In order to compute a power of two, you can take the next-lower power and double it. For example, if you want to compute 211 and you know that 210 = 1024, then 211 = 2 × 1024 = 2048. Based on this observation, write a recursive function int pow2(int n) where n is the exponent. If the exponent is negative, return -1.
Answers
To compute \(2^3\), the function first calls itself with \(n=2,\) which computes\(2^2 = 4\). Then, the function doubles this result to get \(2^3 = 8.\)
Here is the pseudo-code for the pow2 function:
function pow2(n):
if n < 0:
return -1
if n == 0:
return 1
else:
prev_power = pow2(n-1) # Compute 2^(n-1) recursively
return prev_power * 2 # Double the result to get \(2^n\)
The base case for the recursion is when n is 0, in which case the function returns 1 since \(2^0 = 1.\)
The function recursively calls itself with smaller values of n until it reaches the base case. The recursive calls build up the power of 2 by doubling the previous power.
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Related Questions
What is likely to occur after a lava flow has destroyed all life in a natural community?
A:growth of opportunist species
B:climax community
C:primary succession
D:secondary succession
Answers
Answer:
C: primary succession
Explanation:
I took the test :)
Mmoon: 0.0123ME
Rmoon: 0.272RE
MMars: 0.107ME
RMars: 0.530RE
Above, the masses and radii of the moon and Mars are given as fractions of the mass and radius of the earth. Calculate their accelerations due to gravity at their surfaces. [Below, the masses and radii of the moon and Mars are given as fractions of the mass and radius of the earth. Calculate their accelerations due to gravity at their surfaces. [The calculation is simplified if you directly substitute in the equation the lunar and Martian fractional factors for mass over radius squared and multiply the answers times 9.8.]
Answers
The acceleration due to gravity at the surface of a celestial body can be calculated using the formula:
a = G * M / R^2
where G is the gravitational constant, M is the mass of the celestial body, and R is its radius.
Substituting the lunar and Martian fractional factors for mass over radius squared and multiplying the answers by 9.8, we have:
Acceleration due to gravity at the surface of the Moon:
a = G * Mmoon / Rmoon^2 = G * (0.0123ME) / (0.272RE)^2 = 1.62 m/s^2
Multiplying by 9.8, we have:
a = 1.62 * 9.8 = 15.88 m/s^2
Therefore, the acceleration due to gravity at the surface of the Moon is approximately 1.62 m/s^2, or 15.88 m/s^2 when multiplied by 9.8.
Acceleration due to gravity at the surface of Mars:
a = G * MMars / RMars^2 = G * (0.107ME) / (0.530RE)^2 = 3.71 m/s^2
Multiplying by 9.8, we have:
a = 3.71 * 9.8 = 36.41 m/s^2
Therefore, the acceleration due to gravity at the surface of Mars is approximately 3.71 m/s^2, or 36.41 m/s^2 when multiplied by 9.8.
what is acceleration due to gravity ?Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
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2. Gerard is riding his bicycle directly east. His maximum
instantaneous velocity was 8 meters per second and his
minimum instantaneous velocity was 0 meters per second. He
covered 7.20 kilometers in 20.0 minutes. What is his average
velocity for the ride?
Answers
Gerard's average velocity for the ride is 6 meters per second.
To find Gerard's average velocity for the ride, we can use the formula:
Average velocity = Total displacement / Total time
First, we need to convert the distance traveled from kilometers to meters:
7.20 kilometers * 1000 = 7200 meters
Next, we convert the time from minutes to seconds:
20.0 minutes * 60 = 1200 seconds
Now, we can calculate the total displacement by subtracting the initial position from the final position. Since Gerard is riding directly east, there is no change in the east-west direction, so the displacement is equal to the distance traveled:
Total displacement = 7200 meters
Finally, we substitute the values into the average velocity formula:
Average velocity = 7200 meters / 1200 seconds
Average velocity = 6 meters per second
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Water enters a typical garden hose of diameter 0.016 m with a velocity of 3 m/s. Calculate the exit velocity of water from the garden hose when a nozzle of diameter 0.0050 m) is attached to the end of the hose in units of m/s.
Answers
Answer:
v₂ = 306.12 m/s
Explanation:
We know that the volume flow rate of the water or any in-compressible liquid remains constant throughout motion. Therefore, from continuity equation, we know that:
A₁v₁ = A₂v₂
where,
A₁ = Area of entrance pipe = πd₁²/4 = π(0.016 m)²/4 = 0.0002 m²
v₁ = entrance velocity = 3 m/s
A₂ = Area of nozzle = πd₂²/4 = π(0.005 m)²/4 = 0.0000196 m²
v₂ = exit velocity = ?
Therefore,
(0.0002 m²)(3 m/s) = (0.0000196 m²)v₂
v₂ = (0.006 m³/s)/(0.0000196 m²)
v₂ = 306.12 m/s
A cheetah can accelerate from rest to 25.0 m/s in 6.22 s. Assuming constant acceleration, how far has the cheetah run in this time
Answers
Answer:
The distance covered by the cheetah during the motion is 77.75 m
Explanation:
Given;
initial velocity of cheetah, u = 0
final velocity of cheetah, v = 25 m/s
time of acceleration, t = 6.22 s
Apply kinematic equation;
\(s = (\frac{v+u}{2} )t\)
where;
s is the distance covered by the cheetah during the motion
\(s = (\frac{v+u}{2} )t\\\\s = (\frac{25+0}{2} )6.22\\\\s = 77.75 \ m\)
Therefore, the distance covered by the cheetah during the motion is 77.75 m
The diagram shows a charge moving into an electric field. Two horizontal parallel plates have equally spaced vectors going from the bottom plate to the top plate. A negatively charged sphere labeled Z in traveling horizontally in between the plates. A vector is pointing right. The top plate is labeled W. There is an X at the far end of the top plate and a Y at the far end of the bottom plate. The charge will most likely leave the electric field near which letter? W X Y Z
Answers
The negatively charged sphere Z is most likely to leave the electric field near the center of plates, which is closest to letter Y.
What is an electric field?Physical field that surrounds electrically charged particles and exerts force on all the other charged particles in the field is called an electric field.
Negatively charged sphere labeled Z will experience a force due to electric field created by parallel plates. Since the vector is pointing right, we can assume that electric field is also pointing right.
Electric field lines are perpendicular to plates and are equally spaced. Therefore, electric field is uniform in magnitude and direction between the plates.
As the negatively charged sphere Z travels horizontally between plates, it will experience force in the direction opposite to electric field due to its negative charge. This force will cause sphere to slow down and stop.
Since the electric field lines are equally spaced between the plates, electric field will be strongest at the edges of plates and weakest in the center. Therefore, negatively charged sphere Z is most likely to leave the electric field near the center of plates, which is closest to letter Y.
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This illustration shows two opposing forces pulling on a wagon. Which description best describes how the wagon will move?
10N
30N
The wagon will slow down
The wagon will move to the left.
The wagon will not move because the forces are opposite
The wagon will move to the right.
4 5 6 7 8
9 10 11 12 13
Next
Type here to search
Answers
Answer:
The wagon will move to the right.
Explanation:
From the question given above, the following data were obtained:
Force applied to the left (Fₗ) = 10 N
Force applied to the right (Fᵣ) = 30 N
Direction of the wagon =.?
To determine the direction in which the wagon will move, we shall determine the net force acting on the wagon. This can be obtained as follow:
Force applied to the left (Fₗ) = 10 N
Force applied to the right (Fᵣ) = 30 N
Net force (Fₙ) =?
Fₙ = Fᵣ – Fₗ
Fₙ = 30 – 10
Fₙ = 20 N to the right
From the calculations made above, the net force acting on the wagon is 20 N to the right. Hence the wagon will move to the right.
URGENTTTT
Referring to the graph in the section header, what was his displacement between 100 and 300 seconds?
Referring to the graph in the section header, what was the runner's velocity during segment D?
Answers
The displacement of the runner according to the graph is obtained as 250 m.
What is the displacement?The term displacement has to do with the distance that is covered in a specified direction. The difference between distance and displacement is that displacement is a vector while distance is a scalar quantity.
Thus we bring the direction into play when we are talking about the displacement of the object. Now we have a graph that shows the displacement of the runner in the vertical axis and then shows the time that is taken in the horizontal axis.
Given the graph as we have it, we can be bale to pick out the following from the graph;
1) Displacement of the runner at 100 s = 500 m
2) Displacement of the runner at 300 s = 750 m
Therefore;
Displacement of the runner between 100 and 300 seconds;
750 m - 500 m = 250 m
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20pts!
Alex slides a 170 g hockey puck across a sheet of ice. The coefficient of kinetic friction between the puck and the ice is 0.09. What is the puck's rate of acceleration as it slides across the ice?
-0.88 m/s2
−1.74 m/s2
−1.16 m/s2
−2.09 m/s2
Answers
The rate of acceleration of the hockey puck with a mass of 170 g is 0.88 m/s².
What is acceleration?Acceleration can be defined as the rate of change of velocity.
To calculate the acceleration of the puck, use the formula below.
Formula:
a = gμ................ Equation 1Where:
a = Acceleration of the puckg = Acceleration due to gravityμ = Cofficient of kinetic frictionFrom the question,
Given:
g = 9.8 m/s²μ = 0.09Substitute these values into equation 1
a = 9.8×0.09a = 0.88 m/s²Hence, puck's rate of acceleration is 0.88 m/s².
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An engine develops a power of 750watts while moving a car at constant velocity 3m/s therefore the work exerted on the car by the engine is. And please I need the solution
Answers
The work exerted on the car by the engine is 250 Joules.
What is Work?
Work is a physical quantity that is defined as the force applied to an object over a distance. It is a scalar quantity and is measured in units of joules (J) in the International System of Units (SI). The formula for work is W = F x d, where F is the force applied and d is the distance over which the force is applied.
The work exerted on the car by the engine can be calculated using the formula:
Work = Power x Time
Since the car is moving at a constant velocity, we can calculate the time it takes for the engine to exert the given power by using the formula:
Velocity = Work / Time
So, we can find time by using:
Time = Work / Velocity
Substituting the given values, we have:
Time = (750 watts) / (3m/s)
Therefore, the work exerted on the car by the engine is:
Work = Power x Time
Work = 750 watts x (750 watts / 3m/s)
Work = 750 * 250 Joules
So, the work exerted on the car by the engine is 250 Joules.
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A factory is closing in 15 minutes. A box on one of the factory's conveyor belts is 8meters from a storage area and is moving at a constant velocity of 40metersperminute down the conveyor belt. How long will it take the box to get to the storage area?
Answers
The time taken for the box to get to the storage area, given that the box is moving at a constant velocity of 40 meters per minute is 0.2 minutes
How do i determine the time taken?Speed is defined as the distance travelled per time as shown below:
Speed = Distance / time
Cross multiply
Speed × time = distance
Divide both sides by speed
Time = Distance / speed
The following data were obtained from the question:
Distance from storage area = 8 metersConstant speed of box = 40 meters per minuteTime taken =?The time take can be obtained as follow:
Time = Distance / speed
Time = 8 / 40
Time = 0.2 minutes
Thus, the time taken to get the storage area is 0.2 minutes
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What happens when acetate rubs with wool
Answers
When a Cellulose Acetate rod is rubbed with a woolen duster, friction occurs, rubbing loosely held electrons from the rod onto the duster. So, this time, the rod loses electrons. Since the Acetate rod now has fewer electrons than protons it has become positively charged. Hope this helps!
Answer:
The charge becomes positive.
Explanation:
When rubbed with cellulose acetate the charge of the fur/wool will become negative.
What is the scientific study of how animals are classified?
Answers
Answer:
biology
Explanation:
Animals and plants
True or False
In newton's 2nd law, f=ma there is a correlation between the force and acceleration. This supports that there is a causal relationship that acceleration has on the net force.
Answers
Answer: See explanation
Explanation:
Please see attached picture. Due to the fact one of the words in the equation F=ma contains a word not allowed.
An object is launched at a speed of 20 m/s. If it rises to a height of 12 m, at what angle was it launched? ________° above the +x direction
Answers
Given:
The initial speed of the object is,
\(u=20\text{ m/s}\)The maximum height is,
\(H=12\text{ m}\)To find:
The angle of launch above the X-axis
Explanation:
The maximum height above the X-axis is,
\(H=\frac{u^2sin^2\theta}{2g}\)Here, the angle above the X-axis is,
\(\theta\)Substituting the values we get,
\(\begin{gathered} 12=\frac{(20)^2sin^2\theta}{2\times9.8} \\ sin^2\theta=\frac{12\times2\times9.8}{400} \\ sin\theta=0.7668\text{ \lparen taking positive value only\rparen} \\ \theta=50.1\degree \end{gathered}\)Hence, the angle of launch is,
\(50.1\degree\)A penny is dropped from the top of the
Chrysler Building (320 m high). How fast is
it moving when it hits the ground?
Answers
Answer:
As the penny falls 320 meters, its vertical velocity increases at the rate of 9.8 m/s
Explanation:
Which scenario is an example of a physical change?
Wood is burned in a campfire and is turned into ash and smoke.
A piece of metal is left in the rain and forms rust.
Lead is melted into a liquid to form pellets.
Yeast turns sugar into energy, water, and carbon dioxide gas.
Answers
Answer:
Lead is melted into a liquid to form pellets.
Answer:
C. lead is melted into a liquid to form pellets
Explanation:
Which statement best explains why sensors (or senses) are necessary to produce a change in behavior?
A.
Organisms cannot sense stimuli without a central nervous system.
B.
Stimuli must be sensed in order to produce a response.
C.
Stimuli must be responded to in order to be sensed.
D.
Organisms cannot respond to stimuli without a central nervous system.
Answers
Answer:
It is (B) Stimuli must be sensed in order to produce a response.
Explanation:
Which form of energy has the most potential globally
a) Solar energy
b) Bio energy
c) Wind energy
d) Geothermal energy
Answers
Answer:
i think the answer is solar,
Explanation:
because it is a natural resource im sorry if im wrong
A cylindrical water tank open to the atmosphere, 10 m tall and 6 m in diameter, is mounted with its base 25 m above ground level, and filled with water.
Calculate
a) the water pressure and force at the base of the tank?
b) the pressure in a water pipe at ground level?
c) the speed with which water will push out of a leak at a height of 8 m above the ground?(hint: force is equal to horizontal rate of change of momentum of water)
Answers
The bottom of a cylindrical water tank, 10 m tall and 6 m in diameter, is 25 m above the ground. According to calculations, the water pressure and force at the bottom of the tank are 343,000 Pascal and 9,685,941 Newtons, respectively.
A water pipe at ground level has the same pressure as one at the tank's base. The rate of water egress from a leak 8 metres above the ground is around 19.6 metres per second.
These calculations are based on the conservation of energy and hydrostatic principles.This pressure can also be found in a ground-level water pipe. Water will seep from a leak 8 metres above the ground at a speed of about 19.6 metres per second.
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Using the concepts of impulse and momentum, describe how to win a water balloon contest by not breaking the balloon.
Requirements:
o Focus on the catch.
o You must mention how momentum, impulse, force and impact time play a part in the catch.
o You may use diagrams to support your reasoning.
o Remember the equation: ∆p = m∆v = F∆t
Answers
You must concentrate on the catch to win a water balloon contest without breaking the balloon. Momentum, impulse, force, and impact time are all important factors in the catch's success. The key to catching a water balloon without breaking it is to reduce the balloon's impact force. The momentum of the balloon, the impulse applied to the balloon, and the impact time all contribute to the impact force.
What is the momentum?The product of an object's mass and velocity is its momentum. As it is thrown towards you, the water balloon has a certain mass and velocity. The greater the balloon's momentum, the more difficult it will be to catch it without breaking it.
In order to catch a water balloon, you must apply an impulse to the balloon. The higher the impulse, the more effectively you can stop the balloon. To catch a water balloon without breaking it, apply a large impulse to the balloon in a short period of time. This reduces the impact force on the balloon and keeps it from breaking.
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Group B[1] 12 State Huygens's Principle [2] b) In a Young's double slit experiment, the fringe width obtained is 0.6 cm. When light of wave length 4500 Aº is used if the distance between the screen and the slit is reduced in half, what should be the wavelength of light used to obtain fingers 0.0045 m wide? [3]
Answers
The wavelength of light that should be used to obtain fringes that are 0.0045 m wide after reducing the distance between the screen and the slit by half is 2.25 * 10^7 Å.
Huygens's Principle states that every point on a wavefront can be considered as a source of secondary spherical wavelets that spread out in all directions with the same speed as the original wave. The new wavefront is formed by the envelope of these secondary wavelets at a later time.
Now, let's consider a Young's double-slit experiment. In this experiment, when light passes through two narrow slits, it creates an interference pattern on a screen behind the slits. The fringe width is the distance between two consecutive bright or dark fringes in the pattern.
Given that the fringe width obtained is 0.6 cm and the wavelength of light used is 4500 Å (Angstroms), we can calculate the wavelength of light required to obtain fringes that are 0.0045 m wide.
We can use the formula for fringe width in Young's double-slit experiment:
w = (λ * D) / d
Where:
w is the fringe width,
λ is the wavelength of light,
D is the distance between the screen and the double slits, and
d is the distance between the two slits.
Let's calculate the value of D/d using the given information:
D/d = w / λ
= 0.006 m / 4500 Å (1 m = 10^10 Å)
= 0.006 * 10^10 / 4500 m^-1
Now, if the distance between the screen and the slit is reduced by half, the new value of D/d would be:
(D'/d) = (0.006/2) * 10^10 / 4500 m^-1
Now, we can rearrange the equation to solve for the new wavelength (λ'):
(λ' * D') / d = (D/d)
λ' = (D/d) * d / D
= [(0.006/2) * 10^10 / 4500] * (4500 / 0.006) Å
= 0.0045 m * 10^10 / 2 Å
= \(0.00225 * 10^{10\) Å
=\(2.25 * 10^7\)Å
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(Need help pls)!!!!!
Answers
Answer:
I assume they want answer A, but it's a silly question.
Explanation:
Well, if we assume that the girls are applying equal force, as they are the same size and strength (apparently also the same resolve etc.).
Equal force in opposite directions means the composite force is null. An object that no force is applied to continues moving in the same direction, so if the doll was moving somewhere, it would keep doing so, except all of this makes no sense the doll is not in gravityless vacuum what are we even talking about.
The answer A is the least ridiculous.
a sprinter accelerates from rest to 14m/s in 1.38 s. what is her acceleration in km/h^2
Answers
The acceleration of the sprinter is approximately 131,426 km/h^2.
To find the acceleration in km/h^2, we need to convert the units from meters per second (m/s) to kilometers per hour (km/h) and adjust the time units accordingly. Here's the step-by-step calculation:
1. Convert the final velocity from m/s to km/h:
14 m/s * (3.6 km/h) / (1 m/s) = 50.4 km/h
2. Convert the time from seconds (s) to hours (h):
1.38 s * (1 h) / (3600 s) = 0.0003833 h
3. Calculate the acceleration using the formula:
Acceleration = (Final velocity - Initial velocity) / Time
Since the initial velocity is 0 m/s (rest), we have:
Acceleration = (50.4 km/h - 0 km/h) / 0.0003833 h
Acceleration = 131425.955 km/h^2
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How might writing an online journal be different than writing in a paper one?
A. It's ok to talk badly about people in an
online journal.
O B. It's easier to communicate online.
O C. You should expect less privacy.
O D. You should expect more privacy.
Answers
Writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online (option B).
What is a journal?A journal is a newspaper or magazine dealing with a particular subject.
A journal is an efficient medium to communicate the findings or results of an investigation to the public.
However, a journal can be virtual (online) or paper (hard copy). In this 21st century, it is easier to communicate to the masses online because more audience will be captured.
Therefore, writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online.
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What kind of object are the light rays interacting with in the model below?
Convex mirror
Convex lens
Concave mirror
Concave lens
Answers
Answer:
Concave lens
.............
What is the force on a 1,000 kg elevator that is falling freely at
25 m/s?
Answers
Explanation:
Force=mass*acceleration
Mass=1000kg
Acceleration=25m/s
F=1000*25
F=25000N
Find the kinetic energy of a ball of mass 200 grams moving at a speed of 20 m/s
Answers
Answer:
40 J
Explanation:
\(KE = \frac{1}{2} mv^{2} \\KE = \frac{1}{2} (0.200 kg)(20 m/s)^{2} \\KE = 40 J\)
An electron traverses a vacuum tube with a length of 2 m in 2 X 10- 4
sec. What is the average speed of the
electron during this time?
Answers
Answer:
\(v=10^4\ m/s\)
Explanation:
Given that,
The length of a vacuum tube, d = 2 m
Time, \(t=2\times 10^{-4}\ s\)
We need to find the average speed of the electron during this time. Average speed is equal to total distance covered divided by total time taken.
Here, total distance = length of the vacuum tube
\(v=\dfrac{2}{2\times 10^{-4}}\\\\=10^4\ m/s\)
So, the average speed of the electron is \(10^4\ m/s\).
A 5kg objects is sliding across a floor at 10m/s. How much work is done by friction to bring it to a stop?
Answers
If A 5kg objects is sliding across a floor at 10m/s.then the work done by friction to bring the 5 kg object to a stop is -250 Joules.
To calculate the work done by friction to bring the object to a stop, we need to determine the change in kinetic energy.
Given:
Mass of the object, m = 5 kg
Initial velocity, u = 10 m/s
Final velocity, v = 0 m/s (object comes to a stop)
The work done by friction can be calculated using the equation:
Work = Change in Kinetic Energy
The change in kinetic energy (ΔKE) can be calculated as:
ΔKE = (1/2) * m * (v^2 - u^2)
Plugging in the values:
ΔKE = (1/2) * 5 kg * (0 m/s)^2 - (10 m/s)^2
= (1/2) * 5 kg * (0 - 100 m^2/s^2)
= (1/2) * 5 kg * (-100 m^2/s^2)
= -250 J
The negative sign indicates that the work done by friction is in the opposite direction of the displacement of the object.
Therefore, the work done by friction to bring the 5 kg object to a stop is -250 Joules.
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