Ssuming that the relationship between spring compression and height is quadratic, how far will the ball go at the highest setting, which compresses the spring 3 cm ?

On a circle of radius r, a central angle of radians subtends an arc of length(s) is r; the area of the sector formed by this angle is a 12r2Θ. The central angle of radians subtends an arc of length(s) that is multiple of radius (r) and central angle().

The concept of area is always associated with two dimensions. Any two-dimensional object can combine to form a plane. As a result, every two-dimensional figure has an area. Every point in a plane that is a particular distance away from some other point forms a circle. The circle's radius and fixed distance are both referred to as the circle's center and radius, respectively.

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The following statements which best describes what the phrase "rate of change" is the difference in some quantity over some period of time and is denoted as option B.

This is referred to as the ratio between quantities such as velocity, acceleration etc. This is because velocity is referred to as the rate of change of displacement with time and the S.I unit is referred to as metre per second.

This is therefore the reason why difference in some quantity over some period of time was chosen as the most appropriate choice in this type of scenario.

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Answer:

the ball will travel for 2 seconds and complete a distance of 20 metres upwards.

Explanation:

v = final velocity

u = initial velocity

a = acceleration

t = time

s = distance

In your question, the initial velocity is given as 20m/s , i.e., u=20m/s ,

the final velocity that the ball can achieve at the maximum height is 0m/s

, hence, v=0m/s .

Since the only first that cause the acceleration is gravity, a is taken as g where g is acceleration due to gravity, and had a value of 9.81m/s2 . But for simplicity, we can take the value of a to be 10m/s2 , so a=10m/s2 . Now, we need to find, what's s and t.

Note: Since the ball is thrown upwards, which is against the force of gravity (gravity always acts downwards), we need take the value of a (in this case, g) as −10m/s2 .

Using the first equation,

v=u+at

0=20−10t

10t=20

t=2

Using the third equation,

v2=u2+2as

02=202+2×(−10)×s

20s=400

s=20

Hence, the ball will travel for 2 seconds and complete a distance of 20 metres upwards.

The mass of the ore required to make the lead sphere 7 cm is 17.7 kg.

The radius of the lead sphere = 7 cm

The density of the lead = 11.4 g/cm³

The efficiency of lead extraction = 92.5 %

Let the mass of the lead = m.

Let the mass of the ore = M.

So the mass of the lead is,

[tex]m =(Density) \times[ \frac{4}{3} \pi(Radius) ^{3} ][/tex]

[tex]m = 11.4 \times \frac{4}{3} \times \frac{22}{7} \times( 7 )^{3} [/tex]

[tex] = 16385.6 \: g[/tex]

[tex] = 16.38 \: kg[/tex]

The efficiency constant is,

[tex]η = \frac{mass \: of \: lead}{mass \: of \: ore} [/tex]

[tex]η = \frac{m}{M}[/tex]

[tex]92.5\% = \frac{16.38}{M}[/tex]

[tex]M = \frac{16.38}{ \frac{92.5}{100} } [/tex]

[tex]M = \frac{16.38}{0.925} [/tex]

[tex] = 17.7 \: kg[/tex]

Therefore, the mass of the ore required to make the lead sphere of 7 cm is 17.7 kg.

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The most highly redshifted electromagnetic radiation that astronomers have detected to date is from the radiation left over from the Big Bang.

Radiation travels in waves and possesses both an electric and magnetic field. Both natural and artificial sources contribute to it. The energy levels of electromagnetic radiation can range from low to high. It consists of x-rays, gamma rays, infrared light, visible light, ultraviolet light, radio waves, and microwaves. Also known as EMR, electromagnetic radiation (EMR) is a category of energy carried by waves of the electromagnetic (EM) field that travel across space. These waves include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The electromagnetic spectrum includes all of these waves. Electromagnetic radiation is often made up of electromagnetic waves, which are coordinated oscillations of electric and magnetic fields. Due to the periodic alteration of the electric or magnetic field, electromagnetic radiation or waves are produced.

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The density of the metal is 5.096 g/cm^3

Weight of the metal W = 17.9g

Length of the cube of metal = l = 15.2 mm = 1.52 cm

Density = w/v

= w/l*l*l

= 17.9 / (1.52)^3

= 17.9 / 3.512

= 5.096 g/cm^3

The Density = 5.096 g/cm^3

Density is a measurement that is seen as one that compares the amount of matter an object has to its volume. The density of a substance indicates how dense it is in a given area.

Density can be formulated as:

D = mass / volume

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The resulting speed of weight B is 4m/s

Here we have the end of the cable A pulled with the speed of 12m/s

To find the speed at which block B move:

At the top of pully. We have length at A is Sa and length of B is Sb.

The length from the top pulley to the small pulley which is held by the bar that Lint we built label it H

The pulley system made of only one chord, so we need only one equation to represent the rope.

Sa +Sb +(2Sb -h) = l

When the rope is pulled at block B the whole part moves up.

Sa + 3 Sb = L+2h

In order to find the velocity, we take derivative of the above equation.

here we get

Va + 3Vb = 0

Va = 12m/s

vb = -12/3 = -4m/s

negative sign shows that block is going against the direction. That is upward direction.

The resulting speed of weight B is 4m/s

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According to the given statement the speed of sirius is =2.3275862×10¹²km/s.

A waveform signal's wavelength, which is the distance between two identical locations (adjacent crests) in the succeeding cycles, determines whether it is sent through space or via a wire. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimetres (mm).

Hydrogen has a spectral line at = 116nm=116×10⁻⁹m

Line is observed at = 107 nm=107×10⁻⁹m

Now, from the Hubble's law

V=[tex](\Delta \lambda / \lambda)[/tex]×C

Where,

v is the velocity

Δλ = Change in wavelength = 116 - 107= 9nm=9×10⁻⁹m

λ = Actual wavelength=116nm=116×10⁻⁹m

C is the speed of the light=3×10⁸m/s

on substituting the respective values, we get

V=(9/116)×3×10⁸=23275862.069×10⁵m/s

V=2.3275862×10¹²km/s.

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The correct answer is 0.75 liters.

One liter of soda produced 250 ml of beverage.

1 liter is equal to 1000 milliliters.

250 ml was consumed, or 250/1000 or 0.25 liter.

There was 1 - 0.25 liters of soda left

0.75 liter of soda was left and the correct answer is 0.75 liter.

Four glasses of water make up one liter, to be precise.

Let us understand this using the following explanation. Despite the fact that there is no set standard size for glasses, their capacity varies. In contrast, we calculate that a liter holds 32 ounces and a glass holds 8 ounces of water.

Convert the object's dimensions into centimeters before performing the volume calculation in litres. Next, determine a shape's volume using the volume formula. For instance, you could use Volume = length times width times height to determine the volume of a cube, and the result would be in cubic centimetres.

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The work done in the isothermal process is 10 joule.

We need to know about the isotherm process to solve this problem. The isotherm process can be described as a process where the initial temperature system will be the same as the final temperature. Hence, the internal energy change will be zero.

ΔU = 0

Hence,

ΔU = Q - W

0 = Q - W

Q = W

It means that the heat transferred is the same as the work done.

From the question above, we know that the heat transferred is 10 joule. Thus, the work done in the isothermal process is 10 joule.

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Given only a mass number, one can deduce the number of protons plus neutrons in each atom of an element and is denoted as option A.

This is also referred to as the nucleon number which is the total number of protons and neutrons in the atom of an element.

Protons are referred to as the positively charged subatomic particles which are present in a atom while the neutrons are subatomic particles which are neutral and the both of them make up the nucleus of an atom.

This is therefore the reason why proton plus neutron was chosen as the most appropriate choice.

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The options are:

a) protons plus neutrons

b) neutrons

c) protons

d) electrons

e) protons plus electrons

The horizontal force Superman must apply to throw the boulder is 3670N.

According to Newton's Second law of motion,

Force F = Mass m * Acceleration a

We know that Weight W = Mass m * Gravity g

Given,

Weight W = 2400 N

Acceleration a = 15 m/[tex]s^{2}[/tex]

Gravitational force g = 9.81 m/[tex]s^{2}[/tex]

W = m * g

Mass m = 2400 / 9.81 = 244.65 kg

Horizontal force F = 244.65 * 15 = 3669.7 N

Newton's Second law of motion states that acceleration of an object depends on force acting on the object and mass of the object.

Therefore the horizontal force Superman must apply to throw the boulder is 3670N.

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If a train starts from rest and accelerates uniformly until it has traveled 7.1km and acquired a forward velocity of 36m/s. the train then moves at a constant velocity of 36m/s for 2.1min. The train then slows down uniformly at 0.072m/s^2, until it is brought to a halt.  Then the entire process take (in minutes ), approximately 17.1 minutes.

Here, we have the following values,

u = 0

v = 36 m/s

s = 7.1 which is 7100 m

now we know that [tex]v^{2} = u^{2} + 2at[/tex]

As u = 0 hence the equation we have is [tex]v^{2} = 2at[/tex]

Now to find acceleration (a), a = [tex]\frac{36 *36}{2*7100}[/tex] = 0.091 m/[tex]s^{2}[/tex]

Now we know that a = 0.072 v = 0 u = 36 m/s then for t

v = u+at

[tex]\frac{36}{0.072}[/tex] = 500 sec

Putting the values in v = u +at

t' = (36)/(0.09) = 400 seconds

t'' = 2.1 min which is 126 seconds

and t''' is 500 seconds

Adding them up gives us the total time, which is

Total time = 400 +120+500

= 1026 second

=17.1 minutes

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A solar eclipse that occurs when the moon's umbra does not reach earths surface is called Annular Solar Eclipse.

An Annular Solar Eclipse is a phenomenon during solar eclipse in which Moon covers the center part of Sun when seen from Earth. But the Sun's outer edges are visible. This looks like a Ring of fire which is called as an Annulus.

An Umbra is a point in a shadow from which you cannot see the light source which formed the shadow.

Therefore, a solar eclipse that occurs when the moons umbra does not reach earths surface is called Annular Solar Eclipse

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The correct answer of terrestial weather:

The solar insolation in the visible and infrared regions of the solar electromagnetic spectrum is much more than the energy that space weather occurrences release into the troposphere and stratosphere. Despite claims to the contrary, there may be some connection between the Earth's climate and the 11-year sunspot cycle. There is no proof of this. For instance, it has frequently been suggested that the Maunder minimum, a 70-year period almost devoid of sunspots, is correlated to a cooler climate, but these correlations have vanished after further research. Changes in cosmic ray flux are hypothesized to affect how much cloud formation occurs.

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The approximate radius is 6370 Km

The radius of the Earth is approximately 3,960 miles, while the radius of the Moon is approximately 1,080 miles.

Earth is the third planet from the Sun, the largest of the solar system's four terrestrial planets, the planet with the highest density, and the only planet in our solar system known to support life.

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The maximum number of comparison is 4502

Binary array : it is an array consist of only 0s and 1s only.

Binary search - an efficient algorithm for finding items from a sorted list.

it is called binary because it divide array into tow halves.

It is used to excess data more faster when the space is tight.

binary search will search the array by dividing it into two halves till it find the value.

The main advantage of it is that is more quicker than a serial search.

binary search algorithm can be implemented in the two ways :

1. Iteration method

2. Recursive method

the maximum number of comparisons is 4502.

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If you are using standard tons, then each ton is  907.18474 kg.

Multiply that and your answer is 5,443,108.44 kg.

If you are using metric tons, then multiply by 1,000.

6,000 * 1,000 = 6,000,000 kg

5.3 km

This question involves continuous displacement in various directions. When it becomes difficult to imagine, vector analysis becomes handy.

Let us denote each of the individual displacements by a vector. Consider the unit vectors as the unit vectors in the direction of East and North respectively.

By simple calculations, we can derive the unit vectors j,[tex]\frac{-i-j}{2}[/tex] and in the directions North,  South of West, and  North of West respectively.

So Total displacement vector = The Sum of individual displacement vectors.

Displacement vector = -4.25i + 3.165j

The magnitude of Displacement =| -4.25i + 3.165j |  = 5.3km

∴ Total displacement = 5.3km

A displacement is a vector in geometry and mechanics that have a length equal to the shortest distance between a point P's initial and final positions.  It measures the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

The final location xf of a point relative to its beginning position xi, or a relative position (derived from the motion), is another way to express a displacement. The difference between the final and initial coordinates can be used to define the equivalent displacement vector.

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The functions such as non-vertical, continuously differentiable, non-vertical tangent satisfy the conditions.

In mathematics, a differentiable function of one real variable is a function that has a derivative at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.

A smooth, differentiable function lacks any breaks, angles, or cusps (it is locally well approximated as a linear function at each interior point).

If the derivative f'(x 0) exists, a function f is said to be differentiable at x0 if x0 is an inner point in the domain of the function.

In other words, the point (x0, f(x0)) on the graph of f has a non-vertical tangent line. If f is differentiable at every point along U, then U is said to be differentiable.

If the derivative off is also a continuous function over the domain of the function ff, then f is said to be continuously differentiable.

In general, if f’s initial k derivatives are f prime (x), f prime (x), and lots, f(k)(x), then f is said to be of class Ck. f prime (x), f prime (x), lots, and f (k) prime (x) exist and are continuous across the function’s domain.

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Answer:

Physical science

Explanation:

As a result, the provided sphere's intersection with the yz-plane would be (y-2)²+(z-5)²=7.

When two streets or lines cross, it is known as an intersection. The two places where crossings are most likely to occur are in math class and in traffic. An intersection in mathematics is the place where two lines converge. This is the common theme among the lines.

Equation (x+3)²+(y-2)²+(z-5)²=16

Intersection (y-2)²+(z-5)²=7

We are asked to write an equation of the sphere with center (-3,2,5) and radius 4.

We know that equation of a sphere with radius 'r' and center (h,k,l) at is in form:

(x-h)²+(y-k)²+(z-l)²=r²

Since center of the given sphere is at point (-3,2,5) , so we will substitute h=-3,k=2 ,l=5 and r=4 in above equation as:

(x-(-3))²+(y-2)²+(z-5)²=4²

(x+3)²+(y-2)²+(z-5)²=16

Therefore, our required equation would be (x+3)²+(y-2)²+(z-5)²=16

To find the intersection of our sphere with the yz-plane, we will substitute x=0 in our equation as

(0+3)²+(y-2)²+(z-5)²=16

9+(y-2)²+(z-5)²=16

9-9+(y-2)²+(z-5)²=16-9

(y-2)²+(z-5)²=7

As a result, the provided sphere's intersection with the yz-plane would be:

(y-2)²+(z-5)²=7.

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The charge on each capacitor is Q.

Capacitor is device which stored electrical energy i.e. the ratio of charge (Q) given to the potential difference (V) applied across the conductors.

C = Q/V.

Therefore the capacitance of each capacitor is C₁ , C₂, C₃ and their equivalent be Ceq. These capacitance are connected in series, thus the charge on each capacitance is Q.

When connected across a source such as battery, the potential difference of battery is V and divided across each component as V₁, V₂, V₃. Then the total potential difference V is written as ,

V = V₁+V₂+V₃

V=Q/C

Then for equivalent capacitance Ceq in series combination is written as,

Q/Ceq= Q/C₁+ Q/C₂ +Q/C₃

According to the principle of conservation of charge . so that charge Q is same for each capacitance

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The correct answer for the affect in the stage capacity is that it will increase.

The stage's capacity will increase .

The capacity formula is as follows:

Capacity = (Batch size) / (Total setup time + processing time x batch size) 

Clearly, increasing the batch size twice will increase capacity, but not in the same proportion because the batch size is the same in the numerator and denominator. Increasing the batch size will increase the capacity but in very small proportions. Furthermore, if the batch size is too large, goods will be produced even if there is no demand, and if the batch size is too small, capacity will be lost. As a result, there is a trade-off between batch size and capacity.

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Answer:43

Explanation: 30,30,40,40,40,50,50,50,50,50

A small hydraulic jump at location where the channel has a width of 5 m. at the crest of the jump the depth appears to be about 1 m, Fr = 1.

Hydraulic Depth is the area of a cross-section divided by the highest width. Hydraulic Width is especially useful for irregularly shaped channels (not rectangular), as seen within the equation for calculating the Froude Number.

A hydraulic jump may be a phenomenon within the science of hydraulics which is often observed in open channel flow like rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs within the liquid surface.

Hydraulic jump, Sudden change in water level, analogous to a blast wave, commonly seen below weirs and sluice gates where a smooth stream of water suddenly rises at a foaming front. The very fact that the speed of water waves varies with wavelength and with amplitude ends up in a large type of effects.

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The power generated by 1.4 m high waves is 1.69 kW.

We need to know about power to solve this problem. The power generated by waves can be determined as

P = 1/2 . μ . ω² . A² . v

where P is power, μ is the constant of wave media, ω is angular speed, A is amplitude and v is wave speed.

Power is proportional to amplitude squared. Hence

P ~ A²

From the question above, we know that

P1 = 8.5 kW

A1 = 1.4 m

A2 = 0.625 m

By using the ratio of power, we can write

P1 / P2 = A1² / A2²

8.5 / P2 = 1.4² / 0.625²

P = 1.69 kW

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The acceleration of the motor bike is 4 m/s².

To find the acceleration, the given values are,

Final velocity = 60 m/s

Initial velocity = 0 m/s

Time period = 15 seconds.

                     a = (vf - vi) / t m/s²

Acceleration  =  (change in speed) / (time for the change)

a = acceleration

vf = final velocity

vi= starting velocity

t  =  time

So the formula,

           a = Δv / t m/s²  

              =  (60 m/s)  /  (15)        

              = 4 m/s².

The acceleration of the motor bike is 4 m/s².

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The flow rate of incoming solar energy, as measured at the top of the atmosphere is called: insolation

The insolation is known as the amount of radiation from the sun's energy that the planet receives. A portion of the energy is absorbed or reflected by the atmosphere and another portion reaches the surface.

The insolation is caused major by:

The solar energy is a type of energy whose source is the sun that radiates heat.

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