Answer:
Billing experts at the entry level are normally expected to have a high school diploma or equivalent, as well as skills, certifications, and experience. Some jobs require at least an associate's or bachelor's degree.
Explanation:
Answer: high school diploma
Explanation:
A book that weighs 5 newtons is sitting on a table 1.5 meters above the floor. How much gravitational potential energy does the book have?6.5 joules
4.5 joules
7.5 joules
3.33 joules
Answer:7.5J
Explanation:7.5
J
Explanation:
P
E
=
m
g
h
Since
F
=
m
g
in this case
P
E
=
F
h
P
E
=
5
N
⋅
1.5
m
=
7.5
For the following types of electromagnetic radiation, how do the wavelength, frequency, and photon energy change as one goes from the top of the list to the bottom?
a. radio waves
b. infared radiation
c. visible light
d. ultraviolet radiation
e. gamma radiation
Answer:
Wavelength, frequency and the photon energy changes as the one goes across the ranges of the electro-magnetic radiations.
Explanation:
Electro-magnetic radiations may be defined as the form of energy that is radiated or given by the electro-magnetic radiations. The visible light that we can see is the one of the electro-magnetic radiations. Other forms are the radio waves, gamma waves, UV rays, infrared radiations, etc.
The wavelength of the radiations decreases as we go from a. radio waves -- b. infrared radiation -- c. visible light -- d. ultraviolet radiation -- e. gamma radiation.
The frequency of the radiations increases when we move from a. radio waves -- b. infrared radiation -- c. visible light -- d. ultraviolet radiation -- e. gamma radiation.
The photon energy of the radiations increases when we move from a. radio waves -- b. infrared radiation -- c. visible light -- d. ultraviolet radiation -- e. gamma radiation.
What will happen to the wavelength of light uf the frequency is doubled?What will happen to the wavelength of light uf the frequency is doubled?
Answer:
if the frequency is double, the wavelength is only half as long
Explanation:
Considering the definition of wavelength, frequency and propagation speed, if the wavelength is doubled, the frequency is reduced by half.
In a periodic wave the wavelength (λ) is the physical distance between two points from which the wave repeats itself. That is, the wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
The frequency (f) is a measure of the number of cycles or repetitions of the wave per unit of time. Its unit is s⁻¹ or hertz (Hz).
The wavelength and its frequency are related from the speed at which the wave travels. The propagation speed (v) is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave's disturbance propagates along its displacement. So, the speed expression is:
v=λ×f
This indicates that the higher the frequency, the shorter the wavelength and the lower the frequency, the longer the wavelength.
All electromagnetic waves propagate in a vacuum at a constant speed of 300,000,000 m/s, the speed of light. Then, since an inversely proportional relationship is established between the frequency and the wavelength, if the wavelength is doubled, the frequency is reduced by half.
In summary, if the wavelength is doubled, the frequency is reduced by half.
Learn more:
brainly.com/question/2232652?referrer=searchResults brainly.com/question/7321084?referrer=searchResults brainly.com/question/14946166?referrer=searchResultsStrontium chloride, SrCl2
Is ionic or covalent
Answer:
it is a ionic bond because electrons are transferred from chlorine to strontium
Strontium chloride, SrCl₂, is an ionic compound because Ionic compounds are formed through the transfer of electrons from one atom to another, resulting in the formation of positively charged ions (cations) and negatively charged ions (anions).
In the case of strontium chloride, strontium (Sr) is a metal, and chlorine (Cl) is a non-metal. Strontium readily donates two valence electrons to chlorine, which has a strong affinity for gaining one electron to achieve a stable electron configuration. The electron transfer between strontium and chlorine leads to the formation of S\(r^2^+\) cations and C\(l^-\) anions. The resulting ionic bond holds the cations and anions together in a crystal lattice structure. The attraction between the oppositely charged ions creates the ionic bond, making strontium chloride an ionic compound.
Learn more about the ionic compound here.
https://brainly.com/question/30420333
#SPJ6
A 101 kg basketball player crouches down 0.380 m while waiting to jump. After exerting a force on the floor through this 0.380 m, his feet leave the floor and his center of gravity rises 0.920 m above its normal standing erect position. (a) Using energy considerations, calculate his velocity (in m/s) when he leaves the floor. m/s (b) What average force (in N) did he exert on the floor
Answer:
\(4.25\ \text{m/s}\)
\(3391.22\ \text{N}\)
Explanation:
y = Height of compression = 0.38 m
m = Mass of basketball player = 101 kg
h = Height of center of gravity after jump = 0.92 m
g = Acceleration due to gravity = \(9.81\ \text{m/s}^2\)
Energy balance of the system is given by
\(mgh=\dfrac{1}{2}mv^2\\\Rightarrow v=\sqrt{2gh}\\\Rightarrow v=\sqrt{2\times 9.81\times 0.92}\\\Rightarrow v=4.25\ \text{m/s}\)
The velocity of the player when he leaves the floor is \(4.25\ \text{m/s}\)
\(Fy=mgy+\dfrac{1}{2}mv^2\\\Rightarrow F=\dfrac{mgy+\dfrac{1}{2}mv^2}{y}\\\Rightarrow F=\dfrac{101\times 9.81\times 0.38+\dfrac{1}{2}\times 101\times 4.25^2}{0.38}\\\Rightarrow F=3391.22\ \text{N}\)
The force exerted on the floor is \(3391.22\ \text{N}\).
A soccer ball is kicked with an initial horizontal velocity of 11 m/s and an initial vertical velocity of 17 m/s.
1)what is the initial speed of the ball?20.25 m/s
2)what is the initial angle 0 of the ball with respect to the ground? 57.09 degrees
3)what is the maximum height the ball goes above the ground? 14.74m
I need help with 4,5 and 6
4)How far from where it was kicked will the ball land?
5) what is the speed of the ball 2.5 second after it was kicked?
6)how high above the ground is the ball 2.5 seconds after it is kicked?
The answers are 4. The distance from where the ball was kicked is 38.06 meters, 5. The speed of the ball 2.5 seconds after it was kicked is 13.82 m/s, and 6. The ball is 21.88 meters above the ground 2.5 seconds after it is kicked.
4) To calculate the distance from where the ball was kicked, we need to find the time it takes to reach the ground. We can use the fact that the vertical displacement of the ball is zero at the highest point. Using the formula vf = vi + at, the time it takes to reach maximum height is t = vf / g where g is the acceleration due to gravity which is -9.8 m/s² since it is downward and vf is the final velocity which is 0 because the ball comes to rest at the highest point. t = 17 / 9.8 = 1.73 s. This means the total time for the ball to hit the ground is 2 x 1.73 = 3.46 s. Using the formula for horizontal distance traveled d = vt, we get d = 11 x 3.46 = 38.06 m. So, the distance from where the ball was kicked will be 38.06 meters.5) To calculate the speed of the ball 2.5 seconds after it was kicked, we need to find the horizontal and vertical components of the velocity of the ball at 2.5 seconds. The horizontal component is constant, so it will still be 11 m/s. To find the vertical component, we use the formula vf = vi + at where vi is initial velocity, a is acceleration due to gravity which is -9.8 m/s² and t is the time which is 2.5 seconds. vf = 17 + (-9.8 x 2.5) = -7.5 m/s. Since the ball is moving downward, the velocity is negative. Therefore, the speed of the ball 2.5 seconds after it was kicked is sqrt(11² + (-7.5)²) = 13.82 m/s.6) To calculate how high above the ground is the ball 2.5 seconds after it is kicked, we use the formula for the displacement of an object in the vertical direction y = vi*t + (1/2)*a*t² where vi is initial velocity, a is acceleration due to gravity which is -9.8 m/s² and t is the time which is 2.5 seconds. y = 17*2.5 + (1/2)*(-9.8)*(2.5)² = 21.88 m. So, the ball is 21.88 m above the ground 2.5 seconds after it is kicked.For more questions on speed
https://brainly.com/question/13943409
#SPJ8
How far away are the Stars?
Answer:
25,300,000,000,000 miles away
The components of the displacement A
are A=-1.00 m and A-1.732 m. Find
the magnitude of A
OA 1.90m
O B.2.00 m
OC. 2.30 m
O D. 1.00 m
Answer:1.93
Explanation:
The magnitude of a vector can be found using the Pythagorean theorem, where the components of the vector are the sides of a right triangle.
In this case, the components of displacement vector A are given as A = -1.00 m and A-1.732 m.
The magnitude of A can be calculated as follows:
A = √(-1.00 m)^2 + (1.732 m)^2 = √3.732 m^2 = 1.93 m
So, the magnitude of displacement vector A is 1.93 m.
The values of A, B, C, and D are not related to the displacement vector A, so they cannot be used to find the magnitude of A.
A charge is placed on a spherical conductor of radius r1. This sphere is then connected to a distant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on the spheres are in equilibrium:__________.
1. the electric fields at the surfaces of the two spheres are equal.
2. the amount of charge on each sphere is q/2.
3. both spheres are at the same potential. the potentials are in the ratio V2/V1 = q2/q1.
4. the potentials are in the ratio V2/V1 = r2/r1 .
Answer:
Option 3 = both spheres are at the same potential.
Explanation:
So, let us complete or fill the missing gap in the question above;
" A charge is placed on a spherical conductor of radius r1. This sphere is then connected to a distant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on the spheres are in equilibrium BOTH SPHERES ARE AT THE SAME POTENTIAL"
The reason both spheres are at the same potential after the charges on the spheres are in equilibrium is given below:
=> So, if we take a look at the Question again, the kind of connection described in the question above (that is a charged sphere, say X is connected another charged sphere, say Y by a conducting wire) will eventually cause the movement of charges(which initially are not of the same potential) from X to Y and from Y to X and this will continue until both spheres are at the same potential.
Answer questions based on the lab activity.
Assignment
Throughout the reflection, make sure you have a copy of the Student Guide and your data tables. Use the drop-down
menus to complete the statements.
was
This experiment was divided into two parts. For the first part of the experiment, the
intentionally manipulated. This was the independent variable. The dependent variable measured was the
was intentionally manipulated. This was the
by the second part of the experiment, the
independent variable. The dependent variable measured was the
Answer: 1. height of cylinder 2. temperature of cylinder 3.mass of cylinder 4.temp. of cylinder
Explanation:
im doing it rn ! hope this helps :)
The dependent variable gets impacted by changes to the independent variable. Therefore, in the below given ways blanks can be filled.
What are dependent and independent variable?The variable that the experimenter controls is the independent variable. The variable that adapts to the independent variables is known as the dependent variable. The two factors could be connected through cause and effect. The dependent variable gets impacted by changes to the independent variable.
The experiment was divided into two parts. For the first part of the experiment, the height of cylinder was intentionally manipulated. This was independent variable. the dependent variable measured was the temperature of cylinder.
For the second part of experiment, the mass of cylinder was intentionally manipulated. This was the independent variable. The dependent variable measured was the temperature of cylinder.
Therefore, in the above given ways blanks can be filled.
To know more about dependent and independent variable, here:
https://brainly.com/question/1479694
#SPJ7
Differentiate between mass and weight
Answer:
The difference between mass and weight is that mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass.
Explanation:
How does the amount of radiant energy on Mars compare to that on the Earth? What effect would that have on average temperature?
Answer:
(a) radiant energy on Mars is about 1/8 that on Earth
(b) the average temperature will be lower
Explanation:
(a) The parameters relevant to the amount of radiant energy flux on the planet are ...
diameter (thousand km): Earth: 12.756; Mars: 6.792
distance from sun (million km): Earth: 149.6; Mars: 227.9
The energy hitting the planet will be proportional to the square of the diameter and inversely proportional to the square of the distance from the sun. That is the energy hitting Mars compared to Earth will be ...
(6.792/12.756)²(149.6/227.9)² ≈ 0.122 . . . about 1/8
__
(b) The effect on average temperature depends on the energy budget of the planet--the amount of energy reflected and radiated, and the amount internally generated. If sunlight is the only contributor, the average temperature on Mars will be considerably lower than on Earth.
1. At t=0s, a particle moving in the x-y plane with constant acceleration has a velocity ofv; = (3î-2)) m/s, and is at the origin. At t=3s, the particle's velocity is f = (91+7j) m/s. Find (a)the acceleration of the particle (b) Its coordinates at t=3s
Answer:
the particle is at coordinates (18,15/2)
Explanation:
To find the acceleration of the particle, we can use the formula for velocity: v = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is the time. Since we know the initial and final velocities, as well as the time interval, we can solve for the acceleration:
a = (v - v0)/t = [(9i + 7j) - (3i - 2j)]/3 = (6i + 9j)/3 = 2i + 3j
So the acceleration of the particle is a = 2i + 3j m/s².
To find the coordinates of the particle at t=3s, we can use the formula for position: r = r0 + v0t + 1/2at², where r0 is the initial position. Since the particle starts at the origin, r0 = 0. Plugging in the values we have:
r = 0 + (3i - 2j)(3) + 1/2(2i + 3j)(3)² = 9i - 6j + 9i + 27/2 j = 18i + 15/2 j
We can use the kinematic equations of motion to solve this problem.
Let the acceleration of the particle be a = axî + ayj.
(a) Using the equation of motion v = u + at, where u is the initial velocity:
f = v = u + at
Substituting the given values, we get:
(91+7j) = (3î-2j) + a(3î + 3j)
Equating the real and imaginary parts, we get:
91 = 3a + 3a (coefficients of î are equated)
7 = -2a + 3a (coefficients of j are equated)
Solving these equations simultaneously, we get:
a = î(23/6) + j(1/2)
So the acceleration of the particle is a = (23/6)î + (1/2)j.
(b) Using the equation of motion s = ut + (1/2)at^2, where s is the displacement and u is the initial velocity:
At t = 3s, the displacement of the particle is:
s = ut + (1/2)at^2
Substituting the given values, we get:
s = (3î-2j)(3) + (1/2)(23/6)î(3)^2 + (1/2)(1/2)j(3)^2
Simplifying, we get:
s = 9î + (17/2)j
So the coordinates of the particle at t=3s are (9, 17/2).
the current in bass lake has a speed of 2km/h. charle can paddle their canoe 24 km upstream and 24 km back in the same number of hrs as they can paddle 50 km what is charlie's eped in the stil water
According to the solving Charlie's speed in still water is 5 km/h.
What is relative velocity ?
Relative velocity is the velocity of an object or an observer in relation to another object or observer. It is the difference between the velocities of the two objects, as measured from a common frame of reference.
The concept of relative velocity is important in many areas of physics, including mechanics, astrophysics, and relativity theory. It allows us to understand how objects are moving relative to each other and to analyze their motion from different reference frames.
According to the given information:Let's assume that the speed of Charlie's canoe in still water is "v" km/h. Then, if Charlie paddles upstream against the current, the effective speed of the canoe will be:
v - 2 km/h
Likewise, if Charlie paddles downstream with the current, the effective speed of the canoe will be:
v + 2 km/h
We can use the formula:
time = distance / speed
to set up an equation that relates the time it takes for Charlie to paddle 24 km upstream and 24 km back with the time it takes to paddle 50 km. Since the times are the same, we can write:
24 / (v - 2) + 24 / (v + 2) = 50 / v
Multiplying both sides by the LCD (v - 2)(v + 2) yields:
24(v + 2) + 24(v - 2) = 50(v - 2)(v + 2) / v
Simplifying and rearranging, we get:
48v = 200v - 200
Solving for v, we find:
v = 5 km/h
Hence, Charlie's speed in still water is 5 km/h.
To know more about relative velocity visit :
https://brainly.com/question/17228388
#SPJ4
WILL MARK BRAINLIEST!!
Two people, each with a mass of 65.0 kg, are on the same carousel. One is standing 3.00 meters from the center, and the
other is standing 7.00 meters from the center. If the closer person has an angular momentum of 2,340 kg m²/s, what is the
angular momentum of the person standing at 7.00 meters? (Remember: both people have the same angular velocity.
O 5,460 kg m²/s
O 5,920 kg m²/s
O 12,700 kg m²/s
041,400 kg m²/s
Creating a system to effectively solve problems can help you out in many ways what are some benefits you would like to see in your own life as you begin to apply the 4 step problem solving process you read about this week’s
Creating an effective system to solve problems is beneficial in various ways as it enables an individual to come up with a clear and concise solution to any problem or situation that may arise.
Some of the benefits that I would like to see in my own life as I begin to apply the 4-step problem-solving process are:Improved decision making skills- The 4-step problem-solving process will help me to make better decisions since it requires that I identify the problem, gather information, develop solutions, and implement the most suitable solution. This approach will help me to weigh my options carefully and make decisions based on logic rather than emotions.Improved communication skills- The process of problem-solving requires communication between team members. As I begin to apply the 4-step problem-solving process, I would like to develop better communication skills that will enable me to express my ideas clearly and succinctly.
This will be helpful not only in my personal life but also in my professional life where effective communication is a key to success.Improved critical thinking skills- The process of problem-solving requires critical thinking. By applying the 4-step problem-solving process, I would like to improve my critical thinking skills by learning how to analyze information, assess the problem, and develop solutions based on the available information.Improved productivity- The 4-step problem-solving process is a structured approach that helps to identify problems and develop solutions in a systematic manner. By applying this approach in my life, I would like to improve my productivity since I will be able to solve problems more efficiently and effectively.
for such more questions on system
https://brainly.com/question/28021242
#SPJ8
Saturn is moving with uniform angular speed of 2πf along the circumference of it's orbit around the sun with radius R, having centre O. At any time, the angular position of Saturn is (2πf)t and the displacement in SHM at that time t is given by x(t)=Rcos(2πf)t. Find it's acceleration.
Answer:Sir haymo knows
Explanation:
he gave as homework
The acceleration of the Saturn is - (2πf)²x(t).
What is Simple harmonic motion?A motion in which the restoring force is directly proportional to the body's displacement from its mean position is known as a simple harmonic motion, or SHM. This restoring force always moves in the direction of the mean position. A particle moving in simple harmonic motion accelerates as a(t) = - ω² x (t). Here, ω denotes the particle's angular velocity.
The acceleration of the particle at any position is directly proportional to the displacement from the mean position in simple harmonic motion, which is an oscillatory motion.
Given that:
at any time, the angular position of Saturn is (2πf)t.
the displacement in SHM at that time t is given by x(t)=R cos(2πf)t.
Hence, speed in SHM at that time t is given by
\(v(t) = \frac{dx(t)}{dt} =R \frac{d }{dt} cos(2\pi f)t = -(2\pi f) sin(2\pi f)t\)
it's acceleration is
\(a(t) = \frac{dv(t)}{dt} =-(2\pi f) R \frac{d }{dt} sin(2\pi f)t = -(2\pi f)^2 Rcos(2\pi f)t = -(2\pi f)^2 x(t)\)
hence, at any time t, the acceleration of the Saturn is - (2πf)²x(t).
Learn more about simple harmonic motion here:
https://brainly.com/question/28208332
#SPJ2
How a Motor Works
Figure 5
A motor is made of several basic parts, each of which
is described below. Study the information about each part. Then,
write the number of each description in the appropriate circle on
the image.
Answer:
hi \( \) \( \)
▼
Part D
The quantity represented by v is a function of time (i.e., is not constant).
True or false
Part E a particle moves with constant acceleration a. The expression VI +80 represents the particles velocity at what instant in time.
A. At a time T=zero
B. At the initial time
C. When a time tea has passed since the beginning of the particles motion, when its velocity was the vi
The amount indicated by is not fixed and changes over time. In situations where the linear acceleration is not zero, the velocity is always changing.
The first case is true
Since it depends on time, is not constant?
The amount indicated by is not fixed and changes over time. In situations where the linear acceleration is not zero, the velocity is always changing.
The dimension of the quantity albo will be ufa au av u t when calculating a particle's velocity as a function of time t using the formula v = a(1 - eb), where a and b are constants. (1 - e-b) Greutate, urb'a 221 Aich, a zat a2b3c faut Eleft.
The amount indicated by is not fixed and changes over time. When linear acceleration is absent .
To learn more about time refer to:
brainly.com/question/17146782
#SPJ1
The quantity represented by v is a function of time (i.e., is not constant).
True or false
A particle moves with constant acceleration a. The expression VI +80 represents the particles velocity at what instant in time.
A. At a time T=zero
B. At the initial time
A particle starts from the origin at time t = 0 and moves along the positive x - axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s?
why cows have a tapetum (what is its function in the eye?)
Answer:
Behind the retina is a layer of shiny, blue-green stuff called the tapetum. This layer assists night vision by reflecting light back through the retina.
Explanation:
Pls mark me as brainliest plss
Why does heating water affect surface tension
As temperature increases, molecules of liquid become more active and they move more rapidly.
.An airplane accelerates down a runway at
3.20 m/s2 for 32.8 s until is finally lifts off the
ground. Determine the distance traveled before
takeoff.
Starting from rest, the plane travels a distance
x = 1/2 at²
with acceleration a after time t. In this instance, it travels
x = 1/2 (3.20 m/s²) (32.8 s)²
x ≈ 1720 m
Potential difference of a battery is 2.2 V when it is connected
across a resistance of 5 ohm, if suddenly the potential difference
falls to 1.8V, its internal resistance will be
Answer:
1.1ohms
Explanation:
According to ohms law E = IR
If potential difference of a battery is 2.2 V when it is connected across a resistance of 5 ohm and if suddenly the voltage Falls to 1.8V then the current in the 5ohms resistor I = V/R = 1.8/5
I = 0.36A (This will be the load current).
Before we can calculate the value of the internal resistance, we need to know the voltage drop across the internal resistance.
Voltage drop = 2.2V - 1.8V = 0.4V
Then we calculate the internal resistance using ohms law.
According to the law, V = Ir
V= voltage drop
I is the load current
r = internal resistance
0.4 = 0.36r
r = 0.4/0.36
r = 1.1 ohms
A ball is dropped from the top of a building.
When does the ball have the least potential energy?
O after it has hit the ground
O half way through the fall
O as it is released
O just before it hits the ground
Answer:
after it has hit the ground
.........
Answer: A. after it has hit the ground
Calculating Displacement under Constant Acceleration
Use the information from the graph to answer the
question.
Velocity (m/s)
40
30
20
10
0
Velocity vs. Time
0 5
10
15
Time (s)
20
25
What is the total displacement of the object?
I
m
Answer:
1 km
Explanation:
displacement =velocity ×time
displacement =40m/s ×25s
displacement =1000m equivalent to 1km
The cylinder of a heat engine is filled with an air-fuel mixture. Which property of gases is essential to heat engines ability to do work?
Answer: Pressure of gases.
Explanation:
In a heat engine, the air-fuel mixture is ignited, which causes an increase in pressure of the gases inside the cylinder. This pressure pushes the piston, which is connected to a crankshaft, causing it to rotate and do work. Therefore, pressure is an essential property of gases for the ability of a heat engine to do work.
A brick is dropped from a high scaffold.
a. How far does the brick fall during this time?
Answer:
a: after 1 seconds it will have fallen 0.2452
after 2 seconds it will have fallen 0.981
after 3 seconds it will have fallen 2.2072
after 4 seconds it will have fallen 3.924
Explanation:
the formula for acceleration due to gravity is (ignoring friction I think)
g = G*M/R^2
earths gravitational constant is about 9.807
g = 9.807*M/R^2
The average weight of a brick is 5 pounds and I'm going to say it's 10 feet off the ground.
g = 9.807*5/10^2. g = 0.4905 so every second the brick will go 0.4905 fps faster. (fps means feet per second.)
after 1 seconds it will have fallen 0.2452
after 2 seconds it will have fallen 0.981
after 3 seconds it will have fallen 2.2072
after 4 seconds it will have fallen 3.924
22. How do we correct the issue of flipped imagery caused by mirrors?
To correct the issue of flipped imagery caused by mirrors you can use a technique called "mirror flipping". Mirror flipping involves using a second mirror to reflect the reflected image from the first mirror which then flips it back to its original orientation
Alternatively you can use a prism to correct the orientation of the image. A prism is a transparent object that can bend light. By placing it infront of the mirror you can reflect the twice, effectively helping in the correction of the orientation of the image
To know more about Flipped Images refer to this link:
https://brainly.com/question/29023559
1. The surface considered for Gauss’s law is called
(a) Closed surface
(b) Spherical surface
(c) Gaussian surface
(d) Plane surface
Answer:
C) Gaussian surface
Explanation:
Answer:
c
Explanation:
riley is building a pool with a surrounding deck in their backyard. the pool has a fixed area, , but the pool's dimensions can vary (for instance, a pool can have infinitely many length-width combinations, including , , , or ).
The minimum area for a pool and deck built as in the application such that the pool's area is 1800 square meters is \(1400 \mathrm{~m}^2\)
Let ' l ' be the length of the pool and ' b ' be the breadth of the pool.
\($\Rightarrow l \times b=1800$\)
This gives:
Length of Total area (deck and pool)
\($=(l+5+5) \mathrm{m}$\)
Breadth of Total area (deck and pool )
\(=(b+10+10) m$\)
Area of Total space (deck and pool)
\($=(l+10)(b+20)$\)
Area:
\($=(l+10)\left(\frac{1800}{l}+20\right)$\)
\(A(l)=1800+20 l+\frac{18000}{l}+200$\)
Our aim is to minimize A(l), for this put \(A^{\prime}(l)=0$\)
\(\Rightarrow 20-\frac{18000}{l^2}=0\\ \Rightarrow \frac{1800 \phi}{l^2}=2 x \\\Rightarrow l^2=900$\\$\Rightarrow l=\pm 30$.\)
But length can not be negative
\(\Rightarrow l=30 \mathrm{~m} \\\Rightarrow b=\frac{1800}{300}=60$ m\)
Now:
\(A^{\prime \prime}(l)=-\frac{18000}{l^3} \times\left(-2 l^{-3}\right)=\frac{36000}{l^{\prime \prime}}$\\$\Rightarrow A^{\prime \prime}(t=30)=\frac{36000}{(30)^3} > 0$\)
Therefore \(A(l)$\) is minimum for l=30 m.
Hence minimum area:
\(=A(l=30)=(30+10)(60+20) \mathrm{m}$\\\\=40 \times 80 \mathrm{~m}^2$\\\\=3200 \mathrm{~m}^2$$\)
And minimum area of deck:
\(=(3200-1800) \mathrm{m}^2 \\& =1400 \mathrm{~m}^2\end{aligned}$$\)
Therefore the minimum area of deck is \(1400 \mathrm{~m}^2\)
For more questions on area
https://brainly.com/question/26638297
#SPJ4