Invasive species often display a wave of advance as they colonize new areas. Mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the expression 2 Dr , where r is the reproductive rate of individuals and D is a parameter quantifying dispersal. Calculate v'(r), the derivative of the wave speed with respect to the reproductive rate r.

Answer:

a.) 10Hz

b.) 0.1 s

c.) 187.4 m/s

d.) -412.6 m/s^2

Explanation:

Given that an object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?

from the equation given,  the angular speed w = 20π

but w = 2πf

where f = frequency.

substitute w for 20π

20π = 2πf

f = 20π/2π

f = 10 Hz

(b) What is t the first time that the object is at its farthest right?

since F = 1/T

T = 1 / f

T = 1/10

T = 0.1 s

Therefore, the t of  first time that the object is at its farthest right is 0.1 s

(c) At the time found in part (b), what is the object's velocity?

The velocity can be found by differentiating the equation;

x(t) = 3sin(20πt)

dx/dt = 60πcos(20πt)

where dx/dt  = velocity V

V = 60πcos(20π * 0.1)

V = 187.4 m/s

(d) At the time found in part (b), what is the object's acceleration?

to get the acceleration, differentiate equation  V = 60πcos(20πt)

dv/dt = -1200πSin(20πt)

dv/dt = acceleration a

a = -1200πSin(20πt)

substitute t into the equation

a = -1200πSin(20π * 0.1)

a = - 412.6 m/s^2

The type of motion the object undergoes that consist of a back-and-forth

movement that is repetitive is a simple harmonic motion.

The correct responses are;

Reasons:

The equation that represents the motion of the object is x(t) = 3·sin(20·π·t)

Where;

t ≥ 0

x(t) is in cm, and t is in seconds.

(a) The general sine function is y = A·sin(B·(t - C) + D

[tex]\mathrm{The \ period \ P} = \dfrac{2 \cdot \pi}{B}[/tex]

By comparison, we have;

B = 20·π

Therefore;

[tex]P = \dfrac{2 \cdot \pi}{20 \cdot \pi} = \dfrac{1}{10} = 0.1[/tex]

The period, which is the time to complete one cycle = 0.1 seconds

The number of cycle completed per second, is the frequency, f

[tex]f = \dfrac{1}{P} = \dfrac{1}{0.1} = 10[/tex]

f = 10 Hz = 10 cycles

The number of cycle completed per second is f = 10 cycles

(b) When the object is at the farthest right, we have;

sin(20·π·t) = Maximum = 1

[tex]\mathbf{sin\left(\dfrac{\pi}{2}\right)} = 1[/tex]

Therefore,

[tex]20 \cdot \pi \cdot t = \dfrac{\pi}{2}[/tex]

[tex]t = \dfrac{\pi}{20 \cdot \pi \cdot 2} = \dfrac{1}{40} = 0.025[/tex]

The first time it is at the farthest right is t = 0.025 seconds after start

(c) [tex]\mathrm{Velocity, \ v, \ is \ given \ by \ v = \dfrac{dx(t)}{dt}}[/tex]

Therefore;

[tex]v = \dfrac{dx(t)}{dt} = \dfrac{dx(t)}{dt} \left(3 \cdot sin \left(20 \cdot \pi \cdot t \right) = 60\cdot \pi \cdot cos \left(20 \cdot \pi \cdot t \right)[/tex]

At t = 0.25 seconds, we have;

[tex]v = \dfrac{dx(t)}{dt} = 60\cdot \pi \cdot cos \left(20 \times \pi \times 0.025 \right) = 0[/tex]

The velocity of the object at the t = 0.025 seconds is v(t) = 0

(d) Acceleration, a, is given by [tex]a = \dfrac{dv(t)}{dt}[/tex]

Therefore;

[tex]a = \dfrac{dv(t)}{dt} = \dfrac{d}{dt} \left( 60\cdot \pi \cdot cos \left(20 \times \pi \times t\right) \right) =-1200 \cdot \pi ^2 \cdot sin(20 \cdot t \cdot \pi)[/tex]

a = -1200·π²·sin(20·t·π)

∴ a = -1200×π²×sin(20×0.025×π)

sin(20×0.025×π) = 1

∴ a = -1200×π²×1 ≈ -11843.53

At the time found in part b the acceleration of the object, a ≈ -11843.53 m/s²

Learn more here:

https://brainly.com/question/21731826

Answer:

on earth yes, but in space no because there is no gravity

Explanation:

plz can i have some points

The force exerted by an object depends on the mass of the object. Greater mass results in greater force. Hence, the statement is true.

Force is an external agent acts on a body to change the substance from the state of rest or motion. There are various kinds of force such as nuclear force, magnetic force, frictional force etc.

According to Newton's law of motion force in a moving body is the product of its mass and acceleration. Hence, force is directly proportional to mass and acceleration and an increase in these quantities will increase the force exerted by the body.

Thus, greater force is needed to a move a body with greater mass. If two objects of different masses exerts force each other, the greater force will be exerted by the massive body.

To find more on force, refer here:

https://brainly.com/question/13191643

#SPJ3

Answer:

6.7

Explanation:

Answer:

A. 50 km south

Explanation:

hope this helps!

Answer: Vx = 2.5m/s and Vy = 0m/s

Explanation: The ball is rolling horizontally on the floor, meaning there isn't a change in the vertical position, only horizontal. The ball is rolling with pure horizontal motion and isn't moving in the vertical direction.

Answer:

9,200 m

Explanation:

1 kilometer = 1000 meters so if there is 9 kilometers then it is 9000 meters, then .2 kilometer is equal to 200 meters. Add the numbers together to get 9,200 meters

To make this problem solvable and you can get the help you need, I'll complete and arrange some data.

Answer:

Acceleration: [tex]0.0417\ m/s^2[/tex], Distance=7,500 m

Explanation:

Uniform Acceleration Motion

It's a type of motion in which the velocity of an object changes uniformly over time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:

[tex]v_f=v_o+at\qquad\qquad [1][/tex]

The distance traveled by the object is given by:

[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]

Using the equation [1] we can solve for a:

[tex]\displaystyle a=\frac{v_f-v_o}{t}\qquad\qquad [3][/tex]

The problem will be rewritten as follows:

A train starting from rest reaches a velocity of 90 km/h in 10 minutes. Assuming that the acceleration is uniform, find the acceleration and the distance traveled by the train for attending the velocity​.

Let's take the relevant data:

vo=0

vf=90 Km/h*1000/3600 = 25 m/s

t = 10 minutes = 10*60 = 600  seconds

Now compute the acceleration by using [3]:

[tex]\displaystyle a=\frac{25-0}{600}=0.0417[/tex]

[tex]a=0.0417\ m/s^2[/tex]

Finally, compute the distance:

[tex]\displaystyle x=0*600+\frac{0.0417\cdot 600^2}{2}[/tex]

[tex]x=7,500\ m[/tex]

Note: We used the value of the acceleration with more precision than shown.

Acceleration: [tex]\mathbf{0.0417\ m/s^2}[/tex], Distance=7,500 m

Answer:

Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater ...

Answer:

80

Explanation:

Answer:

Encoding

Explanation:

Encoding is the initial learning of information. Encoding is the process of passing new information coming from sensory input  into our brain so that it can be easily retrievable. In a nutshell, it is the sum total of the processes by which external information such as the list of items your mother asked you to pick up at the grocery store to be converted into a manner that can be stored within the brain and recalled later from long-term memory.

Encoding has to do with transferring external stimuli into short term and subsequently long-term memory.

Answer:

It's 31

Explanation:

add 15 and 16

Answer:

162

Explanation:

When the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units. Therefore, option C is correct.

The term amplitude is defined as the maximum distance moved by a point on a vibrating body or wave calculated from its equilibrium position.

We have given,

first amplitude, A = 1, corresponding energy = 2

second amplitude, A = 2, corresponding energy = 8

The energy of a string at  a given amplitude is calculated as follows;

E ∝ A²

Energy varies as the square of the change in amplitude.

If amplitude of one has energy of two

Amplitude of 2 (double of 1)

= ( 2 x 2 ) = 4 x 2

= 8  4 times the energy at amplitude of 1.

Then for 8 units of amplitude change

8 x 8 = 64 x 2

= 128  

Thus, When the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units, option C is correct.

To learn more about an amplitude, follow the link;

https://brainly.com/question/15930409

#SPJ2

Your question is incomplete, most probably your question was

The data table shows how the amplitude of a mechanical wave varies with the energy it carries. Analyze the data to identify the mathematical relationship between amplitude and energy. Use your equation to find the energy if the amplitude is 8 units.

Amplitude

1

2

3

4

energy

2

8

18

32

A.66 units

B. 108 units

C. 128 units

D. 88 units ​

Answer:

40 km/h

Explanation:

First...

Look at the formula speed is equal to the distance over time or s = d/t.

Next...

Use the formula: 240/6.0

Finally...

Solve: 40

So the answer: 40 km/h

Answer:

wavelength

Explanation:

the definition of wavelength is the distance from one Crest to the next crest,or one trough to the next trough

The phenomenon that refers to the distance between two crests or two troughs on a transverse wave is wavelength.

Wavelength is simply defined as the distance between successive crests of a wave, particularly in a sound.

In conclusion, wavelength refers to a traveling particle.

Read more about Wave

https://brainly.com/question/3004869

Answer:

the answer is A.) Wedge

A knife to cut a piece of bread is a A. Wedge

A simple machine, any of several devices with few or no moving parts that are used to modify motion and the magnitude of a force in order to perform work.

since , a wedge is a simple machine  with two inclined planes which when put together forms a sharped edge, which forms a triangular shaped tool which can be used to separate portion of  two objects .

hence , a knife to cut a piece of bread is a A. Wedge

learn more about simple machine

https://brainly.com/question/10075890?referrer=searchResults

#SPJ2

Answer:

[M L2 T-2]

Explanation:

hope this is what you're looking for.

Answer:

8.8 hours

Explanation:

plz give me a Brainliest

Answer:

D

Explanation:

I could be wrong, But I'm pretty sure it's D

Answer:

it all is force I the barly kick you then it won't do that much date but If the full force kick you then it might hurt.

Explanation:

i hope this helps

The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal best describes Zach’s error.

A device that uses stimulated emission of photons from excited atoms or molecules to produce a strong beam of coherent monochromatic light is a laser.

When electrons in optical materials like glass, crystal, or gas absorb energy from an electrical current or light, a laser is formed.

The increased energy excites the electrons, causing them to migrate from a lower-energy orbit around the nucleus to a higher-energy orbit.

The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal. This statement is incorrect.

Hence Option A best describes Zach’s error.

To learn more about the laser refer to the Link ;

https://brainly.com/question/14783882

Answer:

D. Light escapes through the partially reflective mirror, not the highly reflective mirror.

Explanation:

edge 2022, I took the test.

Answer: The process is called artificial selection because people (instead of nature) select which organisms get to reproduce.

Explanation: This is evolution through artificial selection and the characteristics to reproduce, causing the evolution of farm stock.

Answer:

Capacidad de almacenamiento ofrecida por los DVD

Hay que mencionar que es posible conseguir DVD de una o dos capas. Los DVD que cuentan con una capa son capaces de almacenar aproximadamente 4.7GB de datos, mientras que los de doble capa ofrecen la posibilidad de almacenar alrededor de 8.5GB

Explanation:

Answer:

4 layers

Explanation:

i took the quiz

Answer: Approximately 302 m/s^2

================================================

Work Shown:

s = starting velocity = 0

f = final velocity  = 46

d = distance = 3.5

a = acceleration = unknown (we're solving for this)

[tex]f^2 = s^2 + 2a*d \ \ \text{ ..... one of the kinematics equations}\\\\46^2 = 0^2 + 2a*3.5\\\\2116 = 7a\\\\7a = 2116\\\\a = \frac{2116}{7}\\\\a \approx 302.28571\\\\a \approx 302[/tex]

The acceleration to three sig figs is roughly 302 m/s^2

The acceleration is so large because the ball's final velocity is incredibly fast in such a short amount of time.

Answer:

This has 5 significant figures.

Explanation:

Acceleration is the rate of change in the speed of an object. If initial and final speed are v₁ and v₂. It changes speed in time t. Its formula is given by :

[tex]a=\dfrac{v_2-v_1}{t}[/tex]

The problem is "A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? "

In this problem,

v₁ = 2 , v₂ = 10 m/s and t = 3 s

Acceleration of the object,

[tex]a=\dfrac{10-2}{3}\\\\a=2.67\ m/s^2[/tex]

So, the acceleration of the skater is [tex]2.67\ m/s^2[/tex].

Answer:

I believe the correct answer is 30m/s/s

Answer:

The magma, molten rock under the surface, and lava (molten rock on the surface) harden into igneous rock. The igneous rock then breaks apart over time through the process of weathering.

Explanation:

Gravitational force between two cars are 2.92 × 10 ⁻¹¹ Nm²/kg.

The universal force of attraction happened between two objects is called as gravitational force.

The mass of the two cars, m₁ = 2565 kg

                                            m₂ = 4264 kg

                                             r = 5m

                                            G = 6.67 ₓ 10 ⁻11 Nm²/kg

How gravitational force can be calculated?

Definition of gravitational force: The force of attraction between any two bodies is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

                            F ∝ m₁ m₂ ÷ r²

where the force exerted between the two masses m₁ and m₂,

                            F = G (m₁ m₂) ÷ r²

where as,  F - Gravitational force between two bodies,

                 G - Gravitational constant,

                 m₁ - mass of the first body,

                m₂ - mass of the second body,

                r² - square of the distance between two bodies.

                        F= 6.67 × 10⁻¹¹ Nm²/kg ( 2565 kg × 4264 kg) ÷ ( 5²)

         Hence,

                         F = 2.92 × 10⁻⁵ N

Option D is correct answer.

Learn more about Newton's law of Gravitation,

https://brainly.com/question/9373839

#SPJ5

Answer:

The correct option is;

C. The temperature of the air affects the speed of sound

Explanation:

The information given are;

The speed with which sound travels in the desert air = 358 m/s

The speed with which sound travels in the polar air = 330 m/s

The major difference between the desert air and the polar air is that the temperature of the desert air is hotter than the temperature of the air in the polar region. Therefore the speed of sound is affected by the air temperature.

The equation that gives the relationship of the speed of sound in air, [tex]v_{air}[/tex], to temperature is presented as follows;

[tex]v_{air} = 331\frac{m}{s} \times \sqrt{\dfrac{T_K}{273 K} } = 331\frac{m}{s} \times \sqrt{1 + \dfrac{T_{^{\circ}C}}{273 ^{\circ} C} }[/tex]

Which shows that the speed of sound in air, [tex]v_{air}[/tex], rises as the temperature of the air rises.

Where;

[tex]T_{^{\circ}C}[/tex] = The temperature of the air in degrees Celsius

[tex]T_K[/tex] = The temperature of the air in degrees Kelvin.