Final answer:
The student's question requires estimating the rate of change of the turkey's temperature after cooling for an hour, which is determined by the slope of the tangent on the temperature graph. This mathematical concept also has a real-life application in ensuring that turkey is cooked to a safe internal temperature of 165°F using a food thermometer.
Explanation:
The student's question involves calculating the rate of change of the turkey's temperature after allowing it to cool for an hour. To accomplish this, one would measure the slope of a tangent line drawn on the graph at the point corresponding to one hour post removal from the oven. The slope of the tangent represents the rate at which the turkey's temperature is changing at that specific time—essentially, how quickly it is approaching room temperature.
While this problem is primarily mathematical, it involves knowledge about cooking temperatures as context. This includes knowing the safe internal temperatures for various meats—a roast turkey should reach a safe minimum internal temperature of 165°F to ensure it is safe to consume. The mathematics involved in graphing and calculating slopes can help in ensuring that these safety standards are followed by providing precise information about how quickly the food is cooling and when it has reached a safe temperature.
When using a food thermometer to check for these safe temperatures, the concepts of rates of change are at work as the thermometer relays how quickly the internal temperature is reaching the desired heat level. This practical application shows the importance of mathematical concepts in everyday life.
The estimated rate of change of the temperature of the turkey after an hour is about -10°F per minute, indicating it is cooling down.
Understanding the Concept of Rate of Change:
The rate of change of temperature is represented by the slope of the tangent line on the graph at a specific time. In this case, after one hour, we can look at the graph to find the corresponding temperature and its change over a small time interval.
Finding the Slope at t = 1 hour:
The slope of the tangent line at a point on a graph is calculated using the formula:
[tex]\text{slope} = \frac{\Delta y}{\Delta x}[/tex]
where [tex]\Delta y[/tex] is the change in temperature and [tex]\Delta x[/tex] is the change in time.
Locate the point on the graph that corresponds to 1 hour after placing the turkey on the table. Let's say the temperature at that point is roughly 150°F (you would need to confirm this from the actual graph).
Let's assume that right before the 1-hour mark (at approximately 59 minutes), the temperature was about 160°F.
Calculate the Change:
Change in temperature:
[tex]\Delta y = y_1 - y_0 = 150 - 160 = -10 \text{ F}[/tex]
Change in time:
[tex]\Delta x = 60 - 59 = 1 \text{ minute}[/tex]
Calculate the Slope:
Now apply the values into the slope formula:
[tex]\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-10 \, \text{F}}{1 \, \text{min}} = -10 \, \text{F/min}[/tex]
How is the equilibrant related to the net force?
It is always larger in magnitude than the net force.
It is always smaller in magnitude than the net force.
It is equal in magnitude and acts in the same direction.
It is equal in magnitude and opposite in direction.
Final answer:
The equilibrant force is equal in magnitude but opposite in direction to the net force. It is introduced to achieve equilibrium, cancelling out the net force and resulting in no acceleration.
Explanation:
The equilibrant is a force that is equal in magnitude but opposite in direction to the net force acting upon a point or object. When forces are perfectly balanced, the net force is 0 N, and the object remains in a state of equilibrium. In contrast, when there is a resultant force, the object will experience acceleration in the direction of the net force. However, by introducing an equilibrant force, we can return the system to equilibrium, effectively cancelling out this acceleration.
For instance, if two unequal forces act on an object in opposite directions, the net force would be the difference between those two forces, in the direction of the larger force. To achieve equilibrium, an equilibrant force must be introduced with the same magnitude as this net force but directed oppositely. If both forces act in the same direction, then the net force is the sum of the two forces, and an equilibrant, to balance the system, would again need to be of the same size but act in the opposite direction.
who wins a tug-of-war one who pushes harder at the ground or pulls harder at the rope
What happens during the intake and compression strokes of a four stroke engine?
In a four stroke engine, the intake stroke pulls in air mixed with fuel as the piston expands, then the compression stroke rapidly compresses this mixture in a nearly adiabatic process with the valves closed, causing the fuel-air mixture's temperature to rise.
Explanation:The intake and compression strokes are the first two phases of the four-stroke cycle in an internal combustion gasoline engine, often explained in terms of the Otto cycle. During the intake stroke, air is mixed with fuel in the combustion chamber as the piston expands. This causes an increase in the volume of the cylinder and draws in a mixture of gasoline and air.
In the second phase, the compression stroke, the air-fuel mixture is rapidly compressed in a nearly adiabatic process. The piston rises, with the valves closed, causing the temperature of the mixture to rise. Work is done on the gas during this stage as the piston compresses it from the expanded volume to a smaller volume. This prepares the mixture for ignition, which will occur in the succeeding phases of the four-stroke cycle. These processes convert chemical potential energy in the fuel into thermal energy and eventually into work, as part of the cyclical operation of the engine.
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The velocity of sound on a particular day outside is 331 meters/second. What is the frequency of a tone if it has a wavelength of 0.6 meters?
5.52 × 102 hertz
2.56 × 102 hertz
459 × 102 hertz
675 × 102 hertz
990 × 102 hertz
Answer:
[tex]5.52 \cdot 10^2[/tex] Hz
Explanation:
For a wave, the relationship between velocity, wavelength and frequency is given by the wave equation:
[tex]v=f\lambda[/tex]
where
v is the velocity
f is the frequency
[tex]\lambda[/tex] is the wavelength
For the sound wave in this problem, we have:
v = 331 m/s
[tex]\lambda=0.6 m[/tex]
Solving the equation for f, we find the frequency:
[tex]f=\frac{v}{\lambda}=\frac{331}{0.6}=5.52\cdot 10^2 Hz[/tex]
A child standing on a bus remains still when the bus is at rest. When the bus moves forward and then slows down, the child continues moving forward at the original speed. This is an example of
The best answer would be, Newton's first law of motion.
A trailer mechanic pushes a 2500 kg car, home to a speed v, performing a job during the 5000 J. In this process, the car moves 25 m. Neglecting friction between the car and roadway:
(A) What is the final velocity v of the car? (B) What horizontal force exerted on the car?
Final velocity [tex]V_{f}[/tex] of the car will be 2 meters per second
Horizontal force exerted on the car will be = 200 newtons
What will be the final speed and horizontal force of the car ?
It is given that mass= 2500 kg
Total energy =5000 j
Car distance = 25 m
So the change in KE [tex]=\dfrac{1}{2} mv_{f} ^{2} -\dfrac{1}{2} mv_{i} ^{2}[/tex]
[tex]=\dfrac{1}{2} mv_{f} ^{2}[/tex] Since [tex]V_{ i} =0[/tex]
[tex]=\dfrac{1}{2} \times2500\times v_{f} ^{2}[/tex]
[tex]5000=\dfrac{1}{2} \times2500\times v_{f} ^{2}[/tex]
[tex]V_{f} =2 \dfrac{m}{s}[/tex]
Now the Total change in energy = Work done
[tex]=F\times d[/tex]
[tex]5000= F\times 25[/tex]
[tex]F= 200 N[/tex]
Hence
Final velocity [tex]V_{f}[/tex] of the car will be 2 meters per second
Horizontal force exerted on the car will be = 200 newtons
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A 0.5 kg air-track car is attached to the end of a horizontal spring of constant k = 20 N/m. The car is displaced 15 cm from its equilibrium point and released.
a) What is the car's maximum speed? b) What is the car's maximum acceleration? c) What is the frequency f of the car's oscillation?
I need help please! Do it step by step and then substitute the numbers into that equation
two forces have the same magnitude F, what is the angle between the two vectors if their sum has a magnitude of (a) 2F? (b) sqrt of 2F (c) zero? Sketch the three vectors in each case. ...?
The angle between two equal forces depends on the resultant force when these two are added. It's 0 degrees if their sum is 2F (same direction), 90 degrees if their sum is sqrt of 2F (perpendicular), and 180 degrees if their sum is zero (opposite directions).
Explanation:The angle between the two forces with the same magnitude F depends on the resultant force when the two forces are added vectorially.
If the magnitude of their sum is 2F, the two forces are in the same direction, meaning the angle between them is 0 degrees. If the magnitude of their sum is sqrt of 2F, the two forces are perpendicular to each other, meaning the angle between them is 90 degrees. If the magnitude of their sum is zero, the two forces are in opposite directions, meaning the angle between them is 180 degrees. Learn more about Vector Addition of Forces here:
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What property must a refrigerant of a cooling system have? Why?
Refrigeration compressors turn gases into high-pressure and -temperature gases, are also used to maintain a low boiling point.
The crystals that form in slowly cooling magma are generally ____. a. nonexistent c. tiny b. invisible d. large
The height of a helicopter above the ground is given by h = 2.80t3, where h is in meters and t is in seconds. At t = 1.55 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground? ...?
Answer:
The time is 4.692 sec.
Explanation:
Given that,
Height [tex]h = 2.80t^3[/tex]
Time t = 1.55 s
We know that,
The rate of change of height is the velocity.
So, the velocity is at t = 1.55 s
[tex]\dfrac{dh}{dt}= v = 3\times2.80\times(1.55)^2[/tex]
[tex]v=20.181\ m/s[/tex]
The velocity is upward with respect to the ground
We need to calculate the distance above the releasing point
Using equation of motion
[tex]v^2=u^2-2gs[/tex]
Put the value into the formula
[tex]s=\dfrac{v^2}{2g}[/tex]
[tex]s=\dfrac{20.181^2}{2\times9.8}[/tex]
[tex]s=20.77\ m[/tex]
The height of the helicopter releases a small mailbag
[tex]h=2.80\times(1.55)^3[/tex]
[tex]h = 10.43\ m[/tex]
We need to calculate the time
Using equation of motion
[tex]s=ut-\dfrac{1}{2}gt^2+h[/tex]
Put the value into the formula
[tex]0=20.77\times t-\dfrac{1}{2}\times9.8\times t^2+10.43[/tex]
[tex]t=-0.454,4.692[/tex]
On neglecting negative value of time
Hence, The time is 4.692 sec.
All simple machines are variations of two basic machines.
True
False
...?
Simple machines are not variations of two basic machines; there are actually six types of simple machines: levers, pulleys, screws, inclined planes, wedges, and wheels and axles.
Explanation:False. Simple machines are not variations of two basic machines. In fact, there are six types of simple machines: levers, pulleys, screws, inclined planes, wedges, and wheels and axles.
a star’s apparent brightness is dependent upon
Which energy-level change shown in the diagram below emits electromagnetic radiation with the longest wavelength?
a) an electron moving from 4 to 5
b) an electron moving from 5 to 2
c) an electron moving from 6 to 1
d) an electron moving from 2 to 1
The smallest change in energy levels corresponds to the longest wavelength of emitted radiation. Based on the options, the electron moving from 2 to 1 would result in the longest wavelength.
Explanation:The energy-level change which emits electromagnetic radiation with the longest wavelength would be the smallest change in energy levels. According to the Planck-Einstein relation, the energy of a photon is inversely proportional to the wavelength. Thus, less energy transition implies longer wavelengths. Referring to the available options, an electron moving from 2 to 1 (option d) represents the smallest energy change and therefore emits radiation with the longest wavelength.
The energy-level change that emits electromagnetic radiation with the longest wavelength is when an electron moves from energy level 6 to energy level 1. This is because the energy difference between the highest and lowest energy levels is the greatest, resulting in the emission of photons with longer wavelengths.
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A student squeezes several oranges to make a glass of orange juice. The juice contains pieces of orange pulp mixed with the juice. Explain why this drink can be considered a combination of a suspension and a solution.
Answer:
The juice contains sugars, plant pigments, and other chemicals dissolved in water. This is a solution. The pieces of orange pulp will rise to the top or settle to the bottom of the juice if it is allowed to sit. The pieces of pulp mixed with the juice form a suspension.
Explanation:
Final answer:
The orange juice can be considered a combination of a suspension and a solution because it contains both suspended particles of orange pulp and dissolved species, such as juice molecules and ions.
Explanation:
The orange juice can be considered a combination of a suspension and a solution because it contains both suspended particles of orange pulp and dissolved species, such as juice molecules and ions.
The orange pulp in the juice is an example of a suspension, which is a heterogeneous mixture composed of relatively large particles that are visible. The pulp particles are suspended in the juice and can settle out over time.
On the other hand, the juice itself is a solution, which is a homogeneous mixture where no settling occurs. The dissolved juice molecules and ions are evenly distributed in the liquid, giving it a transparent appearance.
Which of the following is the most appropriate unit to describe the rate at which water flows out through a standard household faucet?
Minutes per gallon, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.
Gallons per minute, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.
Minutes per gallon, because the independent quantity is time in minutes and dependent quantity is volume of water in gallons.
Gallons per minute, because the independent quantity is time in minutes and dependent quantity is volume of water in gallons.
Answer:
Gallons per minute, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.
Explanation:
As we know that gallons is the unit of volume which is used in US to measure volume of gas as well as liquids while time is measured in minutes.
Now we know that if we need to find the volume flow rate then in that case the measurement is done to find the amount of fluid flow per unit of time
so here since volume flow is an independent variable which do not depends on any other parameter while time is a dependent variable here which is given as
[tex]flow \: rate = \frac{dV}{dt}[/tex]
so correct answer will be
Gallons per minute, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.
Victoria has a crate of vegetables that weighs 100 newtons she exerts a force of 100 Newtons to lift the crate with a pulley what's the mechanical advantage in this situation.
Less than 1
Equal to 1
Equal to 0
More than 1
By definition, the mechanical advantage is the relationship that exists between the output force or load lifted and the value of the force applied.
Thus, using the definition, we have that the mechanical advantage is given by:
[tex] MA = \frac{100}{100}
MA = 1
[/tex]
Therefore, the mechanical advantage of lifting the box by using a pulley is equal to 1.
Answer:
The mechanical advantage in this situation is:
Equal to 1
Which of the following parts of an organism is most likely to become fossilized? A.)tooth B.)skin C.)heart D.)Lung
A dolphin emits ultrasound at 100kHz and uses the timing of reflections to determine the position of objects in the water. What is the wavelength of this ultrasound? Assume that temperature of water is 20C.
Final answer:
The wavelength of the ultrasound is approximately 0.01482 meters.
Explanation:
The wavelength of ultrasound can be calculated using the formula:
λ = v/f
Where:
λ is the wavelength
v is the speed of sound in the medium
f is the frequency of the ultrasound
In this case, the frequency of the ultrasound is 100 kHz, which can be converted to 100,000 Hz. The speed of sound in water at 20°C is approximately 1482 m/s. Substituting these values into the formula, we get:
λ = 1482 m/s / 100,000 Hz
λ ≈ 0.01482 m
The wavelength of the ultrasound is approximately 0.01482 meters.
HELP PLEASE! im stuck Solve 4cos2A = 3cosA for 90º≤A≤180º. (Enter only the number.) PLEASE I NEED IT ...?
A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver sees a small gap between a van and an 18-wheel truck and accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 25.0 m/s when it reaches the end of the ramp, which has length 129 m.
What is the acceleration of the car?
What are two ways to increase the acceleration of an object?
a train is travelling up an a 3.73 degrees incline at a speed of 3.25m/s when the last car breaks free and begins to coast without friction.
How long does it take for the last car to come to rest momentarily?
The train car's stopping time on a 3.73-degree incline at a speed of 3.25 m/s can be found using kinematic equations in physics after calculating the component of gravitational acceleration along the incline.
Explanation:To determine how long it takes for the last car of a train to come to rest when traveling up a 3.73 degrees incline at 3.25 m/s, we can use kinematics, a subdivision of mechanics in physics. The force pulling the train car back down the incline is due to gravity, which creates an acceleration opposite to the movement of the car.
First, find the acceleration due to gravity along the incline using the equation a = g * sin(θ), where g is the acceleration due to gravity (9.81 m/s²) and θ is the incline angle. In this case, a = 9.81 m/s² * sin(3.73 degrees).
Then, we can calculate the time it takes for the train car to come to rest using the kinematic equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (3.25 m/s), a is the acceleration found previously, and t is the time. Rearrange to find t: t = -u/a.
Completing these calculations gives us the time the train car will take to come to rest momentarily.
A boy kicks a football with an initial velocity of 20 m/s at an angle of 30 above the horizontal. What is the vertical component of it's velocity at the highest point of it's trajectory?
The maximum height that the football would reach which is the vertical component of it's velocity at the highest point of it's trajectory is 10m.
What is velocity?Velocity is the directional speed of a moving object as an indication of its rate of change in position. It is observed from a specific frame of reference and measured by a specific time standard.
As, the boy kicks the football at an angle, the ball will follow a parabolic projectile path due to the effect of gravitational force. The velocity of the ball would be equal to zero at its maximum height.
We can derive the following equation from the equations for projectile motion:
Maximum height = velocity × sin Θ
Maximum height = 20 m / s × sin 30°
= 20× 1/2
=10m
Therefore, the maximum height that the ball would reach would be 10 m.
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A positive charge Q is distributed uniformly along the positive y-axis between y=0 and y=a. A negative point charge, -q, lies on the positive x-axis, a distance x from the origin. Calculate the x and y components of the E-field produced by the charge distribution Q at points on the positive x axis.
The electric field components at points on the x-axis are determined concerning a positive charge Q uniformly distributed along the y-axis and a negative charge -q on the x-axis. The x-component is caused only by -q and the y-component is determined by integrating the electric field due to Q over y=0 to y=a.
Explanation:The electric field created by a point negative charge -q on the positive x-axis and a positive charge Q spread evenly along the positive y-axis is the subject of the problem set. The x-component and y-component for the E-field need to be determined.
Given the distribution of positive charge Q along the y-axis between y=0 and y=a, the electric field at any point y on the y-axis due to this distribution is E1 = kQ/y²
where 'k' is Coulomb's constant. The electric field E2 on the x-axis for the negative charge -q is equal to -kq/x² at any distance x from it. The total x-component, being only due to the negative charge, is -kq/x². The y-component, due to the positive charge, will be integrated over the limit y=0 to y=a, ∫kQ/y² dy from 0 to a.
This integral gives the total y-component of the electric field.
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what is slab pull i need help asap
The CORRECT answer is:
Cooler, denser crust sinks into the mantle
I know this because I am an online student, this was a question on my quiz which I got wrong. One I submitted the quiz, it gave me the correct answers to anything I get wrong.
You're welcome.
Niagara Falls is a good example of
a.
kinetic energy being converted into potential energy.
b.
potential energy being converted into kinetic energy.
c.
energy being lost.
d.
energy being created.
An object is launched at 20 m/s from a height of 65 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.9t² + 20t + 65. What is the object's maximum height? the numeric answer only, rounded to the nearest meter.
Answer:
Maximum height will be 85 meter
Explanation:
given that height of an object is function of time and it is given as
[tex]h(t) = -4.9 t^2 + 20t + 65[/tex]
here we can write it as
[tex]h(t) - 65 = 20 t + \frac{1}{2}(-9.8) t^2[/tex]
now we can compare it with the kinematics equation
[tex]y(t) - y_o = v_i t + \frac{1}{2}at^2[/tex]
now if we compare the two equations then we will have
initial height of object = 65 m
initial velocity of projection = 20 m/s
acceleration = - 9.8 m/s/s
now for the maximum height at which its final speed will become zero is given as
[tex]v_f^2 - v_i^2 = 2a(h - h_o)[/tex]
[tex]0 - 20^2 = 2(-9.8)(h - 65)[/tex]
[tex]-400 = -19.6(h - 65)[/tex]
[tex]h = 85.4 m[/tex]
So maximum height in meter in nearest integer will be 85 m
Heat transfer within a fluid takes place by
a. convection currents.
b. radiation.
c. conduction.
d. density. user: the energy from the sun that warms your face is transferred by a process called ______.
Every year, new records in track and field events are recorded. Let's take a historic look back at some exciting races.
On August 20, 1989, in Cologne, West Germany, Said Aouita of Morocco also established a world record when he ran the 3000. m run in 7.00 minutes, 29.45 seconds. What was his average speed (in m/s) for the race? Remember to include your data, equation, and work when solving this problem.