Answer:
9.99
Explanation:
The value of (997)^1/3
(997)^1/3
997 = (1000 - 3)
(1000 - 3)^1/3
Expanding :
[1000(1 - 3/1000)]^1/3
1000^1/3 * (1 - 3/1000)^1/3
Cube root of 1000
10 * (1 - 3/1000 * 1/3)
10 * (1 - 1/1000)
10 * (1 - 0.001)
10(0.999)
= 9.99
Hence, the value of (997)^1/3 according to binomial theorem is 9.99
The value of (997)^(¹/₃) according to binomial theorem is;
9.99
The value of
(997)^(¹/₃)
⇒ (1000 - 3)^(¹/₃)
Factorizing out common terms gives;
⇒ (1000)^(¹/₃) * (1 - 3/1000)^(¹/₃)
Using the given approximations from binomial theorem, we have;
⇒ 10(1 + (¹/₃ × -³/₁₀₀₀) ....
⇒ 10(1 - 0.001)
⇒ 10 × 0.999
⇒ 9.99
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8. What will be the extension of a spring of K = 10 N/m, if the load is 75g?
Answer:
The extension of the spring is 7.35 cm
Explanation:
Spring Force
When a spring is compressed or extended by a distance x, it exerts a force given by the Hooke's Law:
F=k.x
Where k is the constant of the spring.
A mass of m=75 gr is hung to the spring of constant k=10 N/m. The force applied to the spring is the weight of the mass:
W = mg
The mass must be converted to kg:
m = 75/1000 = 0.075 kg
W=0.075*9.8
W = 0.735 N
The extension of the spring can be computed by solving for x:
[tex]\displaystyle x=\frac{0.735}{10}[/tex]
x=0.0735 m
x = 7.35 cm
The extension of the spring is 7.35 cm
A weightlifter lifts a set of 1250kg weights a vertical distance of 2m weight lifting contest. what potential energy do the weights now possess
Answer: The potential energy of the weights is 24,500 J
Explanation:
For an object of mass M, that is at a distance H from the ground, the potential energy can be written as:
U = M*H*g
where g is the gravitational acceleration g = 9.8m/s^2
In this case, we have that:
mass of the weights = 1,250 kg
height = 2m
Then the potential energy of the weights is:
U = 2m*1,250kg*9.8m/s^2 = 24,500 J
3. An element that is malleable is
A. Easily shaped B. Very hard C. Difficult to pour D. Very dense
Answer:
Difficult to Pour.
Explanation:
Someone please help me
I have attached the question
Answer:
Hydrogen
Explanation:
The atomic number is the number of protons in the nucleus :)
Which three statements about gravity and the formation of the solar system
are true?
A. Gravity pulled most of the matter into the center of the solar
system.
B. Gravity caused the planets and Sun to have spherical shapes.
O C. Gravity held the pieces of forming planets together.
D. Gravity evenly distributed matter throughout the solar system.
Answer:
it's answer is B
A planet is round because of gravity. A planet's gravity pulls equally from all sides. Gravity pulls from the centre to the edges like the spokes of a bicycle wheel. This makes the overall shape of a planet a sphere, which is a three -dimensional circle
Hope it helps you
A rolling ball with a mass of 1.01 kg crashes into a wall. The wall exerts a force of 2.40 Newtons and stops the ball. What was the magnitude of the acceleration of the ball at the time of the crash?
Answer:
Acceleration, a = 2.38m/s²
Explanation:
Given the following data;
Mass = 1.01 kg
Force = 2.4N
To find the acceleration;
Force is given by the multiplication of mass and acceleration.
Mathematically, Force is;
[tex] F = ma[/tex]
Where;
F represents force.m represents the mass of an object.a represents acceleration.Making acceleration (a) the subject, we have;
[tex]Acceleration, a = \frac{F}{m}[/tex]
Substituting into the equation, we have;
[tex]Acceleration, a = \frac{2.4}{1.01}[/tex]
Acceleration, a = 2.38m/s²
Therefore, the magnitude of the acceleration of the ball at the time of the crash is 2.38 meters per seconds square.
Why is studying the Earth important? What advantage is the
study of the Earth to all scientists?
Answer: It is important to study Earth because it is the one place in the entire solar system where humans can live. Earth is a planet too! The advantage is Earth science or geoscience includes all fields of natural science related to planet Earth. This is a branch of science dealing with the physical and chemical .
quote explanation: I hope that was helpful and please mark me as brainliest!
The amount of air resistance acting on an object depends on the objects
Answer:
Shape of the object
Explanation:
This depends on the shape of the object. For a spherical object, a unitless value of 0.47 is typical. The magnitude of the velocity squared. The faster you go, the greater the air resistance force
A substance has a boiling point of 220 degrees Celsius and a melting point of −120 degrees Celsius. What state will it be at room temperature?
The substance with a boiling point of 220°C and a melting point of -120°C will be liquid at room temperature. The room temperature ranges from 15-35°C.
What is state of matter?The state of matter is the behavior of atoms and molecules present in a substance at a particular condition. There are three states of matter which include:
a. Solids: These are relatively rigid with a definite volume and shape, the atoms and molecules are attached to each other and vibrate in place,
b. Liquids: These are fluid in nature with a definite volume but not a definite shape, atoms and molecules are attached to each other by chemical bonds, and have more energy than solids,
c. Gases: In this state molecules do not have a definite shape nor a definite volume, the molecules are unstable as they carry maximum energy.
Boiling point of a substance is the temperature at which the vapor pressure of the liquid becomes equal to the pressure of surrounding (atmospheric pressure) of the liquid and the liquid therefore changes into the vapor state.
The process by which a solid substance changes to a liquid substance is called melting. The melting point is the temperature at which melting of a solid into a liquid takes place. The melting point of a substance is the same as the freezing point.
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If a person is a regular marijuana user, they may be ...
A. under-performing at school.
B. over-achieving at school.
C. average at school.
Answer:
A
Explanation:
marijuana affects the brain
In this case, they may be under-performing at school. Hence, option (A) is correct.
What are habits?Routines that are routinely carried out are referred to as habits. They can also be characterized as behaviors brought on by an internal or external stimulus (Robbins & Costa, 2017). Additionally, habits are the actions you take in specific situations.
Perhaps someone else always brushes their teeth before going to bed. Basically, anything that is repeated frequently enough to become automatic might be considered a habit. You don't really need to consider doing it any more. It simply occurs.
Some would argue that our behaviors are what causes life (or at the very least, success). The routine actions we take shape who we are and the outcomes we attain. Because of this, developing healthy habits and breaking negative ones is a vital life skill that has numerous advantages.
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A 50.0 kg shell is fired from a cannon on Earth's surface to a maximum height of 400 m. It then falls to a height of 100 m. What is the loss of potential energy as it falls?
Answer:
150,000 Joules.
Explanation:
Given that a 50.0 kg shell is fired from a cannon on Earth's surface to a maximum height of 400 m. It then falls to a height of 100 m. What is the loss of potential energy as it falls?
From Potential energy formula,
P.D = mgh
Assuming g = 10m/s^2
P.D = 50 × 10 × 400
P.D = 200000 Joules
Then it fell on 100m
The potential energy will be
P.D = 50 × 10 × 100
P.D = 50000 Joules
The lost Potential energy will be:
Lost P.D = 200000 - 50000
Lost P.D = 150000 Joules
Therefore, the loss of potential energy as it falls will be 150,000 Joules.
5. Graph A plots a race car's speed for 5 seconds. The car's
rate of acceleration is 6 m/s?. True or false
An isotope has a half-life of 25 days. If you start with 50 grams, how much of the substance
will remain after 50 days? *
25 grams
12.5 g
6.75 g
Answer:
12.5
Explanation:
If the half life is 25 days then in 50 days it will half twice
50/2=25
25/2=12.5
The high point on a wave is called its _________
Answer:
I believe its called the crest
Explanation:
Answer:
crest
Explanation:
the highest surface is called crest. the lowest is the trough. the vertical distance between the crest and trough is the wave height. the horizontal distance between two adjacent crests or troughs is known as the wavelength.
How far does a horse travel if it gallops at an average speed of 15km/hr for 2 hours?
Answer:
30km
Explanation:
Distance= speed x time
15x2=30km
Thanks+BRAINLIST
Light refracts when:
a. It changes speed
b. It changes from a particle to a wave
C. Its density changes
d. It encounters a solid object
Answer:
it change speed
Explanation:
its because when light passes through one medium to another (rarer to denser)its velocity change and its speed also changes
5. Susan exerted 400 newtons of force while pushing on a huge boulder. The boulder moved 0 meters. Calculate work.
Answer:
0 J
Explanation:
Work is the product of force and distance in the direction of force.
The formula is ; Work = Force * Distance
Given that :
Force = 400 N
Distance = 0 meters
Work = 400 * 0 = 0 J
No work was done because the boulder did not move.
There are 30 students in Ms. Andrews’ fourth grade class. There are 6 times as many students in the entire fourth grade as there are in Ms. Andrew’s class. Which equation can be used to determine the number of students, n, in the entire fourth grade? *
6 x n = 30
6 + 30 = n
30 x 6 = n
30 ÷ n = 6
Answer:
30×6=n
Explanation:
30 students in her class× 6 = number of students in the entire 4th grade.
Describe the disadvantages and advantages of using this element for dating.
Answer:Each method of dating has constraints around its use and effectiveness. Not all methods are well-suited for each situation – and sometimes it is just not possible to use a particular dating method.
Examples of some of the constraints of using a dating method include:
the size of the sample
the type of sample
contamination of the sample
the type of associated geo-archaeological materials
the need to minimise destructive testing
the chronologies involved
Explanation:
Identify at least two ways in which heavy rain can affect the efficiency of
waste water treatment facilities.
I
Saeed moves 50 m east then 65 m south to reach the garden. What is the displacement of Saeed?
Answer:
82.01m
Explanation:
Using the formula:
R^2=A^2+B^2
R= √ A^2+B^2
Where R= displacement
A=50m
B=65m
R= √ 50^2+65^2
R= √ 2500+4225
R= √ 6725
R=82.01m
Some gas is trapped in a large syringe by a piston.The atmospheric pressure is 100kpa.The pressure gauge indicates that the gas pressurr is 200kpa above atmospheric pressure.The piston moves outwards and the volume of the gas doubles.The temperature remains constant.What is the new gas pressure?
Answer: The new gas pressure is 150 kPa.
Explanation :
Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.
[tex]P\propto \frac{1}{V}[/tex] (At constant temperature and number of moles)
[tex]P_1V_1=P_2V_2[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = (100+200) kPa = 300 kPa
[tex]P_2[/tex] = final pressure of gas = ?
[tex]V_1[/tex] = initial volume of gas = v
[tex]V_2[/tex] = final volume of gas = 2v
[tex]300\times v=P_2\times 2v[/tex]
[tex]P_2=150kPa[/tex]
Therefore, the new gas pressure is 150 kPa.
A smooth wooden block is placed on a smooth wooden tabletop. You find that you must exert a force of 22.0 N to keep this 7.00 kg block moving at a constant
velocity of 4.00 m/s. What is the gravitational force acting on the wooden block?
A.) 7.00 N
B.) 68.7 N
C.) 22.0 N
D.) 78.5 N
Answer:
B . 68.7 N
Explanation:
Given in the question that;
Force = 22 N
Mass = 7.0 kg
Velocity = 4.0 m/s
Gravitational force is the weight of wooden block , calculated as mass times acceleration due to gravity.
F= m* a
F= 7 * 9.81
F= 68.67 N
F= 68.7 N
An automobile with a mass of 1000 kg accelerates at a traffic light with a force of 4000 N. What is the automobile's acceleration?
Explanation:
Given
mass (m) = 1000 kg
Force (F) = 4000 N
Acceleration (a) = ?
We have the relation
F = m * a
or, 4000 = 1000 * a
or a = 4000 / 1000
a = 4 m/s²
The acceleration of the automobile is 4 m/s²
Hope it will help :)❤
Answer:
[tex]\boxed {\boxed {\sf 4 \ m/s^2}}[/tex]
Explanation:
According to Newton's Second Law of Motion, force is equal to the product of mass and acceleration.
[tex]F=m*a[/tex]
We know the mass is 1000 kilograms and the force is 4000 Newtons. Let's convert the units to simplify the question for later.
1 Newton is equal to 1 kilogram meter per square second. The force of 4000 N is equal to 4000 kg*m/s²[tex]m= 1000 \ kg \\F= 4000 \ kg*m/s^2[/tex]
Substitute the values into the formula.
[tex]4000 \ kg*m/s^2=1000 \ kg *a[/tex]
We want to find the acceleration, a. We must isolate the variable on one side of the equation.
1000 kg and a are being multiplied. The inverse operatio of multiplication is division. Divide both sides of the equation by 1000 kg.
[tex]\frac{4000 \ kg*m/s^2 }{1000 \ kg } =\frac{1000 \ kg*a}{1000 \ kg}[/tex]
The kilograms will cancel.
[tex]\frac{4000 \ m/s^2 }{1000 }=a[/tex]
[tex]4 \ m/s^2 =a[/tex]
The autombile's acceleration is 4 meters per square second.
Which of these circuit schematics has an ammeter?
Α. Α
B. B
C. C
D. D
Answer:
d is the correct answer for this question hope it helps
Explanation:
when you see a A in a circle the the ammeter
Answer:
D.
Explanation:
PLATO
Figure 1 shows an astronaut working with the lunar research module on the
surface of the Moon. The mass of the lunar module is 15.000kg. The gravitational
field strength of the Earth is 10N/kg.
Figure 1
(a) Calculate the weight of the lunar module on the Earth. Give your
Answer:
The weight of the lunar research module on Earth is 150.000 N
Explanation:
The given parameters for the mass of the lunar module are;
The mass of the lunar moon, m = 15.000 kg
The gravitational field strength of the Earth, g = 10 N/kg
The weight, 'W', of the lunar research module on Earth is given as follows;
W = m·g
Substituting the known values, we get;
W = 15.000 kg × 10 N/kg = 150.000 N
The weight of the lunar research module on Earth, W = 150.000 N.
which roots are better underwater , taprroots or fibrous?
Answer:
The absorption of water and minerals by taproot is more efficient with the taproot system. Fibrous root absorbs water more efficiently as it reaches deep into the soil. Taproots are capable of withstanding drought.
A train travels 200km/hr. how much distance will the train be from the station in 2.5 hours?
Answer:
500km
Explanation:
Given parameters:
Speed = 200km/hr
Time taken = 2.5hrs
Unknown:
Distance = ?
Solution:
To solve this problem, we use the speed, time and distance equation.
Therefore;
Distance = Speed x time
So;
Distance = 200 x 2.5 = 500km
A student conducts an experiment in which an object travels across a horizontal surface while for 2 s a net force is applied to a 2 kg object that initially travels with a speed of 0.5 m/s. Data collected from the experiment are used to create the graph of the magnitude of the applied force exerted on the object as a function of time is shown. All frictional forces are considered to be negligible. Can the student use the graph and the known data to determine the momentum of the object after the force has been applied?
Yes, because the average force exerted on the object can be used with the time interval of 2 s to determine the change in momentum of the object by using Δp⃗ =F⃗ Δt.
Yes, because the area bound by the best-fit line and the horizontal axis from 0 s to 2 s can be used to determine the change in momentum of the object.
No, because the data is too scattered to determine the average force that is exerted on the object.
No, because the student needs to know the direction that the force is applied to the object because the applied force will be in the same direction as the change in momentum of the object.
Answer:
D. No, because the student needs to know the direction that the force is applied
Explanation:
The change in momentum depends on the direction of the force as well as its magnitude. Since the graph only supplies force magnitude information, it is insufficient to allow the student to calculate the change in momentum.
Convert 1 mm to meters using scientific notation. Include units in your answer.
Answer: The answer in scientific notation with the unit included is (1 × 10^-3m.)
Explanation:
In the field of physics, when working with too large or too small numbers, such can be expressed with the use of scientific notation. This helps to eliminate huge or ambiguous numbers with significant units. It is written is such a way that the first number is greater than or equal to 1 and less than 10 which is then multiplied by a factor of 10.
Units are symbols that are used to represent a measurement For example the unit of meters is (m).
Converting 1mm to m:
1000millimeters = 1meter
1 millimetre = X
Making X the subject of formula,
X = 1 ×1 /1000
X = 0.001m
Therefore expressing X in scientific notation is
1 × 10^-3meter (m)
