math
Determine if the function below is continuous.

graph of a piecewise function, with 2 pieces. The first piece is a line that starts at negative infinity and goes through point (-4,5) and ends with an open dot at (1,0). The second piece is a line that starts with a closed dot at (1,-1), goes through point (2,1) and continues to infinity.

A. not continuous at x = 1
B. not continuous at x = 0
C. not continuous at x = -1
D. continuous

The mechanical advantage of ramp A is greater than others and it will require the least force to move the load to greater distance.

The mechanical advantage of the ramp is calculated as follows;

\(M.A = \frac{L}{h}\)

The mechanical advantage of the ramp B, C, D and E is calculated as;

\(M.A = \frac{L}{h} \\\\\)

The mechanical advantage of the ramp A is calculated as follows;

\(M.A = \frac{2L}{h} \\\\M.A = 2(\frac{L}{h} )\)

Since the length of the ramp A is greater than other ramps, the mechanical advantage will be greater and it will require the least force to move the load to greater distance.

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Answer: true

Explanation: a force can be anything that effects an object, as long as the object moves

The time required to crumple the barrier and safely slow down the person with a force of 1650 N is approximately C, 1.1 seconds.

To determine the time required to crumple the barrier and safely slow down the person with a maximum force of 1650 N, use the equation of motion:

F = m × a

where:

F = force

m = mass

a = acceleration

Given:

m = 68 kg

F = 1650 N

Find the acceleration (a) first. Rearranging the equation:

a = F / m

Substituting the values:

a = 1650 N / 68 kg

a ≈ 24.26 m/s²

Now, use the equation of motion to find the time (t):

v = u + at

where:

v = final velocity (0 m/s as the person comes to a stop)

u = initial velocity (27 m/s)

a = acceleration (24.26 m/s²)

t = time

Rearranging the equation:

t = (v - u) / a

Substituting the values:

t = (0 m/s - 27 m/s) / 24.26 m/s²

t ≈ -27 m/s / 24.26 m/s²

t ≈ -1.11 s

The negative sign indicates that the time is in the opposite direction to the initial velocity. Taking the absolute value, the time required to crumple the barrier and safely slow down the person with a force of 1650 N is approximately 1.11 seconds.

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The term for basic unit of electric current is called the ampere

Electricity is a collection of physical phenomena related to the presence and motion of matter having an electric charge. Both electricity and magnetism are related to the phenomenon of electromagnetic, as defined by Maxwell's equations.

For electricity generation, the three basic forms of energy are fossil fuels (coal, natural gas, and petroleum), nuclear energy, and renewable energy sources. The majority of electricity is produced by steam turbines powered by fossil fuels, nuclear, biofuels, geothermal, and solar thermal energy.

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This question involves the concepts of thickness and length.

"40" gold atoms could stack on top of one another in the gold foil.

We will use the unitary method here to find out the no. of gold atoms that could stack on top of each other in the gold foil of thickness 1 x 10⁻⁷ m, when the side length of each cubic atom is 2.5 x 10⁻⁹ m.

Therefore,

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The pressure of a tank of uniform cross-sectional area 4.0m2 when the tank is filled with water at a depth of 6m is 58800 Pa.

To find the pressure in the tank, we can use the formula for pressure:

Pressure = density x gravity x height

Density of water (ρ) = 1000 kg/m³

Acceleration due to gravity (g) = 9.8 m/s²

Height (h) = 6 m

Thus:

Pressure = 1000 kg/m³ x 9.8 m/s² x 6 m

Pressure = 58800 kg/(m·s²)

Since the unit of pressure is Pascal (Pa), which is equivalent to kg/(m·s²), the pressure in the tank is:

Pressure = 58800 Pa

Therefore, the pressure in the tank when it is filled with water to a depth of 6 m is 58800 Pascal.

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Each day the Moon's appearance changes depending on where it is in its earth orbit. The pattern of day and night is followed only due to the rotation of the earth.

The phrases revolution and rotation describe the various movements of the earth. Rotation is the tendency of the planet on its axis.

The movement of the earth around the sun is a definite path or orbit known as revolution. The earth's axis, a fictional line, makes a 6612° angle with its orbital plane.

The rotation of the earth on its axis does not cause night and day. The occurrence of night and day is caused by the rotation of the earth.

The lunar cycle begins when the Sun, Moon, and Earth are aligned (the Moon is between the Earth and the Sun, and the hemisphere of the Moon faces away from the Earth.

As a result, if the moon took longer to orbit the Earth, the pattern would be disrupted.

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A 66.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. He then drops through a height of 1.59 m, and ends with a speed of 8.51 m/s. The nonconservative work done on the boy is approximately -42.7 kilojoules.

To find the nonconservative work done on the boy, we need to consider the change in the boy's mechanical energy during the process. Mechanical energy is the sum of the boy's kinetic energy (KE) and gravitational potential energy (PE).

The initial mechanical energy of the boy is given by the sum of his kinetic energy and potential energy when he catches the wave:

E_initial = KE_initial + PE_initial

The final mechanical energy of the boy is given by the sum of his kinetic energy and potential energy after he drops through the height:

E_final = KE_final + PE_final

The nonconservative work done on the boy is equal to the change in mechanical energy:

Work_nonconservative = E_final - E_initial

Let's calculate each term:

KE_initial = (1/2) * m * v_initial^2

= (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = m * g * h_initial

= 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * m * v_final^2

= (1/2) * 66.1 kg * (8.51 m/s)^2

PE_final = m * g * h_final

= 66.1 kg * 9.8 m/s^2 * 0

Since the boy ends at ground level, the final potential energy is zero.

Substituting the values into the equation for nonconservative work:

Work_nonconservative = (KE_final + PE_final) - (KE_initial + PE_initial)

Simplifying:

Work_nonconservative = KE_final - KE_initial - PE_initial

Calculating the values:

KE_initial = (1/2) * 66.1 kg * (1.60 m/s)^2

PE_initial = 66.1 kg * 9.8 m/s^2 * 1.59 m

KE_final = (1/2) * 66.1 kg * (8.51 m/s)^2

Substituting the values:

Work_nonconservative = [(1/2) * 66.1 kg * (8.51 m/s)^2] - [(1/2) * 66.1 kg * (1.60 m/s)^2 - 66.1 kg * 9.8 m/s^2 * 1.59 m]

Calculating the result:

Work_nonconservative ≈ -42.7 kJ

Therefore, the nonconservative work done on the boy is approximately -42.7 kilojoules. The negative sign indicates that work is done on the boy, meaning that energy is transferred away from the boy during the process.

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The focal length is the sum of the focal lengths of the front and back surfaces, which equals 70 cm.

The complete question is,

A narrow plano-convex lens' focal length should be determined. This lens's back surface is curved at a radius of R 2R 2 = approximately 35 cm, while its front surface is flat. Let's say the lens has an index of refraction of 1.5.      

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Answer:

To verify that they're polarized, he could hold the two lenses perpendicular (90 degrees) to each other, one lens in front of the other, and point it at a light source. If no light passes through then the lenses are polarized

The test of Polarization of pair of sunglasses is , hold the two lenses perpendicular to each other, one lens in front of the other, and point it towards a light source. If no light passes through then the lenses are polarized.

For example, when fishing on a sunny day, you wouldn't see through the water. You would only see a reflection of the sun hitting the water.

To verify that  pair of sunglasses are  polarized, he could hold the two lenses perpendicular  to each other, one lens in front of the other, and point it towards a light source. If no light passes through then the lenses are polarized.

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The increase in length of the iron wire when warmed from 20°C to 45°C is approximately 8.25 millimeters. The specific heat capacity of the object is approximately 9.62 J/kg°C. The heat capacity of the object is approximately 1.83 J/°C.

ΔL = L × α × ΔT

Where:

ΔL is the change in length

L is the original length of the wire

α is the coefficient of linear expansion for iron

ΔT is the change in temperature

The coefficient of linear expansion for iron is typically 1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\).

Given:

L = 30 m (original length of the wire)

α = 1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\) (coefficient of linear expansion)

ΔT = 45°C - 20°C = 25°C (change in temperature)

ΔL = 30 m × (1.1 x \(10^(^-^5^)\) °\(C^(^-^1^)\)) × 25°C

= 30 m × 1.1 x\(10^(^-^5^)\) × 25

= 8.25 x \(10^(^-^3^)\) m

2) Q = mcΔT

Where:

Q is the heat energy transferred

m is the mass of the object

c is the specific heat capacity

ΔT is the change in temperature

Given:

Q = 2200 J (heat energy transferred)

m = 190 g (mass of the object)

ΔT = 12°C (change in temperature)

a. Specific heat capacity (c):

one need to rearrange the formula to solve for c:

c = Q / (m × ΔT)

Substituting the given values:

c = 2200 J / (190 g × 12°C)

First, need to convert the mass to kilograms:

m = 190 g = 190 g / 1000 = 0.19 kg

Now can calculate the specific heat capacity:

c = 2200 J / (0.19 kg × 12°C)

= 9.62 J/(kg°C)

b. Heat capacity (C):

The heat capacity is the amount of heat energy required to raise the temperature of the object by 1 degree Celsius.

C = mc

Substituting the given values:

C = 0.19 kg × 9.62 J/(kg°C)

= 1.83 J/°C

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Given the frequency is 1/6π

A maximum value is 12

A minimum value is -6

A y-intercept is 3.

The general form of the sinusoidal function,

Given

The maximum value is 12.

The minimum value is -6.

the y-intercept of 3.

Thus, the given option (a) is correct.

Answer:

11948.64 Newtons

Explanation:

The displacement of the box is obtained as 13.48 m along the horizontal surface.

Let us recall that the displacement is the distance covered in a specific direction. The displacement is a vector quantity because it has both magnitude and direction.

In this case, we want to obtain the displacement of the box when;

Initial velocity u = 6.50 m/s

final velocity v =  13.0 m/s

Acceleration a = 4.70 m/s2

Now;

v^2 = u^2 + 2as

s = v^2 -  u^2 /2a

s = (13)^2 - (6.5)^2/ 2 (4.70)

s = 126.75/9.4

s = 13.48 m along the horizontal surface

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Considering the Coulomb's Law, the force between the two ballons is 9.216×10⁻⁸ N.

Charged bodies experience a force of attraction or repulsion on approach.

From Coulomb's Law it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.

From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:

\(F=k\frac{Qq}{d^{2} }\)

where:

The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

In this case, you know that two balloons have a negative charge of 1.6×10⁻¹⁰ C and the balloons are 0.05 m apart.

Replacing in the Coulomb's Law, you get:

\(F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{(-1.6x10^{-10} C)x(-1.6x10^{-10} C)}{(0.05 m)^{2} }\)

Solving:

\(F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{2.56x10^{-20} C^{2} }{(0.05 m)^{2} }\)

\(F=9x10^{9} \frac{Nm^{2} }{C^{2} } 1.024x10^{-17}\frac{ C^{2} }{m^{2} }\)

F= 9.216×10⁻⁸ N

Finally, the force between the two ballons is 9.216×10⁻⁸ N.

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Answer:

A

Explanation:

insects undergo Pupal life cycle

We know that in a collision the momentum of the system is conserved, that is:

In this case, since the railroad cars coupled together and have the same mass we have:

Now, we know the initial velocity of the cars, one is traveling at 5 m/s and the other is at rest; plugging the values and solving for the final velocity we have:

Therefore, the velocity of the combined cars is 2.5 m/s

The run will be able to open in 4 hours when machine-made snow is produced while it is snowing naturally.

Let the rate of production of machine-made snow be m units/hour, and the rate of snowfall be n units/hour. From the given information, we know that:

m × 4 = n × 12 => m/n = 3/1

Let the time taken for the run to open when both types of snow are produced simultaneously be t hours.

In that time, the ski resort will have produced mt units of machine-made snow and nt units of naturally falling snow.

We also know that mt + nt is equal to the amount of snow required to open the run. Therefore:

mt + nt = m × 4 => nt = m(4 - t) (1) and

mt + nt = n × t => mt = n(t - 12) (2)

Substituting the value of m/n obtained above in (1), we have:

nt = 3n(4 - t) => nt = 12n - 3nt => nt = 6n (3)

Substituting the value of mt obtained above in (2), we have:

n(t - 12) = 3nt => t = 4 hours

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When two objects held close together and then released, they move toward each other. The phenomenon can be explained by the Coulomb's Law. Coulomb's Law is given by: $F=k\frac{q_{1}q_{2}}{r^2}$ where F is the electrostatic force, q1 and q2 are the magnitudes of the charges, r is the distance between the centers of the charged objects, and k is Coulomb's constant.

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Answer:

Approximately \(3.967\; {\rm kg\cdot m\cdot s^{-1}}\).

Explanation:

Convert velocity to the standard units (meters per second):

\(\begin{aligned}v &= 246.2 \; {\rm km \cdot h^{-1}} \\ &= 246.2 \; {\rm km \cdot h^{-1}}\times \frac{1\; {\rm h}}{3600\; {\rm s}} \times \frac{1000\; {\rm m}}{1\; {\rm km}} \\ &\approx 68.389\; {\rm m\cdot s^{-1}}\end{aligned}\).

Convert mass to standard units (kilograms):

\(\begin{aligned} m &= 58\; {\rm g} \\ &= 58\; {\rm g} \times\frac{1\; {\rm kg}}{1000\; {\rm g}}\\ &= 0.058\; {\rm kg}\end{aligned}\).

When an object of mass \(m\) travels at a velocity of \(v\), momentum of that object would be \(p = m\, v\). In standard units, the momentum of this tennis ball would be:

\(\begin{aligned}p &= m\, v \\ &\approx (0.058\; {\rm kg})\, (68.389\; {\rm m\cdot s^{-1}}) \\ &\approx 3.967\; {\rm kg \cdot m\cdot s^{-1}}\end{aligned}\).

Answer:

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Substituting the given values, we get:

V = π(5.0 cm)^2(10.0 cm) = 785.4 cm^3

The radius and height are both given to two significant figures, so the answer should also be reported to two significant figures. Therefore, the volume of the cylinder can be determined to 780 cm^3.

Explanation:

Kindly give it a five-star rating.

Answer:

0.25m/s^2

Explanation:

F = ma

a = F/m

(Newton's Second Law)

The current in the series circuit  across a 9.0 V potential difference is determined as 0.333 A.

The current in the series circuit is determined by applying ohms law as shown below;

V = IR

where;

R = 12 Ω  + 15 Ω  = 27 Ω

I = V/R

I = 9/27

I = 0.333 A

Thus, the current in the series circuit  across a 9.0 V potential difference is determined as 0.333 A.

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Answer:

The magnitude of the magnetic field is  \(B = 1.392 *10^{-6} \ T\)

Explanation:

From the  question we are told that

     The distance of the position that is being considered to the conductor is

         \(d = 16 \ cm = 0.16 \ m\)

      The current  flowing through  conductor is  \(I = 3.50 \ A\)

Generally the magnitude of the magnetic  field due to a current carrying conductor  is mathematically represented as

          \(B = \frac{\mu_o I}{2 \pi d}\)

Where   is the permeability of free space with value  \(\mu_o = 4\pi * 10^{-7} N/A^2\)

substituting values

           \(B = \frac{ 4\p *10^{-7} *3.50}{2 * 3.142* 0.16}\)

            \(B = 1.392 *10^{-6} \ T\)

Answer:

upper part second pic

Explanation:

if you observe the trend it increases with each lap and the guy increases the distance he has covered with each lap so distance increases with time

Graph B is correct graph with increase in time distance increases linearly. Displacement is not like that.

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.

Distance is scalar quantity it will increase linearly with time as Hagen is running in the ground.

The two graphs, x vs. t that are distance vs time  appear as linear.

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Answer:

Explanation:

Conservation of momentum

115v + 133(0) = (115 + 133)1.35

v = 2.911304...

v= 2.91 m/s east

Answer:

The velocity east is 2.91

Explanation:

Fill in the box

2.91

Answer:

It will travel 350 meters each second.

Explanation:

The unit rate, 350 m/s, tells us that the jet will travel 350 meters per every second elapsed.

Answer:

5.83 seconds

Explanation:

60 seconds in 1 minute

350 meters per second

350/60

=5.83