What dimensions will produce a box with the largest volume?
A manufacturer wants to design an open top box with a square base having a surface area of 108 square inches.
Answers
Answer: The dimensions that will produce a box with the largest volume and a surface area of 108 square inches are l = h =√(54) and w = (108 - 2lh)/(2l + 2h) = √(54).
Explanation:
To find the dimensions that will produce a box with the largest volume, we need to use optimization techniques. Let's assume that the box has a length of l, a width of w, and a height of h.
We want to maximize the volume of the box, which is given by V = lwh. However, we have a constraint on the surface area of the box, which is given by SA = 2lw + 2lh + wh = 108.
We can solve for one of the variables in terms of the others using the surface area equation. Let's solve for w:
w = (108 - 2lh)/(2l + 2h)
Substituting this expression for w into the volume equation, we get:
V = l(108 - 2lh)/(2l + 2h)h
Now we have a volume equation in terms of two variables, l, and h. To find the dimensions that will produce the largest volume, we need to take the partial derivatives of V with respect to l and h, and set them equal to zero:
∂V/∂l = (108 - 4lh - 2h²)/(2l + 2h)² = 0
∂V/∂h = (108 - 2l² - 4lh)/(2l + 2h)² = 0
Solving these equations for l and h, we get:
l = h = √(54)
Therefore, the dimensions that will produce a box with the largest volume and a surface area of 108 square inches are l = h =√(54) and w = (108 - 2lh)/(2l + 2h) = √(54).
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Related Questions
A ball is thrown vertically upwards from a point on the ground. It was observed at a height h twice with a time interval Δt. The initial velocity of the ball is?
Answers
A person can jump out of an airplane at 5000 feet, without a parachute, AND land on the ground safely (without any injury), IF they can manage to do what physics trick?
Lengthen the moment/time of impact
Bend knees right before impact
Spread out arms and legs to slow down
Shorten the length/time of impact
Answers
Answer:
Momentum is equal to mass for velocity (p1=mv)
But momentum is also equal to Force for time of impact (p1=Ft). Hence the impact force is inversely proportional to the fall time and directly proportional to the mass and fall velocity : F=mv/t^2 or F=p1/t
If he slows down, v diminishes and F diminishes
Hence correct Answer is C
The number of events that take place in a 1 second would be the _________________.
Amplitude,
Wavelength,
Longitudinal,
Transverse,
Frequency
Answers
Answer:
Explanation:Frequency
which equation could be used to find the velocity of the center of the gear
Answers
The equation that could be used to find the velocity of the center of the gear is v = rω, where v is the velocity of the center of the gear, r is the radius of the gear, and ω is the angular velocity of the gear.
To find the velocity of the center of the gear, you can use the following equation that includes important terms such as angular velocity, radius, and linear velocity:
Linear Velocity (v) = Angular Velocity (ω) × Radius (r)
In this equation, linear velocity (v) represents the velocity of the center of the gear, angular velocity (ω) is the rate at which the gear rotates, and radius (r) is the distance from the center of the gear to its edge.
To use this equation, first determine the angular velocity (usually measured in radians per second) and the radius of the gear. Then, simply multiply these two values to find the linear velocity (v) of the center of the gear.
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which truck has more momentum and will collide with more force ?
a small truck that moves slow .
a large truck that moves fast .
a, a small truck that moves slow
b,a large truck that moves fast
c, can not tell
Answers
Answer:
a large truck that moves fast
Explanation:
look at the question and look how it says (more momentum) which means faster and more force
How did the river cause the canyon to form?
Answer options with 4 options
A.
The motion of water compacted soil until it became sedimentary rock.
B.
The motion of water wore away and transported rock away from the area.
C.
The motion of water prevented rock layers from forming beneath the water.
D.
The motion of water prevented plants and animals from forming the land in the river bed.
Answers
Answer:
A
Explanation:
because the water carRies but also compacts
El cuentakilómetros de un coche marca 36 km/h. Un minuto más tarde marca 54 km/h. ¿Qué aceleración ha sufrido el coche? Exprésala en el SI. ¿Qué tipo de velocidades marca el cuentakilómetros?
Answers
The acceleration of the car with initial and final speeds is 8.3×10⁻² m/s². and the odometer shows the distance traveled by the car and the speedometer shows the instantaneous velocity.
Acceleration is defined as the change in velocity per unit time. If the velocity increases, it gives acceleration and if the velocity decreases, it represents deceleration. The SI unit of acceleration m/s².
Acceleration (a) = change in velocity/time
the initial speed of the car (u) = 36km/hr = 36×5/18 = 10 m/s (km/hr is converted to m/min by multiplying 5/18).
the final speed of the car (v) = 54 km/hr = 54 ×5/18 = 15 m/s
time taken of the car = 1 minute = 60 seconds
Acceleration = v-u / t
= 15-10/60
= 5/60
= 0.083 m/s²
= 8.3×10⁻² m/s².
The acceleration of the car = 8.3×10⁻² m/s².
The odometer measures the distance traveled by car.
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The question is incomplete but most probably your full question was,
The odometer of a car reads 36km/hr. A minute later it reads 54km/hr. What acceleration does the car undergo? Express it in the SI unit. What kind of speeds does the odometer show?
Based on this law, if a collapsing cloud is isolated in space with no external forces, what must happen to it as its size decreases?.
Answers
The laws of conservation of energy and conservation of angular momentum direct that any rotating and collapsing cloud will end up as a spinning disk. That implies cloud will spin faster.
According to law of conservation of angular momentum of same mass, if the size of the collapsing cloud decrease, its it angular velocity should increase.
Formula for Angular momentum,
L =mrω^2
As L and m is constant , when r is decreased ω must increase. Then, cloud will spin faster.
Law of conservation when applied to angular momentum, mean that momentum of a rotating object does not change unless external torque is applied. Torque here may refer to any outside force that acts upon the object to cause it to twist or rotate.
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Calculate the kinetic energy of a 1.15 kg bowling ball rolling down the lane at 2 m/s. Include the units.
Answers
We will have the following:
\(\begin{gathered} k=\frac{1}{2}(1.15kg)(2m/s)^2\Rightarrow k=\frac{23}{10}J \\ \\ \Rightarrow k=2.3J \end{gathered}\)So, the nergy is 2.3 J.
If you are
measuring the wavelength
of a transverse wave, why
doesn’t it matter whether
you measure it between
crests or between troughs?
Answers
Answer:
yes it doesn't matter
Explanation:
it doesn't matter because troughs and crests are the same and either can be used
in an experiment searching for the photoelectric effect, an incident beam of green light did not eject any electrons from a metal. in order to eject electrons, the experimenter should
Answers
Increase the frequency of the incident light. The photoelectric effect occurs when light of a sufficient frequency strikes a metal and frees electrons from the metal's surface. The energy of the incident photons must be greater than the energy required to remove the electrons, known as the work function. Thus, increasing the frequency of the incident light will result in higher energy photons, increasing the likelihood of electron ejection in the photoelectric effect.
The kinetic energy of the photoelectrons that are released will grow as the light amplitude increases, according to the wave model of light, yet the measured current will increase as the frequency increases. In contrast to expectations, studies revealed that raising the light's frequency and amplitude raised the current and the photoelectrons' kinetic energy, respectively.
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The next closest star to Earth, Proxima Centuri, is 4.25 lightyears away. How far is that in meters?
Answers
Answer:
4.0208 x 10^16 meters
Explanation:
speed of light in m/s * # seconds in a year * 4.25 years =
2.99792 x 10^8 * 3600*24*365.25 * 4.25 = 4.0208 x 10^16 m
What happens when you push or pull a water tube
Answers
The thing that happens when you push or pull a water tube is that the force makes the tube to speed up, slow down, or be in one place.
It is very hard when pulling water and if a person need to consistently pull air out of the tube before water makes it to the pump, it is very difficult and some pumps may or cannot do it.
What is the pulling about?In regards to pushing, when a person is pushing above the Center of Gravity, one is pushing the said object into the ground and thus is increasing the rate of friction.
If a person is pulling you are said to be pulling above the Center of Gravity and lowering friction.
So, The thing that happens when you push or pull a water tube is that the force makes the tube to speed up, slow down, or be in one place.
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what are the laws of motion
Answers
A fault is formed by the movement of a ___ plate boundary
A.convergent
B.traditional
C.divergent
D.transform
Answers
Hope this helps
What kind of potential energy does a diver on a diving board have?
Answers
Take a look at the image attached.
On my whiteboard, I have showed a picture of this scenario.
First let's review potential energy.
Potential energy is energy that is stored,
which can be used to do work.
However, there are specific types of potential energy.
The potential energy here would be gravitational potential energy.
Anything that is raised above Earth's surface has the potential to
fall which is why we call it gravitational potential energy.
Gravitational potential energy has to do more with position
or the position of an object in a gravitational field.
As the diver dives into the water, that gets
turned into kinetic energy shown at the bottom.
Answer:
Gravitational Potential Energy
Explanation:
Like the diver on the diving board, anything that is raised up above Earth's surface has the potential to fall because of gravity. Sorry about the last one hope this answer helps.
a mass m0 is attached to a spring and hung vertically. the mass is raised a short distance in the vertical direction and released. the mass oscillates with a frequency f0. if the mass is replaced with a mass thirteen times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of f0?
Answers
The frequency of oscillation (f) for the mass thirteen times as large would be 1 / \(\sqrt{13}\) times the original frequency (f₀).
The frequency of oscillation for a mass-spring system is determined by the mass (m) and the spring constant (k). It can be calculated using the following formula:
f = (1 / 2π) * \(\sqrt{(k / m)}\)
Given that the original mass (m₀) oscillates with a frequency f₀, we can rewrite the formula as:
f₀ = (1 / 2π) * \(\sqrt{(k / m0)}\)
Now, if the mass is replaced with a mass thirteen times as large (13m₀), we can calculate the new frequency (f) using the same formula:
f = (1 / 2π) * \(\sqrt{(k / (13m0))}\)
To find the relationship between the original frequency (f₀) and the new frequency (f), we can take the ratio of the two equations:
f / f₀ = [(1 / 2π) * \(\sqrt{(k / (13m0))}\)] / [(1 / 2π) * * \(\sqrt{(k / m0)}\)]
The 2π terms cancel out, and we can simplify the equation:
f / f₀ = \(\sqrt{(k / (13m0))}\) / * \(\sqrt{(k / m0)}\)
f / f₀ = \(\sqrt{(k / (13m0 * k / m0))}\)
f / f₀ = \(\sqrt{(m0 / (13m0))}\)
f / f₀ = \(\sqrt{(1 / 13)}\)
f / f₀ = 1 / \(\sqrt{13}\)
Therefore, the frequency of oscillation (f) for the mass thirteen times as large would be 1 / \(\sqrt{13}\) times the original frequency (f₀).
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Assessment started: undefined. Item 1 Which statement accurately describes what happens when ice melts in terms of energy? A:The ice releases energy which causes chemical bonds to break, changing the ice to water.;B:The ice releases energy which causes the water molecules to have less kinetic and potential energy, changing their configuration from solid to liquid. C:The ice absorbs energy which causes the water molecules to have more kinetic and potential energy, changing their configuration from a solid to a liquid. D:The ice absorbs energy which causes chemical bonds to break, changing ice to water.
Answers
Answer:
A.
Explanation:
it's needed top release energy due to the breaking of chemical bonds.
Answer:
A: the ice releases energy which causes chemical bonds to break, changing the water to ice.
Explanation:
which answer choice correctly indicates the explanatory variable and the response variable of the scatterplot? explanatory variable: voltage response variable: electric motor explanatory variable: voltage response variable: rotation explanatory variable: rotation response variable: electric motor explanatory variable: rotation response variable: voltage save
Answers
The correct answer choice for the explanatory and response variables of a scatterplot depends on the context and the variables being studied.
The correct answer choice for the explanatory and response variables of a scatterplot depends on the context and the variables being studied.
In general, the explanatory variable is the independent variable, which is the variable being manipulated or controlled in the study.
The response variable is the dependent variable, which is the variable being measured or observed in response to changes in the explanatory variable.
For example, if we are studying the relationship between voltage and the rotation of an electric motor, then the explanatory variable would be voltage, and the response variable would be rotation.
As voltage is being manipulated, the resulting changes in the rotation of the motor are being observed and measured.
Conversely, if we are studying the relationship between rotation and the voltage required to achieve that rotation, then the explanatory variable would be rotation, and the response variable would be voltage.
As rotation is being manipulated, the resulting changes in the required voltage are being observed and measured.
It is important to carefully consider the variables and their relationships when interpreting a scatterplot.
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a .5 kg steel ball is suspended from teh ceiling by a 2.5 m long string. the ball is pulled to the side until it is 1 m above its lowest point and then released from rest. the tension in the string when the ball passes through its lowest position is
Answers
The tension in the string when the ball passes through its lowest position is 5N (rounded).
The pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements.
How to calculate the tension in the string when the ball passes through its lowest position?
Tension = m*g
T = 0.5 * 9.8
= 4.9N
Approximately the tension would be equal to 5N (rounded)
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When the laser is directly down over the water what percentage of light enters the water and what percentage is reflected back upwards?
Answers
It's important to understand a few things about how light behaves when it encounters a surface such as water.
When light strikes the surface of the water at a perpendicular angle (i.e. when the laser is directly down over the water), a certain percentage of the light is reflected back upwards and a certain percentage enters the water.
The exact percentages of reflected and transmitted light depend on the refractive index of the two materials involved (in this case, air and water).
The refractive index is a measure of how much a material bends light as it passes through. In general, the refractive index of water is higher than that of air, which means that light passing from air into water is bent more than light passing from water into air.
Based on this principle, we can say that when the laser is directly down over the water, approximately 4% of the light will be reflected back upwards and 96% will enter the water.
This means that the vast majority of the laser light will pass through the surface of the water and into the depths below.
It's worth noting that the exact percentages of reflected and transmitted light will vary depending on factors such as the angle of incidence, the wavelength of the light, and the clarity of the water.
However, for the specific scenario, you described (laser directly down over the water), the approximate values of 4% reflected and 96% transmitted should be accurate.
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consider the 6 stages listed below for the lives of a human being and a star. describe what a 1 solar mass star does in each stage of its existence:
Answers
Note that this is a trick question. It is true that the mass of a star affects its life cycle but all stars must go through the stages listed below. Note that the larger the solar mass of a star, the shorter its life cycle. Hence, in each of the stages given here is what will occur:
Prenatal Stage
Birth Stage
The star is able to sustain itself by making its own energy by nuclear fusionAdolescence/Adulthood
The nuclear fusion continues and maintains equilibriumNote that 90% of the stars life is in the main sequenceMiddle age
The sun is in middle age, in the middle of main sequence cycleIt reaches it's prime of lifeOld age
Nuclear fusion of hydrogen to helium ends in the core and the star goes into another fusion stage of helium to carbonIt then swells into a red giant.Death
All fusion processes stop as the outer part of the star is lost Turns in to a planetary nebula and the hot, inert core begins to cool offWhat is the Solar Mass of a Star?
The solar mass is a unit of mass used to measure the masses of objects in the solar system, including stars. It is defined as the mass of the Sun, which is approximately 1.989 x 10³⁰ kilograms, or about 333,000 times the mass of the Earth.
Hence, since the earth's sun is 1.989 x 1010³⁰ kilograms, a star described as having 1 solar mass is simply a star equivalent of the Earth's sun.
Note however that the solar mass is often used as a standard unit of mass for comparing the masses of objects in the universe, such as planets, asteroids, and stars.
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Full Question:
Compare the following stages in the lives of a human being and a star: prenatal, birth, adolescence/ adulthood, middle age, old age, and death. What does a star with a solar mass of 1 solar mass do in each of these stages?
A microwave is rated at 1,200 watts. if it receives 120 volts of potential difference, what is the current in the microwave?
Answers
The current in the microwave is 10 amps.
To calculate the current in the microwave, we need to use Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). In this case, the resistance is the impedance of the microwave, which we can calculate using the formula: impedance (Z) = voltage (V) / current (I).
First, we need to convert the wattage rating of the microwave to its apparent power, which is given by the formula: apparent power (S) = voltage (V) x current (I).
So, for a microwave rated at 1,200 watts and receiving 120 volts of potential difference, the apparent power is:
S = V x I
1,200 = 120 x I
I = 1,200 / 120
I = 10 amps
Therefore, the current in the microwave is 10 amps.
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An object has a mass of 20kg, what is its weight on Earth?
Answers
Answer:
The formula is W=mg.
W=20×10=200.
Answer:
\(\Huge \boxed{\mathrm{200 \ N}}\)
Explanation:
\(\sf Weight \ (N)= mass \ (kg) \times acceleration \ of \ gravity \ (m/s^2)\)
\(W=mg\)
The mass of the object is 20 kg.
The acceleration of gravity is 10 m/s².
\(W=20 \times 10\)
\(W=200\)
The weight of the object is 200 N.
an object is located 85 cm from a convex lens the focal point is 25 cm what is the average distance is the image real or virtual brainly
Answers
The image is real and is found at a distance of 33.33cm.
What is a convex lens?The term lens is used to describe any refracting surface. We know that a lens could be concave or convex in nature. Given that fact, we are to find the nature of the image that is formed by the convex lens.
Also;
1/f = 1/u + 1/v
1/v = 1/f - 1/u
f = focal length
u = object distance
v = image distance
1/v = 1/25 - 1/85
1/v = 0.04 - 0.001
v = 33.33cm
The image is real and is found at a distance of 33.33cm.
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PLEASE HURRY
A student arrives late to her physics class and misses the beginning of notes. These notes she takes are below. -discovered by Onnes in 1911 using mercury -allows for conductivity with no resistance -requires a very cold temperature What should she title her notes?
Metallurgy
Superconductors
Crystallography
Electromagnetism
Answers
Answer: B superconductors
Explanation:
A physics student stands at the top of a set of bleachers. They drop a basketball and it lands 2.4 seconds later.
d.) How high are the bleachers ?
e.) How fast was the basketball traveling at the time it landed ?
Answers
Answer:
x=48.12 m
Vf=23.544 m/s
Explanation:
a=g
t=2.4
Vf=?
Vø=0
Vf=Vø+at
Vf=0+(9.81)(2.4)=23.544
x=Xø+Vøt+1/2at^2
x=1/2at^2
x=(1/2)(9.81)^2=48.11805
Please help me , I also have to show work on paper
Answers
Answer:
Choose B
Explanation:
Hope Can I help you
Are we real?Should we believe in hell and heaven?Should we take life seriously?Why do we feel like we are being pulled down from our ankle quickly when we have a dream we are falling?Do we die when were asleep then come back when we wake up?Is life just a dream?Should we be scared of sleep?
Answers
Answer:
we Are real, I don’t believe hell or heaven, we should take it seriously,
Explanation:
Two billiard balls having the same mass and speed roll directly toward each other. What is their combined momentum after they meet
Answers
Their combined momentum after they meet is 0.
What is law of conservation of momentum?According to the law of conservation of momentum, absent an external force, the combined momentum of two or more bodies operating upon one another in an isolated system remains constant. As a result, momentum cannot be gained or lost.
Let the mass of each billiard balls = m.
If the initial velocity of first ball is u; according to the question, the initial velocity of the second ball be -u.
Hence, initial momentum of the first ball is: P₁ = mu
initial momentum of the second ball is: P₂ = -mu
Hence, total initial momentum of the two balls = P₁ + P₂ = mu + ( -mu) = 0.
So, according to law of conservation of momentum:
Their combined momentum after they meet is = 0.
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The combined momentum of the two billiard balls after they meet is zero.
When two pool balls of the same size and speed roll directly at each other and collide, their momentum will increase.
Let us denote the speed of the first ball as \(\rm p_1\) and the speed of the second ball as \(\rm p_2\). The momentum of the balls are equal in magnitude but opposite in direction because they have the same mass and velocity.
\(\rm p_1= -p_2\)
When the balls collide, their momentum increases:
Total momentum after the collision= \(\rm p_1+ p_2\)
Substituting the relationship
\(\rm p_1= -p_2\)
Total momentum after the collision
\(\rm p_1- p_1= 0\)
Therefore, the combined momentum of the two billiard balls after they meet is zero.
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