# A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 4 feet. When the radius is 4 ​feet, the area is changing at approximately nothing square feet per minute. ​(Type an integer or a decimal. Round to the nearest thousandth as​ needed.)

Rate of change of area is

Explanation:

Applying values we get

## Related Questions

During World War I, the Germans had a gun called Big Bertha that was used to shell Paris. The shell had an initial speed of 2.07 km/s at an initial inclination of 28.8 ◦ to the horizontal. The acceleration of gravity is 9.8 m/s 2 . How far away did the shell hit? Answer in units of km.

d = 369.38 km

Explanation:

The speed has a x-component and a y-component.

speed,x = 2.07cos(28.8°) = 1.81 km/s

speed,y = 2.07sin(28.8°) = 1.00 km/s

The time the shell flies is determined by the y-component, when it reaches the highest point the speed is 0 due to the gravitational acceleration.

0 = 1000 - 9.8 * t

9.8 * t = 1000

t = 102.04 s

After reaching the highest point the shell takes the same time to reach the ground where it was fired, so the total time it flies is 102.04* 2 = 204.08 s

Now you can calculate the distance it moves horizontally while it flies (constant speed)

d = 1.81 km/s * 204.08 s (I used the speed in km/s because the answer needs to be in km)

d = 369.38 km

Explain why the temperature for freezing point and boiling point are the same.

We have to wonder what substance you're working with.  Under normal, human environmental conditions, there are almost no substances that freeze and boil at the same temperature.

However, EVERY substance has SOME temperature, at some pressure, at which it "sublimes" ... passing directly from solid to gas, or from gas to solid, without existing in liquid form in between.  Even water does that, if the conditions are right.
If you are referring to the rules of Celsius, that applies. Since the freezing point of water in Celsius is 0 degrees and the boiling point of water is 100 degrees, it can be said that the to share an equal distance from each other. (100-100=0 and 0+100= 100) You would have to gain or lose 100 so they both gave the same distance from each other.

A box accidentally drops from a truck traveling at a speed of 20.0 m/s and slides along the ground for a distance of 30.0 m Calculate a) The acceleration of the box (assuming it is constant while sliding)

a= - 6.667 m/s²

Explanation:

Given that

The initial speed of the box ,u= 20 m/s

The final speed of the box ,v=  0 m/s

The distance cover by box ,s= 30 m

Lets take the acceleration of the box = a

We know that

v²= u ² + 2 a s

Now by putting the values in the above equation we get

0²=20² + 2 a x 30

a= - 6.667 m/s²

Negative sign indicates that velocity and acceleration are in opposite direction.

Therefore the acceleration of the box will be  - 6.667 m/s² .

What are the three properties of a magnet?

1. Magnets attract iron and other ferromagnetic materials such as neodymium and cobalt.

2. Magnets attract or repel other magnets.

3. In addition one part of a magnet will always point north when allowed to swing freely.
The properties of a magnet is

all magnets have magnetic fields around them

the field emerges from one pole of the magnet conventionally known as the North Pole or returns to the other such South Pole

Would the phenomenon of parallax affect the precision of a measurement?

No, not the precision, but it can affect the accuracy of the measurement.

Yes parallax affects measurement precision

A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 6.1 105 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.

Radius between electron and proton

Explanation:

The motion of the electron is carried out in the orbit due to the balancing of the electrostatic force between the proton and the electron and the centripetal force acting on the electron.

The electrostatic force is given as =

Where,

k = coulomb's law constant (9×10⁹ N-m²/C²)

q₁ and q₂  = charges = 1.6 × 10⁻¹⁹ C

r = radius between the proton and the electron

Also,

Centripetal force on the moving electron is given as:

=

where,

= mass of the electron (9.1 ×10⁻³¹ kg)

V = velocity of the moving electron (given: 6.1 ×10⁵ m/s)

Now equating both the formulas, we have

=

substituting the values in the above equation we get,

If the speed of an object were to triple, what would be the increase of kinetic energy? KE↓2=_____KE↓1

1. 1/3
2. 1/9
3. 3
4. 9

4. 9

Explanation:

For instance, if the speed of an object becomes double, its kinetic energy changes to four times the initial kinetic energy.Similarly, if the speed of the object triples the kinetic energy becomes nine times the initial kinetic energy.

Therefore the answer is 9.

Technetium (Tc; Z = 43) is a synthetic element used as a radioactive tracer in medical studies. A Tc atom emits a beta particle (electron) with a kinetic energy (Ek) of 4.71 × 10−15 J. What is the de Broglie wavelength of this electron (Ek = mu2/2)?

Answer : The de-Broglie wavelength of this electron,

Explanation :

The formula used for kinetic energy is,

..........(1)

According to de-Broglie, the expression for wavelength is,

or,

...........(2)

Now put the equation (2) in equation (1), we get:

...........(3)

where,

= wavelength = ?

h = Planck's constant =

m = mass of electron =

K.E = kinetic energy =

Now put all the given values in the above formula (3), we get:

conversion used :

Therefore, the de-Broglie wavelength of this electron,

A Galilean telescope adjusted for a relaxed eye is 36.1cm long. If the objective lens has a focal length of 39.5cm , what is the magnification? Follow the sign conventions.

Magnification, m = 11.61

Explanation:

Given that,

Object distance, u = -36.1 cm

Focal length of the objective lens, f = +39.5 cm

Let v is the image distance. Using the formula of lens equation, we get :

v = -419.39 cm

Magnification of the lens is given by :

m = 11.61

So, the magnification of the Galilean telescope is 11.61. Hence, this is the required solution.