(a) The limit of the exponential function is infinity. (b)the limit of the exponential function is infinity. (c)the limit of the exponential function is infinity.
What is differential equation?A differential equation is an equation which has one or more terms and the derivatives of one variable with respect to the other variable dy/dx = f(x), where “x” is an independent variable and “y” is dependent variable.
(a) P(t) = 50e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be a parabola that starts at 50 and increases as t increases.
(b) P(t) = 300e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of the exponential function is infinity. The graph of P(t) would be parabola that starts at 300 and increases as t increases.
(c) P(t) = 500e^(0.02t^2)
The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be parabola that starts at 500 and increases as t increases.
All of the graphs are increasing and have no inflection point. They are increasing because the exponential function e^(0.02t^2) is positive, and it will always increase as the t increases.
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A 0.5 Kg ball is kicked and has a maximum kinetic energy of 225 J. What is the maximum height above the ground the ball will reach?
I am looking more for the formula because i have several to work.
Answer:
45.9 m
Explanation:
KE = 1/2mv² = 225 J
PE = mgh
If all the KE is converted to PE, then:
(0.50 kg)(9.8 m/s²)(h) = 225 J
h = (225 J) / (0.50 kg)(9.8 m/s²) = 45.9 m
(a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (Use the following as necessary: M, L, and T.)
[force] =
(b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons using the fundamental units of mass, length, and time? (Use the following units as necessary: kg, m, and s.)
The behavior of things is predicted by Newton's first law of motion when all external forces are equal.
What is Newton's second law?The first law, sometimes known as the law of inertia, asserts that if an object's forces are balanced, its acceleration will be zero meters per second.
When all forces are balanced, an object is said to be in equilibrium and won't accelerate. Newton postulated that an item will only accelerate in the presence of a net or unbalanced force. An object will accelerate if there is an imbalanced force present, changing its direction, speed, or both.
Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
Therefore, The behavior of things is predicted by Newton's first law of motion when all external forces are equal.
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choose a process and system that match the following energy description: the kinetic energy of an object becomes gravitational potential energy of the system\
One process and system that matches the following energy description: "the kinetic energy of an object becomes gravitational potential energy of the system" is a roller coaster.
How does the conversion of gravitational potential energy to kinetic energy and vice versa in a roller coaster contribute to the thrill and excitement of the ride?The conversion of gravitational potential energy to kinetic energy and vice versa in a roller coaster contributes to the thrill and excitement of the ride because it creates a sense of acceleration, speed and height. As the roller coaster car goes up the hill, the rider feels a pull in their stomach as they gain potential energy, and as the car goes down the hill, they feel a rush of speed as they gain kinetic energy. This back and forth conversion of energy creates a sense of unpredictability and excitement for the rider. Additionally, the change in speed and direction also create an illusion of weightlessness as the riders feel themselves being pulled out of their seats. This all together creates an exciting and thrilling experience for the riders.
In a roller coaster, a train or cars are pulled to the top of a hill using a motor or chain lift. As the train goes up the hill, it gains gravitational potential energy. As the train goes over the hill and down the other side, it loses gravitational potential energy and gains kinetic energy. This process continues as the train goes through various hills and valleys on the roller coaster.
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Taste substance binding elicits conformational change of taste receptor T1r heterodimer extracellular domains
Sweet and umami tastes are perceived by T1r taste receptors in oral cavity. T1rs are class C G-protein coupled receptors (GPCRs), and the extracellular ligand binding domains (LBDs) of T1r1/T1r3 and T1r2/T1r3 heterodimers are responsible for binding of chemical substances eliciting umami or sweet taste. However, molecular analyses of T1r have been hampered due to the difficulties in recombinant expression and protein purification, and thus little is known about mechanisms for taste perception. true or false
Due to challenges with recombinant expression and protein purification, T1r molecular studies have been impeded. The mechanisms underlying taste perception are so poorly understood. The claim is accurate.
How do taste receptors work?The oral cavity's T1r taste receptors can detect sweet and umami flavors.T1rs are G-protein-coupled class C receptors (GPCRs)Chemicals that produce an umami or sweet taste bind to the extracellular ligand binding domains (LBDs) of the T1r1/T1r3 and T1r2/T1r3 heterodimers.The T1r receptors are responsible for the perception of sweet and umami tastes, but due to the challenges in studying them, there is limited understanding of how these receptors function.The units of pressure and temperature must be consistent with the units of R, which has a specific value depending on the units used.In the case of the bicycle tire, psi and Kelvin were used because they are the units that are consistent with the value of R in the ideal gas law.The units of pressure and temperature must be consistent with the units of R, which has a specific value depending on the units used.In this case, while it's possible to use other units, psi and Kelvin are the most convenient and standard units to use in this context.To llearn more about taste receptors refer:
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Macmillan Learning
A black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. Suppose a mongoose and a black mamba find
themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 8.37 m/s² from rest.
How much time ftop does it take the snake to reach its top
speed?
How far dsnake does the snake travel in that time?
How much time freact does the mongoose have to react before
the black mamba's tail passes the mongoose's nose?
ftop
dsnake =
freact=
S
m
S
Answer:
Explanation:
Δt = Δv/a = (4.5 m/s) / (8.37 m/s²) = 0.538 s = time to reach top speed
d = Vi + 1/2at²
d = 0 + 1/2(8.37 m/s²)(0.538 s)² = 1.21 m = distance snake traveled while accelerating
t = d/v = (2.60 m - 1.21 m) / (4.5 m/s) = 0.31 s = reaction time before snake tail passes mongoose nose
According to the question of speed, ftop is 0.9578 s, dsnake is 2.14 m, freact is 0.4773 s.
What is speed?
Speed is the rate at which an object moves from one place to another. It is expressed in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed is a scalar quantity, meaning that it has magnitude but no direction. Acceleration, on the other hand, is a vector quantity that has both magnitude and direction. Speed is directly related to the amount of time it takes an object to move from one point to another, and is inversely proportional to the time it takes to cover a given distance. Speed can also be affected by external factors such as wind, terrain, and friction. Speed is an important concept in physics and is often used to calculate the kinetic energy of an object.
ftop = 0.5 × (8.37 m/s²) / (4.50 m/s) = 0.9578 s
dsnake = 0.5 × (4.50 m/s) × (0.9578 s) = 2.14 m
freact = 2.14 m / (4.50 m/s) = 0.4773 s
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A spring has an unstretched length of 0.40 meter. The spring is stretched to a length of 0.60 meter when a 10.-newton weight is hung motionless from one end. The spring constant of this spring is?
O 10. N/m
O 17 N/m
O 25 N/m
O 50. N/m
The spring constant of this spring is 50 N/m, therefore, 4th option is correct.
What is spring constant?Spring constant is the amount of force (in newtons) required to extend a spring by one meter. In this case, the spring constant is 25 N/m. This can be calculated by taking the force (10 N) divided by the amount of extension (0.60 m - 0.40 m = 0.20 m).
[tex]$ \Rightarrow \mathrm{ \frac{10 N}{0.20 m} = 50N/m}[/tex]
The force necessary to expand or compress the spring by a specific quantity is measured, and the spring constant is then calculated. The force needed to extend or compress the spring by a specific amount may be calculated by measuring it, multiplying it by the extension or compression, and then dividing the result by the force.
The behavior of a system using springs, such as a shock absorber or any other device that employs springs, is significantly influenced by the spring constant. It may also be used to figure out how much force a spring can produce when it is squeezed or expanded.
Thus, The spring constant of this spring is 50 N/m, therefore, 4th option is correct.
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