The speed of a pulse traveling along the cord, v = 19.8 m/s.
What is the speed of the pulse traveling along the cord?The tension, T on the cod is first obtained as follows:
T = 2.0 * 9.8 m/s²
T = 9.6 N
The mass per unit length, μ of the cord is then determined:
μ = 0.3/6
μ = 0.05 kg/m
The speed of the pulse, v = √(T/μ)
v = √(9.6/0.05)
v = 19.8 m/s
In conclusion, the speed of the pulse is the distance covered per unit time.
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Suppose a 65.5 kg gymnast climbs a rope. What is the tension in the rope if she climbs at a constant speed
The tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
Given:
Mass of gymnast, m = 65.5 kg
The speed 'v' of gymnast is constant
Solution:
Consider the free-body diagram of the system as shown below.
Balancing forces along the vertical axis we get:
ΣFy = 0
Thus, we get:
F = ma - (1)
where, m is mass of gymnast
a is acceleration of gymnast (a = 0m/s², as the speed is constant)
Also,
F = T - mg -(2)
where, T is tension in the rope
g is acceleration due to gravity
Equating (1) & (2), we get:
ma = T - mg
Re-arranging the equation, we get:
T = m(a+g)
Applying values in above equation we get:
T = (65.5 kg)(0 m/s²+9.8 m/s²)
T = 641.9 N
Therefore, the tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
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Determine the launch speed of a horizontally launched projectile that lands 26.3m from the base of a 19.3m high cliff
The launch speed of a horizontally launched projectile is 13.28 m/s.
Time of motion of the projectile
The time of motion is calculated as follows;
t = √(2h / g)
where;
h is height of the cliffg is acceleration due to gravityt = √(2 x 19.3 / 9.8)
t = 1.98 s
Launch speed of the projectileX = Vxt
Vx = X/t
Vx = (26.3)/(1.98)
Vx = 13.28 m/s
Thus, the launch speed of a horizontally launched projectile is 13.28 m/s.
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In a certain material there is a current of 18 A flowing through a surface to the right, and there is an equal amount of positive and negative charge passing through the surface producing the current. How much negative charge passes through the surface
The negative charge passes through the surface is 9 A/s
The Intrinsic property of protons and electrons are known as Electric Charge
Protons are known as positive charge
Electrons are known as negative charge
Give that
I =18A
The current is flowing to the right
The equal amount of positive and negative charges.
that is total charge is q= Q+Q=2Q. that is magnitude
Then, the rate of charge that pass though is dq/dt
Give that,
q=it
2Q=it
Let differentiate with respect to t
2dQ/dt=I
Then, dQ/dt=i/2
Since I=18A
Then, dQ/dt=18/2
dQ/dt= 9 A/s. Toward the left
9 A/s negative charge passes through the surface .
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A 10 N force and a 15 N force are acting from a single point in opposite directions. What additional force must be added to produce equilibrium?
Group of answer choices
A) A 5 N force acting in the same direction as the 10 N force.
B) A 10 N force acting in the same direction as the 15 N force.
C) A 25 N force acting in the direction perpendicular to the 10 N and 15 N forces.
D) A 5 N force acting in the same direction as the 15 N force.
The additional force must be added to produce equilibrium is 5 N force acting in the same direction as the 10 N force (Option A)
Data obtained from the questionForce to the left = 10 NForce to the right = 15 NAdditional force =?How to determine the additional forceTo have equilibrium,
Force to the left = force to the right
But
The force to the right is greater than the force to the left.
Thus,
Force to the left + additional force = force to the right
10 + additional force = 15 N
Collect like terms
Additional force = 15 - 10
Additional force = 5 N
Therefore, an additional force of 5 N acting in the same direction of the 10 N force is needed to obtain the equilibrium of the system (Option A)
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Which characteristic is most associated with egalitarian societies?
O Women perform a lot of the domestic labor.
Women have responsibility for child care.
Women have access to education.
O Work is highly segregated by sex.
Answer:
a woman who have responsibility of child care
Explanation:
egalitarian is one who supports equality
The characteristic that is most associated with egalitarian societies is Women have responsibility for child care.
What is society?A society is a bunch of individuals that frequently contact with one another or a significant social group that inhabits the same physical or social area and is typically under the control of the same leadership and prevailing cultural expectations. A given society may be defined as the sum of all of these interactions among its constituent members.
Society is characterized by patterns of interaction (social relations) between people who share a certain culture and institutions. In the social scientists, subgroup dominance or stratification patterns commonly occur in bigger societies. By defining certain behaviors or ideas as acceptable or unacceptable, societies create patterns of behavior. The phrase "societal norms" relates to such behavioral patterns within a particular community. Societies and their standards are continuously and changing slowly.
What is women?Women typically inherit a pair of X - chromosome from their parents, which allows them to get pregnant and give birth from adolescence until menopause. More specifically, the sex determination of the female embryo is controlled by the lack of a present or active on either of the respective s-ex chromosomes. Female anatomy differs from male anatomy due to the female reproductive system, which consists of the ovaries, ut-erus, v-agina, and vulva. A lady is a grown-up female. Before being an adult, a woman is referred to as a girl (a female child or adolescent).
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How much water will flow in 30 secs through 200 mm of capillary tube of 1.50 mm in diameter, if the pressure difference across the tube is 6660N/m² and viscosity is 8.01x10 kg/ms
The water outflow in 30 secs through 200 mm of the capillary tube is mathematically given as
[tex]Qo=1.6 \times 10^{2} \mathrm{~mL}[/tex]
What is the water outflow in 30 secs through 200 mm of the capillary tube?[tex]\begin{aligned}\Delta P &=6660 \mathrm{~m} / \mathrm{m}^{2} \\\mu &=8.01 \times 10^{-4} \text { Pas } \\t &=30 \mathrm{~s} \\L &=200 \mathrm{~mm}=200 \times 10^{-3} \mathrm{~m} \\D &=1.5 \mathrm{~mm}=1.5 \times 10^{-3} \mathrm{~m} \Rightarrow \gamma=\frac{1.5 \times 10^{-3}}{2} \mathrm{~m}\end{aligned}[/tex]
Generally, the equation for Rate of flow of Liquid is mathematically given as
[tex]\\$$Q=\frac{\pi r^{4} \times \Delta P}{8 \mu L}[/tex]
$$
Where dP is pressure difference r is the radius
[tex]\mu[/tex] is the viscosity of water
L is the length of the pipe
[tex]Q=\frac{\pi \times\left(\frac{1.5 \times 10^{-3}}{2}\right)^{4} \times 6660}{8 \times 8.01 \times 10^{-4} \times 200 \times 10^{-3}}[/tex]
[tex]Q=5.2 \mathrm{~mL} / \mathrm{s}[/tex]
In $30s the quantity that flows out of the tube
[tex]&Qo=5.2 \times 30 \\&Qo=1.6 \times 10^{2} \mathrm{~mL}[/tex]
In conclusion, the quantity that flows out of the tube
[tex]Qo=1.6 \times 10^{2} \mathrm{~mL}[/tex]
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If the satellite has a mass of 3900 kg , a radius of 4.3 m , and the rockets each add a mass of 210 kg , what is the required steady force of each rocket if the satellite is to reach 30 rpm in 5.4 min , starting from rest?
Answer:
The required steady force of each rocket is 28.79 N
Explanation:
mass of the satellite, M=3900 kg
radius, r=4.3 m
mass of rocket, m=210 kg
time, t=5.4 min
Moment of Inertia:
I = 1/2 (Mr^2) + 4mr^2
I = 1/2 ( 3900* (4.3)^2) + 4 (210)*(4.3)^2
I = 51587.1 kg m^2
the angular acceleration is:
a= w/t
here w= 2*π*30
so,
a= 2*π*30 / 5.4* 3600
a=0.0096 rad/ s^2
the Torque becomes:
T=I*a = 4r*F
( 51587.1 )*(0.0096) = 4*4.3* F
F= 28.79 N
the required steady force of each rocket is 28.79 N
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Heat engine x has an efficiency of 67%. heat engine y has an efficiency of 82%. which best compares these two heat engines? heat engine x moves more thermal energy from cold to warm areas than heat engine y. heat engine x releases more energy to the surroundings than heat engine y. heat engine y releases more energy to the surroundings than heat engine y. heat engine y moves more thermal energy from cold to warm areas than heat engine x.
Heat engine y releases more energy to the surroundings than heat engine y compares the two heat engines in a better way.
Heat Engine:
It mainly works by bringing the working substance from warmer temperature to lower temperature. So, in the process of going through this cycle, the system performs some work on the surrounding. Then more work will be done by a more efficient engine.In the question, it is said that x has an efficiency of 67% and y has an efficiency of 82%.
Therefore, Heat Engine y releases more energy to the surroundings than heat engine y. Hence, option (c) is correct.
Incorrect options:
(a) It is incorrect because Heat engines work by taking heat from hotter regions to colder regions.
(b) It is incorrect because the efficiency of x is less than y.
(d) It is also incorrect because Heat engines work by taking heat from a hotter region to a colder one.
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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.
The independent variables in Part I, the ones intentionally manipulated, are the
The independent variable in Part II, the one that is intentionally manipulated, is the [
The dependent variable for both Parts I and II, the one that you measure the response in, is the
The complete statements are;
In Part I ---> mass & type of materialIn Part I ----> type of materialIn Part I----> temperatureThis is further explained below.
What is reflection?Generally, reflection is seen when light, heat, or sound that is reflected back by an object or surface rather than absorbed by it.
In conclusion, The full statements are as follows: Part I: Mass and Material Type For the first section, please refer to the following categories of content: To begin, let's talk about the temperature, as discussed in Part I.
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Answer:
The independent variables in Part I, the ones intentionally manipulated, are the
✔ mass and type of material
.
The independent variable in Part II, the one that is intentionally manipulated, is the
✔ type of material
.
The dependent variable for both Parts I and II, the one that you measure the response in, is the
✔ temperature
got right in edge 2022
Why do astronomers need different telescopes at different locations to observe across the electromagnetic spectrum
Frequency or wavelength-based distribution of all electromagnetic radiation is known as electromagnetic spectrum.
The majority of celestial bodies emit many forms of electromagnetic radiation simultaneously. What they emit depends on a variety of factors, including how hot they are and what materials they are made of.
Different telescopes are used by astronomers to find various electromagnetic spectrum components. Only one region of the electromagnetic spectrum can be detected by each type of telescope.
At radio frequencies, light pollution is more severe than at visible wavelengths.
Light pollution, often known as artificial nighttime light, is the improper or excessive use of artificial outdoor light.
Different energies of photons have a range of wavelengths, some of which are inaccessible from the Earth's surface and need different methods of collection.
As the atmosphere distorts more strongly at shorter wavelengths, telescopes must adjust.
Modern telescopes use new technologies to work more effectively and making innovative telescope designs is a task that engineers and astronomers relish.
That’s why astronomers need different telescopes at different locations to observe across the electromagnetic spectrum.
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. If the moon orbits Earth along the exact ecliptic (as the sun does): a. precession would not occur. b. days and nights would no longer be equal on the dates of the equinoxes. c. a total lunar and a total solar eclipse would occur every month. d. ocean tides would not occur.
If the moon orbits Earth along the exact ecliptic a total lunar and solar eclipse would occur every month.
The answer is option C.
A solar eclipse happens when the Moon passes between the sun and Earth, casting a shadow on earth that either fully or partly blocks the sun's light in some areas. This most effective takes place every so often, due to the fact the Moon does not orbit inside the specific same plane because the solar and Earth do.
The moon's route crosses the ecliptic kind two times every month, and a solar eclipse takes place while the solar happens to be there at some point during the crossing. There's a terrific hazard of this approximately once each six months.
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Make a list of nutrients found in packed items and amount of nutrient present in them
EXAMPLE IS SHOWN IN PIC
If any one will answer this correctly I will mark them as brainlist
Nutrients found in packed items include carbohydrates, fats and proteins and the amount of nutrients present in them is found in calories/grams.
What are macronutrients?Macronutrients are nutrients that contain calories that must be consumed in the diet to perform metabolic functions.
These macronutrients are specified in packed foods, and include proteins, carbohydrates and lipids.
Macronutrients provide 4 calories (proteins and carbohydrates) or 9 calories per gram (fats).
In conclusion, nutrients include carbohydrates, fats (lipids) and proteins and their proportions are expressed in grams.
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Danny Diver weighs 500 N and steps off a diving board 10 m above the water. Danny hits the water with kinetic energy of
Answer:
Danny hits the water with kinetic energy of 5000 J.
Explanation:
Given that,
The Weight of Danny Diver,
F = 500 N
m*g= 500 N
He steps off a diving board 10 m above the water.
h=10 m
when Danny diver hits water he generates the kinetic energy.
We need to find the kinetic energy of the water.
Let kinetic energy is K.
K = m*g*h
Where g is acceleration due to gravity.
that g= 9.8 m/s^2
now substituting the values in above equation
K= (500) * 10
K= 5000 J
Hence,
he hits the water with kinetic energy of 5000 J.
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A diagnostic test involving recording the electrical activity within muscle fibers in response to nerve stimulation is known as.
Electromyography (EMG) measures muscle response or electrical activity in response to a nerve's stimulation of the muscle. The test is used to help detect neuromuscular abnormalities.
Electromyography (EMG) :
(EMG) detects the electrical activity that occurs when a muscle is stimulated by a nerve. The test is used to identify aberrant neuromuscular function. One or more tiny needles, commonly known as electrodes, are introduced through the skin and into the muscle during the test. An oscilloscope is then used to display the electrical activity that the electrodes picked up (a monitor that displays electrical activity in the form of waves). In order to hear the activity, an audio amplifier is employed. The electrical activity of muscles during rest, a light contraction, and a strong contraction is measured by EMG. At rest, muscle tissue doesn't typically create any electrical signals. A brief period of activity can be seen on the oscilloscope when an electrode is introduced, but there should be no signal beyond that.
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The maximum displacement of a mass attached to a spring is 0.122 m, while its highest acceleration is 0.953 m/s2. What is its maximum speed
Maximum Speed:
v = 0.9452ω
In SHM as we know that the velocity of the particle as function of displacement from mean position is :
v = ω √A² -x²
Now, substituting the values
v = ω √(0.953)² - (0.122)²
v = ω √ 0.908209- 0.014884
v = ω √0.893325
v = 0.9452ω
So, this is the maximum speed of the spring.
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What is the velocity ratio of the inclined plane h 9 L 12 hypothesis 15 bellow? A. 1.25 B. 0.60 C. 1.67 D. 0.80
B is the answer
hope this helps u
:)
0. If heavy stone and cotton having same masses are dropped from certain height on the surface of the earth. Explain the results according to the presence and obsence of air resistance. V 0. If heavy stone and cotton having same masses are dropped from certain height on the surface of the earth . Explain the results according to the presence and ab
sence of air resistance .
The cotton will fall slower than the heavy stone of same mass because of the density of the substances, which affects air resistance.
What is air resistance?Air resistance is the action of friction that slows something moving through air.
It is worthy to note the air resistance is not dependent on the mass of an object but on the velocity and density of that object.
According to this question, a heavy stone and a cotton having same masses are dropped from certain height on the surface of the Earth.
Based on difference in densities, the cotton will fall slower than the heavy stone because the density of the stone is greater.
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The density of a block of wood is 2.7 g/cm³ and a mass of 583.3 g. What is its volume?
A lump of butter has a volume of 350 cm³ and a mass of 319 g. What is the density of the butter?
Answer:
1) To find the volume of the wood block, divide the mass by the density:
Volume = 583.3 g / 2.7 g/cm³
Volume = 216.24 cm³
2) To find the density of the butter, divide the mass by the volume:
Density = 319 g / 350 cm³
Density = 0.9114 g/cm³
Explanation:
A constant 20N force is applied to a 7kg box to push it along the ground. How much work is done by this force if the box moves 2m?
Answer:
40 J
Explanation:
W = (f)(d)
W = (20)(2)
W = 40 J
If a constant 20 N force is applied to a 7 kg box to push it along the ground , then the work is done by this force if the box moves 2 meters would be 40 Newton meters.
What is work done?The total amount of energy transferred when a force is applied to move an object through some distance .
As given in the problem if a constant 20 N force is applied to a 7 kg box to push it along the ground, then we have to find out the work is done by this force if the box moves 2 meters ,
The work done by the force to push the box = 20 × 2
=40 Newton meters
Thus, the work is done by this force if the box moves 2 meters would be 40 Newton meters.
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A bus decreases its speed from 80km/h to 60km/h in 5 seconds. find the acceleration of the bus.
The acceleration of the bus is 1.1 m/s²
What is acceleration?Acceleration is defined as the change in the velocity of an object with time.
Acceleration = change in velocity/timeChange in velocity = Final velocity - initial velocityChange in velocity of the bus = 60 - 80
Change in velocity of the bus = -20 km/h = -5.5 m/s
Time = 5 seconds
Acceleration = -5.5/5
Acceleration = 1.1 m/s²
In conclusion, acceleration is the rate of change of velocity with time.
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Tommy is awake during a procedure involving his brain his doctor has a test and electrical part of his brain and stimulating it every time she does so tommy start singing showtunes what is the procedure an example of
Repetitive Transcranial Magnetic Stimulation (TMS) is the procedure that is being performed on Tommy, while he is awake.
What is Transcranial Magnetic Stimulation?
Transcranial magnetic stimulation (TMS) is a non-invasive method for mood control. It does not require the patient to be sedated and is usually performed on completely conscious patients.
In this procedure, the nerve cells are stimulated by magnetic pulses by placing electromagnetic coils against the scalp of the patient. The patient is then stimulated repetitively which is why it is known as repetitive TMS.Tommy sings during the procedure because the region of the brain responsible for memory and singing is stimulated by this procedure.
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A diagram shows a measuring cylinder containing a liquid, and that same measuring cylinder when it is empty. What is the density if the mass is 190g and the volume is 24cm3?
The density, given that the mass is 190 g and the volume is 24 cm³ is 7.92 g/cm³
What is density?The density of a substance is simply defined as the mass of the subtance per unit volume of the substance. Mathematically, it can be expressed as
Density = mass / volume
How to determine the density Mass = 190 gVolume = 24 cm³Density =?Density = mass / volume
Density = 190 / 24
Density = 7.92 g/cm³
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i dont understand pojectile motion can someone help with this
When thrown from the balloon, the sandbag has a constant horizontal/forward velocity. As the text puts it, "the sandbag continues forward as if it had not been dropped." What this means is that the sandbag has no acceleration in the horizontal plane of motion, so it moves in this direction at a constant speed. So for any time [tex]t[/tex], the horizontal velocity is given by
[tex]v_x(t) = 12\dfrac{\rm m}{\rm s}[/tex]
In the vertical plane of motion, the sandbag has no vertical velocity until it's released and allowed to fall. As it's falling, however, the sandbag is being pulled down by gravity and is accelerating with magnitude [tex]g=9.8\frac{\rm m}{\mathrm s^2}[/tex], so its vertical/downward velocity at time [tex]t[/tex] is given by
[tex]v_y(t) = -gt[/tex]
So, after 3 seconds have passed, the sandbag has horizontal velocity [tex]v_x = 12\frac{\rm m}{\rm s}[/tex] and vertical velocity [tex]v_y = -g(3\,\mathrm s) = -29.4\frac{\rm m}{\rm s}[/tex]. If the question is specifically asking about speed you would just ignore the negative signs.
3
its out
n
A mom walks into her child's room and finds clothes all over the floor. 20% of the clothes are
clean. She randomly picks up 5 articles of clothing.
1. We can expect 1
2. The standard deviation is 25
3. Because the distribution has a
r
O
5
, the distribution is close to skewed right (positive)
✔
n-
4. Use the probability formula P(r) =n Crp'q" to create a binomial distribution table.
Probability formula
Round to the tenth, if necessary.
6
✔ CO
Dirty Room
out of 5
articles of clothing to be clean.
x. (Round to the nearest tenth, if necessary.)
probability of success (P(S)) that is
5
✓.2 ✓
0
small (closer to 0)
P(r)
Enter the probability only.
Round to the 4th decimal place, if
necessary.
.6
?
The probability computed shows that we can expect 1 out of 5 clothes to be clean.
How to calculate the probability?From the information given, it was stated that 20% of the clothes are clean. Therefore, the probability of clean clothes will be:
= 20% = 1/5.
Therefore, one out fo five clothes are clean.
The standard deviation will be:
= ✓npq
where,
n = 5
p = 0.20
q = 1 - 0.20 = 0.80
SD = ✓(5 × 0.20 × 0.80)
= ✓0.80
= 0.09
The distribution is close to symmetric.
The binomial distribution table will be:
0 = (0.20)^0 (0.80)^5 = 0.3277
1 = (0.20)¹ (0.80)⁴ = 0.4096
2 = (0.20)² (0.80)³ = 0.2040
3 = (0.20)³ (0.80)² = 0.0512
4 = (0.20)⁴ (0.80)¹ = 0064
5 = (0.20)^5 (0.80)^0 = 0.0003
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A soapbox derby race car starts at rest at the top of a track that has a vertical drop of 15 m. The car is to be stopped at the end of the track by colliding with and compressing a spring. In order to avoid injury to the driver, the spring must be compressed to 3.0 m before the car stops. What should be the force constant of this spring
In order to avoid injury to driver, The force constant of this spring should be 73.82 N/m
Calculation of force constant to this spring:
Here
vertical drop is 15 m.
mass of the car, m= 113 kg
gravitational acceleration, g= -9.8 m/s^2
spring compression before car stops, x= 3.0 m
In order to avoid injury to the driver,
we need to use Hooke's law and Newton's second law:
F(net) = F(x)
m*a=-k*x
here a=g
k= -(m*g) / x
here k is force constant of this spring
substituting the values we get,
k = -(113* -9.8) / (15)
k = 73.8266 N/m
Hence, the force constant of this spring should be 73.82 N/m
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6. The volume of a water tank is 5 m × 4 mx 2 m. If the tank is half-filled with water, calculate the pressure exerted at the bottom of the tank.
Answer:
Height (h)=4m so. tank is half filled the debth will be or heigth will be 4m/2 =2m
Explanation:
Acceleration deu to gravity (g)=9.8m/s^2
Density (d)=1000kg/m^3
So
P= hdg
P= 2×9.8×1000
P= 19600pa
A wire of a given material has an electric field of 0.100 mV/m when a potential is applied. The wire has 8.49 x 1028 conduction electrons per cubic meter and a mean free time between collisions of 2.50 x 10-14 s. What is the uniform current density in the wire
The uniform current density in the wire is 5.43 x 10²⁷ A/m².
Current density in the wireThe uniform current density in the wire is calculated as follows;
J = total current / total area
The given parameters:
Conduction of the wire = 8.49 x 10²⁸ e/m²time, t = 2.5 x 10⁻¹⁴ s[tex]J = \frac{I}{A} = \frac{Q}{At} \\\\J = \frac{8.49 \times 10^{28}e/m^3 \ \times \ 1.6 \times 10^{-19} \ C/e}{2.5 \times 10^{-14} \ s \ \times ( 0.1 \times 10^{-3} \ V/m)} \\\\J = 5.43 \times 10^{27} \ A/m^2[/tex]
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Which of the following statements are true about a mass rotating around a string? Select all that apply.
Group of answer choices
A. If you cut the string as the ball is in motion, the ball will continue to move in uniform circular motion due to the centripetal force.
b. The acceleration and velocity vectors on the mass will always be perpendicular to each other.
c. Since the linear speed of the rotating mass is constant, the kinetic energy of the mass is also constant.
d. The acceleration and centripetal force vectors will always be directed inward, towards the center of the arc.
Answer:
Only (C) and (D) are true
a = (v2 - v1) / t since a and v are vector quantities they have the same direction
Also KE = 1/2 M v^2 describes the linear KE of an object moving with a speed of v
Also KE = F * S where S is the displacement - the radius vector is a constant for an object moving in a circle and the centripetal force provides no change in KE
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
Helpful information: h : height of cylinder, r : radius of cylinder
Volume of a cylinder: V = pir²h Area of the sides: A = 2pirh Area of the top/bottom: A = pir²
A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production costs.
h: height of the cylinder, r: radius of the cylinder
The volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
The cost of packaging, C=2πrh*0.02+ πr^2*0.02+ πr^2*0.05 subject to the constraint πr^2h=600
C=πr(0.04h+.07r) and the constraint implies h=600/ πr^2
So C=πr(24/πr^2+.07r)=24/r+.07πr^2
C'=-24/r^2+0.14πr=0
r^3=24/0.14π r=3.79 cm
h=600/πr^2=13.3 cm
C=π*3.79*(0.04*13.3+.07*3.79)=9.48cents
C''=0.14π+48/r^3>0 for all r>=0 so our solution is indeed a minimum.
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1. The planet Jupiter completes a revolution of the sun in 11.5 years. Express it in seconds. Given that one year= 3.154 × 10^7 s.
Answer:
The planet Jupiter completes one revolution of the sun in 362710000 seconds. Long time, right?
Explanation:
3.154x10^7=3.154x10000000=31540000
11.5x31540000=362710000