, we can substitute the values into the formula for the induced emf to find its magnitude:

ε = -N * (-Φ_initial / Δt)

In this problem, the time interval Δt is given as 0.15 s.

ε = N * (Φ_initial / Δt)

Calculating the values, we obtain:

ε = N * (1.3 T * π * (0.0875 m)^2) / 0.15 s

Simplifying this expression will give us the magnitude of the average induced emf in the loop during the rotation.

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Recoil is noticeable if we throw a heavy ball while standing on roller skates. If instead we go through the motions of throwing the ball but hold onto it, our net recoil will be?.

Answers

Answer:

zero

Explanation:

A bowling ball that weighs 70 N is dropped from a tower 15 meters above the ground. Disregarding air friction, what is the KE of the ball when it reaches the ground? What is the ball’s velocity the moment before it hits the ground?

Answers

The kinetic energy of the bowling ball of weight 70 N is 1050 J, and the velocity of the ball the moment before it hits the ground is 17.15 m/s.

What is kinetic energy?

This is the energy of a body in motion.

To calculate the kinetic energy of the ball when it hits the ground, we use the formula below.

Formula:

Since there is no loss due to friction,

Kinetic energy = Potential energyK.E = Wh.............. Equation 1

Where,

K.E = Kinetic energyW = Weight of the ballh = Height of the tower

From the question,

Given:

W = 70 Nh = 15 m

Substitute into equation 1

K.E = 70×15K.E = 1050 J

Also,

To calculate the velocity before the ball hit the ground, we use the formula below.

v = √(2gh)......... Equation 2

Where:

g = Acceleration due to gravity = 9.8 m/s²v = Velocity of the ball before hitting the ground.

Substitute into equation 2

v = √(2×15×9.8)v = √294v = 17.15 m/s

Hence, the kinetic energy and the velocity of the ball before hitting the ground is 1050 J and 17.15 m/s respectively.

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a straight 2.1 m wire carries a typical household current of 1.5 a (in one direction) at a location where the earth's magnetic field is 0.55 gauss from south to north. find the magnitude of the force that our planet's magnetic field exerts on this cord if it is oriented so that the current in it is running from north to south.

Answers

To calculate the magnitude of the force exerted on the wire by the Earth's magnetic field, we can use the formula:

F = I * L * B * sin(θ)

Where:

F is the force,

I is the current in the wire (1.5 A),

L is the length of the wire (2.1 m),

B is the magnetic field strength (0.55 gauss = 0.055 T),

θ is the angle between the direction of the current and the magnetic field.

Since the current is running from north to south and the magnetic field is from south to north, the angle between them is 180 degrees (or π radians). The sine of 180 degrees is 0, so the force becomes:

F = I * L * B * sin(180°)

 = I * L * B * 0

 = 0

Therefore, the magnitude of the force exerted by the Earth's magnetic field on the wire is zero.

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Which transformation of energy occurs when a fan is turned on and the blades start to rotate?

Answers

Answer:

kinetic energy

Explanation:

A wind turbine transforms the mechanical energy of wind into electrical energy. A turbine takes the kinetic energy of a moving fluid, air in this case, and converts it to a rotary motion. As wind moves past the blades of a wind turbine, it moves or rotates the blades. These blades turn a generator

A small rocket fired straight up. When a height of 5.0km and velocity of 200.0m/s, it releases its booster and enters free fall. Calculate the total time of flight between releasing its boosters and falling back nd hitting the ground. A. 20.4s B. 40.8s C. 37.9s D. 58.3 s

Answers

The total time of flight between releasing its boosters and hitting the ground is 40.8s. therefore, B. 40.8s is correct option.


To calculate this, we need to know the initial velocity of the rocket, the height of its release point, and the acceleration due to gravity.

The initial velocity of the rocket is 200.0m/s, the height of its release point is 5.0km, and the acceleration due to gravity is 9.8 m/s^2.

We can calculate the time of flight using the equation:

t = 2v/a.

Plugging in the known values, we get:

t = 2 × 200/9.8

 = 40.8s.

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A proton falls through a potential drop of 400 v. how much is the change of potential energy of this proton in falling through this potential drop?

Answers

Change in potential energy of the proton= (1.6 × 10^-19 C) × (400 V)

To calculate the change in potential energy of the proton, we need to use the formula:

The change in potential energy of a proton can be described as the difference in its stored energy when transitioning from one position to another within an electric field. Potential energy is directly related to the distance between charged particles.

As the proton moves closer to a positively charged object or further away from a negatively charged object, its potential energy increases. Conversely, if the proton moves away from a positively charged object or closer to a negatively charged object, its potential energy decreases.

This change in potential energy is a result of the electric force acting on the proton, with the magnitude of the change depending on the distance and the strength of the electric field.

Change in potential energy = Charge of the proton (q) × Potential difference (V)

The charge of a proton is 1.6 × 10^-19 C (Coulombs), and the potential difference is given as 400 V.

Change in potential energy = (1.6 × 10^-19 C) × (400 V)

By multiplying these values, we can find the change in potential energy.

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Calculate the wavelength of a sound wave with a frequency of 1.2KHz when the speed of
sound in air = 0.33 km/s

Answers

The wavelength of the sound at frequency of 1.2khz will be 0.275 m

we know that,

velocity= frequency x wavelength

0.33 km/s = 1.2khz x wavelength

wavelength = 0.33 km/s/1.2khz

wavelength = 330m/s / 1200hz

wavelength = 0.275m

If a receiver is overly selective:
A) the tank circuits within the tuned amplifiers have insufficient Q.
B) too much noise is picked up and amplified by the receiver.
C) only part of the bandwidth of the AM signal is amplified, causing some of the sideband information to be lost and distortion results.
D) the volume control is turned up to maximum, the desired station is very weak.

Answers

Answer:

C) only part of the bandwidth of the AM signal is amplified, causing some of the sideband information to be lost and distortion results.

Explanation:

Selectivity is the ability of a receiver to respond only to a specific signal on a wanted frequency and reject other signals nearby in frequency.

If a receiver is overly selective, only part of the bandwidth of the AM signal is amplified, causing some of the sideband information to be lost and distortion results. Whereas, if a receiver is underselective, the receiver can pick different signals on different frequencies at the same time.

A capacitor has plates of area
3.61 x 10-4 m2 which are separated
by 4.72 x 10-6 m. What is its
capacitance?
[?] * 10?! F.

A capacitor has plates of area3.61 x 10-4 m2 which are separatedby 4.72 x 10-6 m. What is itscapacitance?[?]

Answers

Answer:

6.76875 • 10 ^-10 F

Explanation:

You just follow the formula:

C = εA/d

ε = 8.85 • 10^-12

A = 3.61 • 10^-4

D = 4.72 • 10 ^-6

So:

C = (8.85 • 10^-12)(3.61 • 10^-4)/4.72 • 10 ^-6 = 6.76875 • 10 ^-10 F

Good Luck!  :)

I need help finding the average acceleration fo tyler and bree

I need help finding the average acceleration fo tyler and bree
I need help finding the average acceleration fo tyler and bree

Answers

fo really bro learn how to spell

In a regression analysis, if sse = 200 and ssr = 300, then the coefficient of determination is:_________

Answers

0.600

In a regression analysis, if sse = 200 and ssr = 300, then the coefficient of determination is: 0.600

1. You have that the data set having SSR=300 and SSE=200

2. Therefore you have the coefficient of determination is:

r²=SSR/SSTO

SSTO=SSR+SSE

3. Then, when you substitute the values, you obtain:

SSTO=200+300

SSTO=500

r²=300/500

4. So, you have that the result is:

r²=0.6

As a result, as you can see, the solution to the previous exercise is that the coefficient of determination is 0.6

What exactly is the connection between SST, SSR, and SSE?The difference between SST and SSR is the amount of Y's variability that is still unaccounted for after using the regression model, also known as the sum of squared errors (SSE). Sum of squares of residual can be used to directly calculate SSE.

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A bat hasa mads of 2kg at the velocity of 45 m/s what is the kinectic energy could he give to a ball

Answers

Answer:

the  kinetic energy the bat can give to a ball is 2,025 J.

Explanation:

Given;

mass of the bat, m = 2kg

velocity of the bat, v = 45 m/s

The kinetic energy the bat can give to a ball is calculated as;

\(K.E = \frac{1}{2} mv^2\\\\K.E = \frac{1}{2} \times \ 2 \ \times \ 45^2\\\\K.E = 2,025 \ J\)

Therefore, the  kinetic energy the bat can give to a ball is 2,025 J.

Using ideas of forces explain why the parachutist reaches terminal velocity and why opening the parachute reduces the terminal velocity

Answers

Don’t download the file it’s a virus

what is the density to the nearest hundredths, of a metal with a volume of 3.00 cm3 and a mass of 8.13g?

Answers

Since D=M/V, the answer would be 2.7

What are the two parts of a force pair?

Answers

These two forces are called action and reaction forces and are the subject of Newton's third law of motion.

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a rocket travels vertically at a speed of 1000 km/hr. the rocket is tracked through a telescope by an observer located 18 km from the launching pad. find the rate at which the angle between the telescope and the ground is increasing 3 min after the lift-off.

Answers

The rate at which the attitude among the telescope and the floor is growing three mins after the lift-off is about 19.157 radians according to hour.

Through trigonometric ratios we've the following expression for the perspective of the telescope:

\(tan\theta = \frac{y}{x}\)----------- (1)

Then, we derive an expression for the rate of change of the angle of the telescope in time (), in radians in line with hour, through differential calculus, trigonometric ratios and the Pythagorean theorem:

\(sec^{2} \theta\theta=\frac{y.x-y.x}{x^2}\)

\(\frac{r.\theta}{x}=\frac{y.x-y.x}{x^2}\\\theta=\frac{x^2.\vec{y}-x.y.\vec{x}}{r.x^2}\\\theta=\frac{x^2.y-x.y.x}{x^2.\sqrt{x^2+y^2}}\) ----------- (2)

As of the rocket is touring vertically, (2) is decreased into this shape:

\(\theta = \frac{y}{\sqrt{x^2+y^2}}\)------------- (2b)

If we recognize that , and , then the price at which the attitude among the telescope and the ground is increasing is:

\(\theta=\frac{1000\frac{km}{h}}{\sqrt{(15km)^2 + (50km)^2}}\\\theta=19.157\frac{rad}{h}\)

Telescopes can be used to observe planets, stars, galaxies, and other celestial bodies. It works by gathering and focusing light from the object being observed, allowing it to be magnified and seen in greater detail. Both types have their advantages and disadvantages, and the choice of telescope depends on the specific needs of the observer.

Telescopes come in many sizes, from small portable models that can be used for casual stargazing, to giant observatory telescopes that are used by professional astronomers to study the universe in detail. Modern telescopes are often equipped with advanced technologies such as computer control systems, digital cameras, and adaptive optics, which help to improve the quality of the images they produce.

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Complete Question: -

A rocket travels vertically at a speed of 1000 km/hr. The rocket is tracked through a telescope by an observer located 15 km from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min after the lift-off.

What’s the sum of all even number from 1-400

Answers

40200 would be the answer!

Answer:

40200

Explanation:

200 even numbers from 1 to 400

so n=200

sum of all even numbers is n(n+1)

so sum = 200(201)

which equals 40200

Which of the following describes an action-reaction pair?
A. You push on a wall, and the wall pushes back on you.
O B. You sit on a chair, and the chair is pulled down by gravity.
O C. A cup pushes down on a table, and the table pushes down on the
ground.
D. The Moon's gravity pulls on Earth, and your gravity pulls on the
Moon.

Answers

Answer:

A) only the wall is involved for both forces (action-reaction)

Which refers to a diagram that shows thermal energy being released by objects?
thermogram
heat sensor
thermal radiator
radiation image

Answers

Answer:

The correct option is thermogram

Explanation:

A thermogram is an image that is produced by thermographic cameras that are usually used to detect radiation (thermal energy released by a body) within a long-infrared range of electromagnetic spectrum. This process is a part of infrared imaging science which is useful in the diagnosis of breast cancer and some other forms of tumors.

Answer:

thermogram

Explanation:

i took the test

Object A represents fixed negatively charged particle and Object B represents fixed. positively-charged particle. Object ( shows a

moving positively charged particle. Identify which arrow would correctly show the force of attraction or repulsion on object C caused

by the other two objects?

Answers

Answer:

Moving electrons by cringing the object near another charged object ... This means that there is a different number of protons and electrons ... the attraction or repulsive electrostatic force between positive and negative charges ... the amount of charge on the particle and the distance between the particles ... fixed in position.ation:

What harsh environment does trailing azalea grow in?.

Answers

Trailing azalea grows in harsh environments such as rocky slopes, cliffs, and other areas with poor soil and low moisture.

Trailing azalea, also known as Rhododendron canescens, is a native plant in the southeastern United States. This plant prefers acidic soils, but it can grow in a variety of soil types, including poor soil with low moisture. Trailing azalea is commonly found growing on rocky slopes, cliffs, and other areas with harsh environmental conditions. It is a hardy plant that can withstand drought and extreme temperatures.

In summary, trailing azalea grows in harsh environments such as rocky slopes, cliffs, and areas with poor soil and low moisture. This plant is adapted to survive in these challenging conditions, making it an important part of the ecosystem in the southeastern United States.

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