F the radius of a sphere is increasing at the constant rate of 2 cm/min, find the rate of change of its surface area when the radius is 100 cm

Answers

Answer 1
The surface area of a sphere of radius r is
A(r) = 4πr²

The rate of change of the surface area with respect to time is
[tex] \frac{dA}{dt} = \frac{dA}{dr} \frac{dr}{dt} [/tex]

The radius increases at the constant rate of 2 cm/min, therefore
[tex] \frac{dA}{dt} = 2 \frac{dA}{dr}=2*(8 \pi r) =16 \pi r [/tex]

When r = 100 cm, the rate of change of the surface area is
16π(100) cm²/min
= 1600π cm²/min
= 5026.5 cm²/min

Answer: 1600π or 5026.5 cm²/min



Related Questions

Which physical layer of earth is broken into tectonic plates?

Answers

The lithosphere is the physical layer of Earth which is broken into tectonic plates.  

Lithosphere is the rigid outermost layer of the Earth's crust. It is composed of the crust as well as the upper part of the mantle.

There are two types of lithospheres:
1- A type associated with oceans called "Oceanic lithosphere" with density about 2.9 gm/cm^3
2- A type associated with land called "Continental lithosphere" with density about 2.7 gm/cm^3
Final answer:

The lithosphere, encompassing Earth's crust and the uppermost rigid portion of the mantle, is the layer divided into tectonic plates. These plates move due to the convection of the mantle and are responsible for many geological processes.

Explanation:

The physical layer of Earth that is broken into tectonic plates is known as the lithosphere, which includes the crust and the uppermost, rigid portion of the mantle. The lithosphere is about 100 kilometers thick and is broken into several tectonic plates that cover Earth's surface, including both continental and oceanic crust.

These tectonic plates fit together like a jigsaw puzzle and move due to the process of mantle convection, where heat from Earth's interior causes the upward flow of warmer mantle material and the downward sinking of cooler material. This movement can cause the plates to drift apart, collide, or grind past each other, leading to various geological phenomena such as earthquakes, volcanic activity, and the formation of mountain ranges.

The asthenosphere beneath the lithosphere is involved in the movement of these plates as well; it acts as a soft, ductile layer allowing the rigid plates of the lithosphere to move over it. The slow but steady motion of tectonic plates is driven by numerous forces, including the heat transfer from Earth's interior which is an essential aspect of planet's cooling system.

Potassium hydroxide (KOH) and hydrochloric acid (HCl) react in a beaker. They form potassium chloride (KCl) and water (H2O). What type of reaction is this? synthesis reaction
double replacement reaction
single replacement reaction
decomposition reaction

Answers

Its the second option

Answer: double replacement reaction

Explanation:

1. Synthesis reaction is a chemical reaction in which two reactants are combining to form one product.

Example: [tex]Li_2O+CO_2\rightarrow Li_2CO_3[/tex]  

2. Double displacement reaction is one in which exchange of ions take place. Neutralization is a special type of double displacement where acid reacts with base to form salt and water.

Example: [tex]KOH(aq)+HCl(aq)\rightarrow KCl(aq)+H_2O(l)[/tex]

3. Single replacement reaction is a chemical reaction in which more reactive element displaces the less reactive element from its salt solution.

Example: [tex]Zn+2HCl\rightarrow ZnCl_2+H_2[/tex]

4. Decomposition is a type of chemical reaction in which one reactant gives two or more than two products.

Example: [tex]Li_2CO_3\rightarrow Li_2O+CO_2[/tex]

How should the flight controls be held while taxiing a tricycle-gear equipped airplane with a left quartering tailwind?

Answers

The flight controls must be held with left aileron up and elevator neutral while taxiing a tricycle-gear equipped airplane with a left quartering tailwind. In aircraft, ailerons are placed on the trailing edge of each wing near the wingtips and can be moved up and down. So when the left aileron is up, the movement of the airplane moves to the left  and turns the wheel in a counterclockwise direction while at the same time, the right aileron is down.

Final answer:

To taxi a tricycle-gear equipped airplane with a left quartering tailwind, hold the elevator control fully forward and the aileron control to the left - to prevent the wind from lifting the tail or wing.

Explanation:

When taxiing a tricycle-gear equipped airplane with a left quartering tailwind, the flight controls should be held in a specific manner to maintain control of the aircraft. The elevator control should be fully forward and the aileron control turned to the left. This means the yoke or stick should be pushed forward and turned to the left.

Why so? This configuration of controls help prevent the wind from getting under the tail or wing and causing a loss of control. The left aileron up bubble helps prevent the left wing from being lifted by the wind. The elevator down bubble will prevent the wind from getting beneath the tail and lifting the nose.

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investigate the relationship between volume and pressure of a gas at a constant temperature.

Answers

Gay Lussac's Law states: At a constant volume Pressure divided by Temperature isconstant P/T = k Together these three laws form the foundation of the Ideal GasLaw. Objective: Students will investigate Gay Lussac's Law relating pressure andtemperature at a constant temperature.

Why does helium have more spectral lines than hydrogen?

Answers

This is because Helium has two valence electrons compared to Hydrogen which has only one. Helium has more energy levels for an electron to jump thus more spectral lines to occur. The spectral lines relating to each change of energy level would be more grouped together and hence the greater chance of them falling in the visible range.

Helium has more spectral lines than hydrogen due to the differences in their atomic structure and electron configurations, leading to a higher number of possible transitions and spectral lines.

Helium has more spectral lines than hydrogen because of the differences in the atomic structure of the two elements. While both elements exhibit similar spectral series, helium has two series of lines for every one series observed in hydrogen. This is due to the presence of two electrons in helium compared to one in hydrogen, resulting in more possible transitions and spectral lines.

What is the first thing to check when a refrigerator stops working?
a. check the food temperature. if it is 35°f or colder, move the food into a working refrigerator
b. check the refrigerator thermometer. if it is below 51°f, move food into working refrigerator.
c. check the food temperature. if it is 41°f or colder, move the food into a working refrigerator
d. check the food temperature. if it is 32°f or colder, move the food into a working refrigerator?

Answers



b. check the refrigerator thermometer. if it is below 51°f, move food into working refrigerator.

Answer:

correct answer is option C (check the food temperature to decide if it is safe. If the thermometer measures under 41 degrees Fahrenheit, then you move it to a working refrigerator)

Explanation:

In a refrigerator there is a thermometer which is  designed for the refrigerator and it should read 40 degrees Fahrenheit or lower inside the refrigerator. If a refrigerator stops working the first thing which should be checked is the food temperature to decide if it is safe. Because if temperature of food is above 40 degree Farenheit for more than 2 hours it should not be used. If the thermometer measures under 41 degrees Fahrenheit, then you move it to a working refrigerator.

The largest driving force for pulling fluid from the interstitial spaces back into the capillaries is

Answers

The main driving force for pulling fluid from the interstitial spaces back into the capillaries is blood colloid osmotic pressure. The oncotic pressure or as called as colloid osmotic pressure is a classification of osmotic pressure transport to bear by proteins notably albumin in a blood vessel's plasma which is blood or liquid that typically inclines to pull water into the circulatory system.

Osmotic pressure, specifically the blood colloidal osmotic pressure, is the main force that moves fluid from interstitial spaces back into the capillaries, driven by protein concentration gradients.

The largest driving force for pulling fluid from the interstitial spaces back into the capillaries is the osmotic pressure, often specifically referred to as blood colloidal osmotic pressure (BCOP). This pressure exists due to the concentration of colloidal proteins such as albumin in the blood. These proteins create a higher solute concentration within the capillaries relative to interstitial spaces, resulting in water being attracted back into the bloodstream due to the solute-to-water concentration gradients established across the semipermeable capillary walls. Fluid re-enters the capillary where the capillary hydrostatic pressure is lower than the BCOP, typically at the venule end of the capillary.

The greatest ocean depths on the earth are found in the marianas trench near the philippines, where the depth of the bottom of the trench is about 11.0 km. calculate the pressure due to the ocean at a depth of 9.1 km, assuming seawater density is constant all the way down. (the validity of the assumption of constant density is examined in one of the integrated concept problems.)

Answers

To find the pressure with a given data for the height, you are asked to get the hydraulic pressure. Hydraulic pressure has the following formula:

P = density*acceleration due to gravity*height

Assume that the density of seawater is the same as that for pure water,density = 1000 kg/m^3.

P = 1000 kg/m3*9.81m/s2*9100m
P = 89271000 Pascals or 89.271 megapascals

What is the speed of a transverse wave in a rope of length 2.00 m and mass 60.0 g under a tension of 500 n?

Answers

The formula we can use in this case would be:

v = sqrt (T / (m / l))

Where,

v = is the velocity of the transverse wave = unknown (?)

T = is the tension on the rope = 500 N

m = is the mass of the rope = 60.0 g = 0.06 kg

 l = is the length of the rope = 2.00 m

Substituting the given values into the equation to search for the speed v:
v = sqrt (500 N/(0.06 kg /2 m)) 
v = sqrt (500 * 2 / 0.06) 
v = sqrt (16,666.67) 
v = 129.10 m/s

In order to be considered a semi-conductor the material must
have insulator and conductor properties.
resist electron flow.
have ions that are negative and accept charges.
easily accept electron flow.

Answers

First one, for instance they become conductors or insulators depending on the temperature!

Answer:

<<<<Have insulator and conductor properties.

>>>>>is your answer

Explanation:

i just take the quiz

A bar magnet is placed on a table so that the north pole faces right.

Which statement describes the magnetic field lines 2 cm above the table?

They are pointing down into the table.
They are pointing right to left.
They are pointing left to right.
They are pointing up out of the table.

Answers

The correct answer is C. They are pointing right to left.


Explanation.

A magnet has two poles, a north pole and a south pole.  When dealing with magnets, we define the concept of a magnetic field. A magnetic field represents the effect of the magnet on magnetic materials and moving charges in the space around the magnet. For every magnet, the magnetic field lines always point away from the north pole of the magnet towards the south pole. Since the north pole of this magnet faces right, the magnetic field lines point towards the left.

The correct answer is C. They are pointing right to left.

Answer:

so b????????

Explanation:

The finding that attention can spread within an object, thereby, enhancing detection at other places within the object is referred to as _____.

a. ?spatial drift

b. ?spreading activation

c. ?same-object advantage

d. ?object location invariance

Answers

The finding that attention can spread within an object, thereby, enhancing detection at other places within the object is referred to as same-object advantage effect (SOA). The effect is that the performance of observers who are judging two targets is better (faster and/or more accurately) when they are from the same object than when they are from different objects.

Final answer:

The phenomenon where attention can enhance detection within other parts of the same object is known as the same-object advantage (option c), based on multisensory integration patterns where multisensory enhancement is more likely when stimuli are related spatially and temporally.

Explanation:

The finding that attention can spread within an object, thereby, enhancing detection at other places within the object is referred to as same-object advantage (option c). This concept implies a form of multisensory integration where sensory processing is enhanced for different parts of a single object when compared to processing parts of different objects. This pattern is based on the principle that multisensory enhancement occurs when the sources of stimulation are spatially and temporally related to one another, contributing to the ability to detect stimuli more efficiently when they occur within the same object.

A motorist travels for 3.0 h at 80 km/h and 2.0 h at 100 km/h. What is her average speed for the trip?

Answers

3x80=240
2x100=200
240+200/5=88 k/hr
☺☺☺☺

Answer:

The motorist average speed for the trip is 88 km/h

Explanation:

In order to know her average speed, we have to refer to the following ecuation:

<V> (average speed) = [tex]\frac{Vfinal+Vinital}{2}[/tex]

So, according to that, we know that the motorist has been having a speed of 80km/h during 3 hours, and a speed of 100 km/h during 2 hours. It means that her speed during all the travel is 5 hours.

Then, we have to affect the 5 hours to the inicial and final speed as follows:

First, at 80 km/h, she travels during 2 hours so:

3h*80km/h= 240 km

And then, at 100 km/h:

2h*100km/h= 200 km

Which leads us to:

initial speed: 240 km/ 5 h= 48 km/h

and final speed of: 200 km/ 5 h= 40 km/h

Then, the average speed is:

<V> = 48 km/h + 40 km/h = 88 km/h

The rate constant of a first-order process that has a half-life of 3.50 min is __________ s-1.

Answers

The process may be represented by
[tex]A(t) = A_{0}\, e^{-kt}[/tex]
where k =  the rate constant (1/s)
            t = time, s

At half life, A = (1/2) A₀, and t = 3.5*60 = 210s.
Therefore
[tex]e^{-210k}= \frac{1}{2} [/tex]
-210 k = ln(0.5)
k = -ln(0.5)/210 = 0.0033

Answer:  0.0033 1/s  or  3.3x10⁻³ s⁻¹

The rate constant of the first-order process that has a half-life of 3.50 min is approximately 0.00330 [tex]s^{-1}[/tex].  

The rate constant of a first-order process is related to its half-life through the equation:

k = 0.693 / [tex]t^{\frac{1}{2}[/tex]

Given that the half-life ([tex]t{\frac{1}{2}[/tex]) of the process is 3.50 minutes, we need to convert this time into seconds:

3.50 min x 60 s/min = 210 s

Now, substituting the half-life into the equation for the rate constant:

k = 0.693 / 210 s

Calculating the rate constant:

k ≈ 0.00330 [tex]s^{-1}[/tex]

Therefore, the rate constant of the first-order process is approximately 0.00330 [tex]s^{-1}[/tex].

When condensation rates decrease, causing fewer clouds to form, how might humans change their behavior?

Answers

Humans might hold a picnic outside because of a lack of precipitation.

Explanation:

Humans might hold picnic outside in the bright sunny daylight and enjoy their day with family and friends. People will relax and will spend time with their near and dear ones. Less condensation means no rainfall, so people will also do few works that they have been willing to do but could not do due to rainfall. Thus people will be in a happy mood doing their work and spending their time with close ones. A sense of positiveness and happiness will surround the atmosphere.

How long will it take you to pass a truck at 60 mph with oncoming traffic?

Answers

This is impossible to calculate without knowing the speed of each vehicle. 

Answer:

4 seconds - Not practical

Explanation:

Length of the truck = 50'

Initial distance behind the truck = 30'

Finish Pass = 50' ahead of truck ,

Pass at =  60mph -- about 3.375 seconds.

- 70mph your closing speed is 130mph.  

If you were less than a 1/4 mile away when you tried the pass you will be dead.

That would be a quick pass.  You will probably want a mile beyond the oncoming traffic.

Energy that is associated with the position or composition of an object is called

Answers

That is potential energy.
Final answer:

Potential energy is the type of energy associated with the position or composition of an object. It's the stored energy that can be fully recovered.

Explanation:

The energy that is associated with the position or composition of an object is called potential energy. This is a type of energy that is stored and can be completely recoverable. Energy comes in different forms and potential energy is one type due to an object's relative position, composition or condition. An object could possess this energy because of its place within a system. For instance, water at the top of a waterfall has potential energy due to its position; when it flows downwards, it has kinetic energy that can be used to produce electricity in a hydroelectric plant. Similarly, a battery has potential energy because the chemicals within it can produce electricity that can perform work.

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How much heat transfer (in kilocalories) is required to thaw a 0.450-kg package of frozen vegetables originally at 0ºc if their heat of fusion is the same as that of water?

Answers

Final answer:

To thaw a 0.450-kg package of frozen vegetables at 0°C, with a heat of fusion equivalent to that of water, 36 kilocalories of heat transfer are required.

Explanation:

Calculating Heat Transfer for Thawing Frozen Vegetables

The question asks about the heat transfer necessary to thaw a 0.450-kg package of frozen vegetables originally at 0°C, given that their heat of fusion is equivalent to that of water. To calculate this, one can use the formula for heat transfer during a phase change:

Q = m × L

Where:
Q is the heat transfer,
m is the mass of the substance (in kilograms), and
L is the latent heat of fusion (for water, it's approximately 334,000 J/kg or 80 kcal/kg).

Plugging in the values, we get:

Q = 0.450 kg × 80 kcal/kg = 36 kcal

This calculation determines that 36 kilocalories of energy is required to thaw the frozen vegetables.

________ describes the total sediment load transported by a stream.

Answers

That is called the capacity.

The term that describes the total sediment load transported by a stream is "stream sediment transport."

What is stream sediment transport?

Stream sediment transport refers to the overall amount of sediment, including sand, silt, and clay particles, that is carried by a stream as it flows. Stream sediment transport is influenced by factors such as the stream's velocity, gradient, and the size and shape of the sediment particles.

It plays a crucial role in shaping stream channels, depositing sediments in floodplains, and influencing the overall geomorphology of a stream system.

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A boy kicks a football with an initial velocity of 28.0 m/s at an angle of 30.0o above the horizontal. what is the highest elevation reached by the football in its trajectory?

Answers

As the boy kicks the football with an angle, due to the effect of the gravitational force, the ball would follow a projectile path which is parabolic in nature. From this idea, we can derive equations pertaining to the maximum height that the ball would reach. At the maximum height of the ball, the velocity of the ball would be equal to zero. From the equations for projectile motion, we would obtain the equation as follows:

Maximum height = v0^2 sin^2 (theta) / 2g 
Maximum height = (28.0 m / s )^2 sin^2 (30.0) / 2(9.8 m / s^2)
Maximum height = 10 m

The maximum height that the ball would reach would be 10 m.
 
Final answer:

The highest elevation reached by the football in its trajectory is approximately 20.7 meters.

Explanation:

To determine the highest elevation reached by the football, we can use the kinematic equations for projectile motion. The initial velocity of the ball can be broken down into its horizontal and vertical components using trigonometry.

The horizontal component of the initial velocity is 28.0 m/s * cos(30.0°) and the vertical component is 28.0 m/s * sin(30.0°). Since there is no vertical acceleration at the highest point of the trajectory, the vertical component of the velocity is zero. We can use this information to find the time it takes for the ball to reach its highest elevation.

Using the equation vf = vi + at, where vf is the final velocity (zero), vi is the initial velocity (vertical component), a is the acceleration (acceleration due to gravity: -9.8 m/s^2), and t is the time, we can solve for t. Plugging in the values, we get:

0 = 28.0 m/s * sin(30.0°) - 9.8 m/s^2 * t

Simplifying and solving for t, we find that t = 2.86 seconds.

Now, we can use the equation hf = hi + vit + (1/2)at^2, where hf is the final height (highest elevation), hi is the initial height (0 m since the ball starts on the ground), vi is the initial velocity (vertical component), a is the acceleration (acceleration due to gravity), and t is the time. Plugging in the values, we get:

hf = 0 + 28.0 m/s * sin(30.0°) * 2.86 seconds + (1/2)(-9.8 m/s^2)(2.86 seconds)^2

Simplifying, we find that the highest elevation reached by the football is approximately 20.7 meters.

Electromagnetic waves are ________ waves.

a. longitudinal

b. surface

c. primary

d. transverse

Answers

D. Transverse waves

According to the big bang theory, after the "bang," the universe remained dark until

Answers

I believe the answer is 300,000 years

According to the Big Bang theory, after the "bang," the universe remained dark until about 380,000 years later, when neutral atoms began to form.

During this period, the universe was filled with a hot, dense plasma of protons, electrons, and photons constantly interacting, which prevented light from traveling freely. This era is known as the "cosmic dark age." Around 380,000 years post-Big Bang, the universe cooled enough for protons and electrons to combine and form neutral hydrogen atoms, a process called "recombination."

This allowed photons to travel unimpeded, making the universe transparent and visible. This transition is marked by the emission of the cosmic microwave background radiation, which we can still detect today as the afterglow of the Big Bang.

Complete Question:

According to the Big Bang theory, after the "bang," the universe remained dark until about _____ later, when neutral atoms began to form.

In order to catch a fast-moving softball with your bare hand, you extend your hand forward just before the catch and then let the ball ride backward with your hand. doing this reduces the catching force because the

Answers

This is a concept of momentum. In equation, momentum is the product of force and distance. When a ball is thrown, its force is constant all throughout unless disturbed by an external force. Therefore, force is the constant of proportionality that relates momentum with distance. When you block a ball from a given distance, you would feel the great force on your hand. In order to reduce the force, you have to follow the direction of the force in order to minimize the impact. By doing this, you gradually decrease the momentum of the ball. 

Final answer:

Catching a fast-moving softball with an extended hand moving backward reduces the catching force because this technique increases the time over which the collision occurs, thus lowering the force applied to the hand according to the impulse-momentum theorem.

Explanation:

The student's question pertains to the physics concept of impulse and how it applies to catching a fast-moving softball with one's bare hands. When you move your hand backward upon catching the ball, you are increasing the time over which the collision between your hand and the ball occurs. According to the impulse-momentum theorem, the impulse on an object is equal to the change in momentum of the object, which is the product of the mass and change in velocity (force applied over a period of time). By increasing the time, the force exerted on your hand by the ball decreases, making it less painful and reducing the likelihood of injury.

Using the formula impulse = force × time, by increasing the time during which the force is applied (the time during which your hand moves backward), you are effectively spreading out the force over a longer period, and thus, the peak force felt by your hand is lower. This is similar to the concept of crumple zones in cars which extend the time of impact and reduce the force felt by the occupants.

Therefore, when catching a fast-moving softball with your hand, extending your hand forward and allowing the ball to ride backward with your hand reduces the catching force due to the longer duration over which the force is applied, resulting in a smaller impulse felt by your hand. This is why this technique is often used by players to catch high-speed balls safely.

When atoms lose more than one electron, the ionization energy to remove the second electron is always more than the ionization energy to remove the first. similarly, the ionization energy to remove the third electron is more than the second and so on. however, the increases in ionization energy upon the removal of subsequent electrons is not necessarily uniform?

Answers

The increase in the ionization energy upon the removal of the subsequent electrons are not necessarily uniform because the affinity of the electrons to the atom in every subshell is different causing to a difference in energy needed to remove these electrons. Each and every subshell in an atom is attached or attracted to the nucleus at different degrees or amounts. As a result, the energy that is required to remove the electrons in every subshell would be different although it increases, it would not be uniform.


Carbon burns in the presence of oxygen to give carbon dioxide. Which chemical equation describes this reaction?

Answers

Carbon + Oxygen gas = Carbon dioxide gas

Answer with Explanation:

The Statement of Chemical Reaction is:

   Carbon burns in the presence of oxygen to give carbon dioxide.

Writing it in terms of Chemical Reaction

   [tex]C (\text{Carbon}) +O_{2}(\text{Two Atoms of Oxygen})=CO_{2}[/tex]

That is Carbon when combines with two molecules of Oxygen gives Carbon Dioxide.

An iron block of mass 45.87 kg is heated from 7 c to 218

c. if the specific heat of iron is 450 j-1 kg k-1 then how much energy is required

Answers

Final answer:

The amount of energy required to heat a 45.87 kg iron block from 7°C to 218°C, given a specific heat capacity of 450 J kg-1 K-1 , is 4364065.5 Joules.

Explanation:

The amount of heat energy required to change the temperature of a substance can be calculated using the formula Q = mcΔT, where:

Q is the heat energym is the mass of the substancec is the specific heat capacityΔT is the change in temperature

Given that the mass of the iron block (m) is 45.87 kg, the specific heat of iron (c) is 450 J kg-1 K-1, and the change in temperature (ΔT = T2 - T1) is (218 - 7) or 211°C, which is equivalent to 211 K in terms of heat calculations. Substituting these values into the formula, we get:

Q = 45.87 kg * 450 J kg-1 K-1 * 211 K = 4364065.5 Joules

So, it would require 4364065.5 Joules of energy to heat the iron block from 7°C to 218°C.

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In all chemical reactions, __________ and ____________ must be conserved. energy, matter atoms, heat enthalpy, energy

Answers

energy and matter atoms is the correct answers. Mass or matter can not be created nor destroyed.

Final answer:

In all chemical reactions, both matter and energy must be conserved. The law of conservation of matter states the quantity of each element remains constant, and the law of conservation of energy (the first law of thermodynamics) states that energy can be transformed but not created or destroyed. Chemical equations must be balanced to reflect these conservation laws.

Explanation:

In all chemical reactions, matter and energy must be conserved. These principles are known as the law of conservation of matter and the energy conservation law. According to these laws, the quantity of each element remains unchanged in a chemical reaction, meaning that there's the same amount of each element in the products as there was in the reactants because matter is conserved. This is reflected in a chemical equation where the same number of atoms of each element appears on each side of the equation.

In addition to matter being conserved, energy is also conserved as described by the first law of thermodynamics. Energy can be transformed from one form to another or transferred between objects, but the total energy before and after a chemical reaction remains constant. The conservation of energy is also important to understand because, despite matter and energy being interchangeable under certain circumstances in physics, in most chemical reactions, the energy changes are modest and the mass changes are negligible, so these two quantities appear to be conserved.

It is important to remember that these conservation laws are a fundamental aspect of chemical equations that need to be balanced to satisfy the law of conservation of matter. Atoms are neither created nor destroyed in chemical reactions so the reactants and products must always have the same total number of each type of atom. This aspect is critical for correctly understanding and performing chemical reactions.

My trip to work is 120 miles. if i go 8 mph faster than my usual speed, i'll get to work 30 minutes earlier. how long does my trip take, in hours, if i go my usual speed?

Answers

Let x be the time it takes for the trip to be completed given that the speed is y.

When the time is 30 minutes (equal to 0.5 hour) shorter than x, the speed is 8 mph more than the original speed. 

The equations that would best represent the given conditions are:
      (1)             120 = (x)(y)
      (2)              120 = (x - 0.5)(y + 8)

Simplifying,
                       y = 120/x
Substitute:
                    120 = (x - 0.5)(120/x + 8)

The value of x from the equation is 3. Thus, if I go with the usual speed, the time it will take me to finish the trip is approximately 3 hours. 

Answer: Hello!

The total distance is 120 miles, and you know that if you go 8 mi/h faster than usual you get there 30(or 0.5 hours) minutes early.

So if v is your usual speed, and t is your usual time, we have the next equations:

1) v*t = 120mi

2) (v + 8mi/h)*(t - 0.5h) = 120 mi

In equation (1) we can write v as a function of t; this is v = 120mi/t, and replace it in the second equation.

(v + 8)*(t - 0.5) = 120

(120/t + 8)(t - 0.5) = 120

120 + 8*t -60/t - 4 = 120

8*t -60/t - 4 = 0

now we need to obtain the value of t. Multiplying by t in both sides we have:

8*t^2 -60 - 4t = 0

Now we can use Bhaskara to obtain the two possible values for t:

[tex]t = \frac{4 +- \sqrt{16 +4*60*8} }{16} = \frac{4+-\sqrt{1936} }{16}  = \frac{4 +-44}{16}[/tex]

So we have two solutions: [tex]t = \frac{4+44}{16} = 3h[/tex] and [tex]t = \frac{4 -44}{16} = -2.5h[/tex].

The second is a negative time, so this has no sense; then we only took the first solution; when you go at your usual speed, your trip takes 3 hours.

The chief physicist in charge of the manhattan project was _____. wernher von braun j. robert oppenheimer albert einstein leslie groves

Answers

it was J. Robert Oppenheimer

J. Robert Oppenheimer

A tipping point in the disappearance of tropical rainforests would be

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In the disappearance of tropical rainforests, a tipping point indicates the change in the patterns of regional weather. This change occurs after the clearance of the forests.This tipping point prevents them from returning.
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