The radius is increasing at a rate of 0.31cm/sec.
We know the volume of the balloon is increasing at a rate of 3.3 [tex]ft^{3} min[/tex]
This is expressed as:
[tex]\frac{dV}{dT}[/tex] = 3.3
The volume of a sphere is given by:
V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
The question asks to find the rate of which the radius is increasing when the radius is 0.65 feet.
We need to find:
[tex]\frac{dr}{dt}[/tex]
Since we don't have t in our equation, we will be differentiating implicitly. We can use the chain rule for this:
[tex]\frac{dV}{dT}[/tex] = [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]
We already know
[tex]\frac{dV}{dT}[/tex] = 3.3
∴
3.3 = [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]
To find [tex]\frac{dV}{dR}[/tex] we differentiate V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
∴
3.3 = 4[tex]\frac{3.3}{5.30}[/tex][tex]r^{2}[/tex].[tex]\frac{dr}{dt}[/tex]
Dividing ,
[tex]\frac{3.3}{5.30}[/tex] = [tex]\frac{dr}{dt}[/tex] = 0.622 ft/min = 0.31 cm/sec
The radius is increasing at a rate of 0.31cm/sec.
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What must the charge (sign and magnitude) of a particle of mass 1. 45 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 660 n/c?
The charge (sign and magnitude) of a particle of mass 1.45 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 660 N/C is -2.19C
A particle with some charge moving in an electric field experience force due to electric field.
For the charged particle to remain stationary the force due to electric field and the weight of the particle should be equal.
Force due to electric field = QE
where, Q is the charge of the particle
E is the electric field = 660N/C
Weight of the particle = mg
where, m is the mass of particle = 1.45g = 0.00145kg
g is the acceleration due to gravity = 10m/s²
Hence, force due to electric field = weight of the particle
QE = mg
⇒ Q × 660 = 0.00145 × 10
⇒ Q = 2.19 C
Since the electric field is downward, hence to balance the charged particle, the force applied should be in the upwards direction. So, this is possible if the charge Q is negative.
So, the charged particle has a charge of -2.19C
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A fisherman's scale stretches 3. 2 cm when a 2. 6 kg fish hangs from it. part a what is the spring stiffness constant?
The spring stiffness constant is 796.25 N/m.
A spring's "spring constant" is a property that quantifies the relationship between the force acting on the spring and the displacement it produces.
The slope of the plot of the straight line W vs x represents the spring constant, K. Weight (W) is defined as mass times the gravitational acceleration (g), where g is equal to approximately 980 cm/sec².
Mass of the fish = 2.6 kg
Length of the fisherman's scale, x = 3.2 cm
= 3.2/100 m
= 0.032 m
We have to find the value of k;
We know that,
F = - kx
Where k is the spring constant,
F is the force applied over x
x is the displacement by the spring expressed in N/m.
mg = - kx
g = 9.8 m/s²
[tex]K = \frac{mg}{x}[/tex]
[tex]= \frac{2.6*9.8}{0.032}[/tex]
[tex]= 796.25 N/m[/tex]
Therefore, the spring's constant is 796.25 N/m.
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The mechanical energy of a system of objects is conserved: Group of answer choices only when the objects move along closed paths none of the above only when the work done by the resultant external force is zero only when external forces act on the objects always
The mechanical energy of a system of objects is conserved only when the work done by the resultant external force is zero.
What is mechanical energy?Mechanical energy is a special class of energy that an object contains due to its relative position or motion/movement level.
This type of energy (mechanical energy) is associated with both kinetic motion energy and potential (stored) energy.
In conclusion, the mechanical energy of a system of objects is conserved only when the work done by the resultant external force is zero.
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2. A rectangular block of weight 300N measures 0.1 m by 0.4 m by 1.5 m.
a) Draw a diagram to show how the block must rest to exert the maximum pressure on the ground. Calculate this
pressure.
b) Draw another diagram showing the position of minimum pressure. Calculate this pressure.
Answer:
that's all I could do.hope it helps.
a lamp marked 100w 250v is lit up for 10hours, costs 2I what is the cost of lighting the lamp
Answer:
2k
Explanation:
100W X 10h = 1000Wh = 1KWh thus cost is 2k
The quartz crystal in a digital watch has a frequency of 32. 8 khz. what is its period of oscillation?
Time Period of Oscillation-1/32800 Hz
Time Period of Oscillation - 3.04 × 10¹.
Two related parameters are oscillation frequency and period. Actually, they are the opposites of one another. As a result, the following formula can be used to determine the quartz crystal's oscillation period:
Time Period of Oscillation = 1/Oscillation Frequency
where.
Frequency of Oscillation-32.8 KHz
Frequency of Oscillation - 32800 H₂
Therefore
Time Period of Oscillation-1/32800 Hz
Time Period of Oscillation - 3.04 × 10¹.
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The time period of oscillation is 3.04×10
what is time period?
A time period (denoted by 'T'' ) is the time taken for one complete cycle of vibration to pass a given point.[1] As the frequency of a wave increases, the time period of the wave decreases. The unit for time period is 'seconds'.
The related parameters are oscillation frequency and period.They are the opposite of the another.As a result the formula to be used is
frequency=1/time
given:
Frequency of oscillation=32.8khz=32800hz
therefore,
time period of oscillation=1/32800hz
time period of oscillation=3.04×10
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A rock with a mass of 3 kilograms is put aboard an airplane in new york city and flown to boston. how much work does the gravitational field of the earth do on the rock?
The amount of work done by the gravitational field of the earth do on the rock is 29.4 d (J).
What is work done?Work is done when energy is transferred from one store to another.
Work is also done when a force causes an object to move.
The amount of work done by the gravitational field of the earth do on the rock is calculated as follows;
W = Fd
where;
F is gravitational force of the rockd is the displacement of the rockW = (mg)d
W = (3 x 9.8)d
W = 29.4 d
Thus, the amount of work done by the gravitational field of the earth do on the rock is 29.4 d (J).
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Open the resistance in a wire simulation, adjust only the length of the resistor, what happens to resistor?
If we increase the length of the resistor, resistance will also increase and vice-versa.
It is given that in a wire simulation, we have to adjust only the length of the resistor.
It required to find the effect on resistor when adjust only the length of the resistor.
What happens to resistor when adjust only the length of the resistor?As we know that the length is directly proportional to the resistance of the wire that means is we increase the size or length of the wire then it also increase the resistance present in the wire. On the other hand if we decrease the length of the wire, it will decrease the resistance. This can be represented as:
Resistance = resistivity × length/area
This is also because there is more collision of the flowing electrons in the wire to the metal ions present there.
Thus if we increase the length of the resistor, resistance will also increase and vice-versa.
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A horizontal 52-n force is needed to slide a box across a flat surface at a constant velocity of 3.5 m/s. what is the coefficient of kinetic friction between the box and the floor?
μk = 0.106 is the coefficient of kinetic friction between the box and the floor
When the box is moving across the flat surface with a constant velocity, the force applied to it must be equal to the kinetic frictional force applied to the object:
F = μk*W = μk*mg
Where,
F = Force applied on box = 52 N
m = mass of box = 50 kg
g = 9.8 m/s²
μk = coefficient of kinetic friction between box and floor
hence,
52 N = μk(50 kg)(9.8 m/s²)
μk = (52 N)/(490 N)
μk = 0.106
Kinetic friction is the name for a force that exists between sliding parts. A force opposing a body's forward motion is applied to one that is moving on the surface. The kinetic friction coefficient between the two materials will determine the magnitude of the force.
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The electric field inside a metallic conductor that is in electrostatic equilibrium is?
The electric field inside a metallic conductor that is in electrostatic equilibrium is zero.
An electric field is a physical field that surrounds electrically charged particles and acts as an attractor or repellent to all other charged particles in the vicinity. It can also refer to a system of charged particles' physical field.
Since there are many electrons, there is also a strong force of repulsion between them. Therefore, the electrons travel to the conductor's surface to reduce the repulsion between them. Therefore, we can state that there is no net charge present inside the conductor.
So, The electric field inside a metallic conductor that is in electrostatic equilibrium is zero.
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What is (a) the wavenumber and (b) the wavelength of the radiation used by an fm radio transmitter broadcasting at 92. 0 mhz?
The wavenumber and (b) the wavelength of the radiation used by an fm radio transmitter broadcasting at 92. 0 mhz will be 31.25 * [tex]10^{2}[/tex] [tex]m^{-1}[/tex] and 0.032 * [tex]10^{2}[/tex] m respectively
Forms of electromagnetic radiation like radio waves, light waves or infrared (heat) waves make characteristic patterns as they travel through space. Each wave has a certain shape and length. The distance between peaks (high points) is called wavelength.
Wavenumber, also called wave number, a unit of frequency, often used in atomic, molecular, and nuclear spectroscopy, equal to the true frequency divided by the speed of the wave and thus equal to the number of waves in a unit distance.
wavelength = ?
frequency = 92 m Hz = 92 * [tex]10^{6}[/tex] Hz
speed of light = 3 * [tex]10^{8}[/tex] m/s
speed of light = frequency * wavelength
wavelength = speed of light / frequency
= 3 * [tex]10^{8}[/tex] / 92 * [tex]10^{6}[/tex]
= 0.032 * [tex]10^{2}[/tex] m
wavenumber = 1 / wavelength
= 1 / 0.032 * [tex]10^{2}[/tex] m
= 31.25 * [tex]10^{2}[/tex] [tex]m^{-1}[/tex]
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A stationary observer observes a spaceship fly-by. As the spaceship's velocity gets closer to the speed of light, the stationary observer:
A stationary observer observes a spaceship fly by. As the spaceship's velocity gets closer to the speed of light, the stationary observer would see the spaceship as being “blue-shifted” on the visible light spectrum.
This would also lead to the feeling of a faster time on the clock.
What is the Speed of Light?
This refers to the speed in which light waves propagate through different materials.
Hence, we can see that based on the fact that the observer is stationary and is observing a spaceship that is in outer space get to the speed of light, the stationary observer would see the spaceship as being “blue-shifted” on the visible light spectrum.
This is because the observer would come to the conclusions that the
Earth would appear blue-shifted its clocks would be moving more quickly than expected.
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A 1300 kg sports car can accelerate from 0 to 27 m/s in 5.2 seconds. How much power from the engine is directly going into accelerating the car? Group of answer choices 474,000 W 3375 W 35,100 W 91,100 W
The power expended is calculated as 91,100 W.
What is the power?We know that the acceleration can be obtained by the use of the equation;
v = u + at
v = final velocity
u = initial velocity
t = time
a = acceleration
a= v - u/t
a = 27 - 0/ 5.2 = 5.2 m/s^2
Thus;
v^2 = u^2 + 2as
but u= 0 m/s
v^2 = 2as
s = v^2/2a
s = (27)^2/2 * 5.2
s = 70 m
Now;
Work done = 1300 kg * 5.2 m/s^2 * 70 m = 473200 J
Power = 473200 J/5.2 seconds
Power = 91,100 W
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Calculate the energy of the violet light emitted by a hydrogen atom with a wavelength of 410. 1 nm
The energy of the violet light emitted by a hydrogen atom with a wavelength of 410. 1 nm will be 4.85 * [tex]10^{-19}[/tex] J
Light energy is a form of electromagnetic radiation that comprises wavelengths that the common human eye can detect. Light is a type of kinetic energy. It consists of particles like photons, which have wave-like properties. It can affect the physiology of an organism, like photosynthesis or the sense of sight.
Energy = h*c / lambda
where
h = plank's constant = 6.626 * [tex]10^{-34}[/tex] J-s
c = speed of light = 3 * [tex]10^{8}[/tex] m/s
lambda = wavelength = 410. 1 nm = 410. 1 * [tex]10^{-9}[/tex] m
Energy = 6.626 * [tex]10^{-34}[/tex] * 3 * [tex]10^{8}[/tex] / 410. 1 * [tex]10^{-9}[/tex]
= 4.85 * [tex]10^{-19}[/tex] J
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Our milky way galaxy is 100000 lyly in diameter. a spaceship crossing the galaxy measures the galaxy's diameter to be a mere 1. 0 lyly. what is the speed of the spaceship relative to the galaxy?
The speed of the spaceship relative to the galaxy is 0.99999995c.
A light-year measures distance rather than time (as the name might imply). A light-year is a distance a light beam travels in one year on Earth, which is roughly 6 trillion miles (9.7 trillion kilometers). One light-year equals 5,878,625,370,000 miles. Light moves at a speed of 670,616,629 mph (1,079,252,849 km/h) in a vacuum.We multiply this speed by the number of hours in a year to calculate the distance of a light-year (8,766).
The Milky way galaxy is 100,000 light years in diameter.
The galaxy's diameter is a mere 1. 0 ly.
We know that ;
[tex]L = L_0 \sqrt{1-\frac{v^2}{c^2} }[/tex]
L = 1 light year
L₀ = 100,000 light year
[tex]1 = 100,000 \sqrt{1-\frac{v^2}{c^2} }[/tex]
[tex]1 = 100,000 \sqrt{1-\frac{v^2}{(3*10^8)^2} }[/tex]
[tex]\frac{1}{100,000} = \sqrt{1-\frac{v^2}{c^2} }[/tex]
[tex]v = 0.999999995[/tex] [tex]c[/tex]
Therefore, the speed of the spaceship relative to the galaxy is 0.99999995c.
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A laser emits light with a frequency of 4. 75×1014 s−1. What is the wavelength of this radiation, in nm?.
A Final statement or concluding statement
The equation that relates wavelength, frequency, and speed of light is
c=λ × ν
To find wavelength, λ = c / f
λ = wavelength in meters
ν = frequency in Hertz (Hz) or 1s or [tex]s^{-1}[/tex].
= 3 ×[tex]10^{8}[/tex] m/s / 4. 75 × [tex]10^{14}[/tex] [tex]s^{-1}[/tex](Using velocity of light as 3 x 108 m/s)
= [tex]6.3[/tex]×[tex]10^{-7}[/tex]m
= [tex]6.3[/tex] × [tex]10^{2}[/tex] nm
How is wavelength related to radiation?Electromagnetic radiation is an electric and magnetic disturbance that travels at the speed of light through space. It has no mass or charge and travels in packets of radiant energy known as photons or quanta.Radio waves and microwaves, as well as infrared, ultraviolet, gamma, and x-rays, are examples of EM radiation. Electromagnetic radiation moves at a constant speed in the form of a waveform.
The relationship of velocity to wavelength and frequency reveals the wave characteristics of EM radiation.
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Write an expression for elastic potential energy of a spring?
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\leadsto[/tex] The elastic potential energy of a spring can be said to be the energy possessed by a spring due to a force that compresses or stretches the spring. This can also be said to be the work which is done by the applied force against the restoring force of the spring, which is stored as the elastic potential energy.
The elastic potential of a spring can be expressed as:
▪ [tex]\longrightarrow \sf{PE= \: \dfrac{1}{2} kx}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \bm{PE= \: \dfrac{1}{2} kx}[/tex]
Select the correct answer from the drop-down menu. anne applies a force on a toy car and makes it move forward. what can be said about the forces acting on the toy car at the moment anne applies the force? the forces acting on the toy car are .
Answer:
The forces could be gravity, friction between the car and the ground, the force Katie is applying and the normal reaction.
a man uses a 900 watt electric iron to press his clothes for an average of 4 hours a week for five weeks if the cost of an electric energy is 3 Kobo per unit calculate the cost of electric energy for pressing
Answer:
[tex] \boxed{\sf54 \: kobo}[/tex]
Explanation:
Energy = Power × Time
Energy = 900× 4 ×5 = 18000 wh
Energy = 18000 wh = 18 kwh
Cost of 1 unit electricity = 3 kobo
cost of 18 unit electricity= 18 × 3 = 54 kobo
Answer:
54 Kobo
Explanation:
Units of electricity are measured in kilowatt hours (kWh).
Given information:
900 watt electric ironAppliance usage = 4 hours a week for 5 weeksUnit cost of electricity = 3 Kobo per kWhStep 1Convert the wattage of the electric iron from watts to kilowatts.
1000 watts (W) = 1 kilowatt (kW)
⇒ 900 watts = 1 ÷ 1000 = 0.9 kilowatts
This means that the power consumption of the electric iron is 0.9 kW per hour of use.
Step 2Total hours spent pressing clothes:
= 4 hours per week for 5 weeks
= 4 × 5
= 20 hours
Total power consumption:
= number of kW × number of hours
= 0.9 × 20
= 18 kWh
Step 3To find the total cost, multiply the total kWh by the cost per kWh:
⇒ Cost = 18 × 3 = 54 Kobo
When we come out in the sun, we feel warm. How does the heat from the sun reach us?
Answer:
RadiationExplanation:
Greetings !The Sun reaches us by propagating through the vacuum of space. Sunlight reaches the Earth in about 8 minutes and 20 seconds. When this energy reaches the Earth's atmosphere, both conduction and convection play key roles to scatter it throughout the planet.
Answer: The heat from the sun reaches us through radiation and processes such as conduction and convection helps to scatter that heat on the surface of our planet.
Explanation:
The phenomenon behind the Sun's heat reaching us is radiation. It does this by propagating through the vacuum of space.
The amount of time it takes for the sunlight to reach us on Earth is approximately 8 minutes and 20 seconds. When it reaches our planet, conduction, the movement of heat or electricity through a medium or passage, as well as convection, the rising of hotter and less dense material and sinking of colder and more dense/denser material, helps to scatter the heat on Earth's surface.
Approximating the eye as a single thin lens 2. 75 cmcm from the retina, find the eye's near-point distance if the smallest focal length the eye can produce is 2. 20 cm.
The near-point distance of the eye is 11 cm.
What is the eye's near-point distance?The near-point distance of the eye is the closest possible distance an object can be from the eye in order for its image to be formed on the retina. It can also be termed the closest distance of accommodation.
The near-point distance of the eye in the given scenario can be calculated using the lens formula given below:
1/f = 1/v + 1/u
where;
f = focal length
v = image distance
u = object distance
From the data provided;
f = 2.20 cm
v = 2.75 cm
u = ?
Solving for u:
1/u = 1/f - 1/v
1/u = 1/2.20 - 1/2.75
1/u = 0.91
u = 11 cm
In conclusion, the lens formula is used to determine the eye's near-point distance.
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What do the mural paintings at dura-europos suggest was a component of the decoration of many late antique synagogues?
The mural paintings at Dura-europos suggested narrative scenes were part of the component of the decoration of many late antique synagogues in this type of context.
What is Mural painting?This refers to a type of graphic work which is usually done on walls, ceilings etc. This is usually done by a professional known as a painter and uses different techniques to get the right shades and shape.
This type of painting was used at Dura-europos in which different narrative scenes served as a component for the many late antique synagogues in this aspect and context of artwork present during that period of time.
This therefore makes narrative scenes the most appropriate choice.
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A sound wave has a speed of 340 m/s and a frequency of 1000 hz. The period of the sound is closest to?
The frequency and the period are inversely proportional.
[tex]f=\dfrac{1}{T}[/tex] where T is the period
Solving the QuestionWe're given:
v = 340 m/sf = 1000 HzBecause the frequency and the period are reciprocals of each other, we can find the period of the sound by finding the reciprocal of the frequency:
[tex]T=\dfrac{1}{1000}[/tex]
Answer[tex]T=\dfrac{1}{1000}[/tex]
What was the possible impact of the maunder minimum on earth?
a) lower temperatures
b) higher temperatures
c) more hours of daylight
d) less hours of daylight
The possible impact of the maunder minimum on earth is a) lower temperatures
The Maunder Minimum, also known as the "prolonged sunspot minimum", was a period around 1645 to 1715 during which sunspots became exceedingly rare. During a 28-year period (1672–1699) within the minimum, observations revealed fewer than 50 sunspots.
The most recent grand solar minimum occurred during Maunder Minimum (1645–1710), which led to reduction of solar irradiance by 0.22% from the modern one and a decrease of the average terrestrial temperature by 1.0–1.5°C
During the Maunder Minimum, the Sun emitted less strong ultraviolet light, and so less ozone formed. The decrease in ozone affected planetary waves, the giant wiggles in the jet stream that we are used to seeing on television weather reports
correct option is
a) lower temperatures
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How much work is needed to stretch this spring a distance of 5. 0 cm , starting with it unstretched?
The work done by the unstretched spring is 5 J.
What is the Hooke's law?Hooke's law states that the extension of a given material is directly proportional to the force applied as log as the elastic limit is not exceeded. Thus we have to know that; F = Ke
F = force applied
K = force constant
e = extension
Using the graph;
K = F/e
F = 200N
e = 5 cm or 5 * 10^-2 m
K = 200N/ 5 * 10^-2 m
K = 4000 N/m
Now;
Work = 1/2Ke^2
Work = 0.5 * 4000 N/m * (5 * 10^-2 m)^2
Work = 5 J
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I WILL MARK U BRAINLIEST IF U ANSWER THIS QUESTION! NEED IT ASAP PLS
A concave mirror is also referred to as a converging mirror and it can be defined as a type of mirror that is designed and developed with a reflective surface that is typically curved inward and away from the source of light.
Basically, one common use of a convex mirror include the following:
Shaving mirrorsSearchlightsDental mirrors.What is a convex mirror?A convex mirror is also referred to as a diverging mirror and it can be defined as a type of mirror that is designed and developed with a reflective surface that typically bulges outward toward the source of light.
Basically, one common use of convex mirror is as rear-view mirrors in automobiles vehicles.
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John and henry are both workers at a retail store. their direct supervisor has told them to maintain quick service above all else. later, their customer relations director tells them that they should always work to maintain excellent customer service above all else. both john and henry are confused as to what their priorities should be. this is an example of a conflict based on ______. a. personality differences b. power struggle c. poor communication d. jealousy please select the best answer from the choices provided a b c d
Poor communication
This is an example of a conflict based on poor communication. Because of the reason is that in customer service a person should have skills to communicate in a good manner. It is important because if the person has this skill that he can communicate with others best.
Then he can impress the customer and realize customer about the qualities of their product. In every kind of business, communication skills play major role. Therefore, both john and Henry are confused as their priorities should be on focus to improve their communication skills.
What is poor communication ?When there is a disconnect between what is said and what is heard, poor communication frequently results. In other words, the individual to whom the communication is being directed misinterprets what you are trying to convey. There is no longer mutual understanding.
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Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65. The component of the longer vector along the line of the shorter is?
Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65. The component of the longer vector along the line of the shorter is 6.33 .
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.
The taller component will be 15 . There will be two components taller component , one in the direction of shorter component and other perpendicular to the shorter wavelength .
The component of longer wavelength in the direction of shorter will be
= 15 cos (theta ) = 15 cos (65) = 6.33
where theta is the angle between both the vectors
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If the resistance in a circuit connected to a constant current is halved, how is the voltage in the circuit affected?.
Answer:
Voltage will be 1/2 original
Explanation:
V = I R if I is constant
V = k R now multiply both sides by 1/2
1/2 V = k 1/2 R <===== you can see the voltage is halved too
Newton’s ____________ law of motion states that the acceleration of a person or object is proportional to the force applied to it and inversely proportional to its mass.
Newton’s second law of motion states that the acceleration of a person or object is proportional to the force applied to it and inversely proportional to its mass.