Answers
Answer:
x=± 2
=±1.4142
x=0
Explanation: If this does not help then I'm sorry.
STEP
1
:
1
Simplify —
2
Equation at the end of step
1
:
1
k - ((— • k) • x2) = 0
2
STEP
2
:
Equation at the end of step 2
kx2
k - ——— = 0
2
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
k k • 2
k = — = —————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
k • 2 - (kx2) 2k - kx2
————————————— = ————————
2 2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2k - kx2 = -k • (x2 - 2)
Trying to factor as a Difference of Squares:
4.2 Factoring: x2 - 2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
4
:
-k • (x2 - 2)
————————————— = 0
2
STEP
5
:
When a fraction equals zero
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-k•(x2-2)
————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-k • (x2-2) = 0
Theory - Roots of a product :
5.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
5.3 Solve : -k = 0
Multiply both sides of the equation by (-1) : k = 0
Solving a Single Variable Equation:
5.4 Solve : x2-2 = 0
Add 2 to both sides of the equation :
x2 = 2
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 2
The equation has two real solutions
These solutions are x = ± √2 = ± 1.4142
Three solutions were found :
x = ± √2 = ± 1.4142
k = 0
Terms and topics
Related Questions
328,000 mm + 137 m = ______________m?
Answers
Answer:
465m.
Explanation:
Convert all units to meters. So,
328 + 137 = 465m.
If you were to measure your pulse rate while in a spaceship moving away from the Sun at a speed close to the speed of light, you would find that it was
Answers
Answer:
Your pulse rate will be the same as it was while you were on Earth.
Explanation:
Since you are on the ship, and you have the same speed with the ship, then, you'll observe your heart rate to be the same as your heart rate while you were on Earth. This is because there is no relative speed between you and the ship, since you're both on the same frame of reference.
why do we accelerate forward when we run?
Answers
It depends on what direction you are running in, if it's forward, you'll have to keep to accelerating forward to keep running.
If you stop accelerating forward, you wouldn't be able to move forward.
A water strider bug is supported on the surface of a pond by surface tension acting along the interface between the water and the bug’s legs. Assume the bug weighs 10−4 N and the surface tension force acts vertically upward. Determine the minimum length of the interface needed to support the bug
Answers
Answer:
minimum interface length = 1.36 mm
Explanation:
given data
weight of the bug = [tex]10^{-4}[/tex] N
solution
we will apply here Surface Tension formula that is
Surface Tension ,σ = Force ÷ length ........................1
and we consider here surface tension for water is 7.34 × [tex]10^{-2}[/tex] N/m
so that here minimum interface length needed to support the bug is
minimum interface length = Force ÷ σ
minimum interface length = [tex]10^{-4}[/tex] ÷ 7.34 × [tex]10^{-2}[/tex]
minimum interface length = 1.36 mm
A student leaves a sidewalk corner walks 3.0 blocks north then walks 3.0 blocks west.what is the students displacement from the starting position
Answers
Answer:
The students displacement is 3·√3 blocks, 45° North of West
Explanation:
From the question, we have;
The distance North in which the student walks = 3.0 blocks
The next walking distance West by the student = 3.0 blocks
The displacement of the student = The shortest distance between the student start and final point
By representing the motion of the student in vector format, we have;
[tex]\mathbf{d} = 3\cdot \hat{i} + 3\cdot \hat{{j}}[/tex]
Therefore the magnitude of d is given as follows;
[tex]\left | d\right | = \sqrt{3^2 + 3^2} = 3\cdot \sqrt{3} \ blocks[/tex]
The direction of the student = tan⁻¹(3/3) = 45° West of North
The students displacement = 3·√3 blocks, 45° North of West.
A ball is shot into the air with initial speed of 40 m/s. How high will the ball go before falling back down?
A. 20m
B. 40m
C. 60m
D. 80m
Answers
Answer:
B. 40m
Explanation:
What is the volume of a box that is 3 m long, 0.5 m high, and 2 m wide?
Answers
If a car travels 23.8 meters in 4.2 seconds, what is its speed?
Put your units in the form of a correct abbreviation (example, write s for seconds, m
for meters, or m/s for meters per second).
Answers
Initial velocity * time = 0 since we assume that the car is launching from start without motion.
So, displacement = 0.5 * acceleration * time ^ 2
23.8 = 0.5 * acceleration * 4.2^2
23.8 = 0.5 * 17.64 * acceleration
23.8 = 8.82 * acceleration
23.8/8.82 = acceleration = 2.69 m/s^2
Final Velocity = initial velocity + acceleration * time
Final velocity = 0 + 2.69 * 4.2 = 11.3 m/s
Denise heats a beaker of dilute acid on a hot plate in a fume hood. What should Denise wear to best protect herself when she transports the beaker to a balance outside the hood?
Answers
Answer:
D . goggles, a lab coat, heat-proof gloves, and close-toed shoes
Explanation:
Answer:
goggles, a lab coat, heat-proof gloves, and close-toed shoes
Explanation:
a student records the feather colors and beak shape of every bird observed in the park. which kind of data is the student recording
Answers
Answer:
This question is incomplete. The completed question is below
A student records the feather colors and beak shapes of every bird observation in a park. What kind of data is the student recording? A. Qualitative B. Quantitive C. Empirical D. Theoretical
The correct option is C
Explanation:
Empirical data is the data recorded during the course of an experiment/research by means of observing (it could be direct or indirect) certain properties/quality. From the question, it was described that the student observed and recorded the feather colour and beak shapes of birds that came to the park.
Observing the feather colors and beak shapes of birds and recording it is an example of empirical analysis where the student is analyzing based on an observable data.
What is empirical analysis?Empirical analysis is a method for studying and interpreting data that is based on empirical research. Information that can be obtained through experience or by using the five senses is known as empirical evidence. Empirical research is the name given to it in a scientific setting.
Evidence is needed in empirical analysis to support any theory. An empirical method collects observable data and establishes a repeatable procedure to yield results that can be independently verified. Statistics are frequently used in empirical analysis to back up a thesis.
An empirical research needs the stages namely, observation, induction, deduction, testing and evolution.
To find more on empirical analysis, refer here:
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This question is incomplete. The completed question is below
A student records the feather colors and beak shapes of every bird observation in a park. What kind of data is the student recording? A. Qualitative B. Quantitive C. Empirical D. Theoretical
An atom with the expected number of neutrons, protons, and electrons is called a(n)
Answers
Answer:
Stable atom
Explanation:
A stable atom is one that has a balanced nuclear inter-particle force reaction as such the binding energy of a stable atom is sufficient to permanently keep the nucleus as one unit. Examples of a stable atom are the atoms of monoisotopic elements such as fluorine, sodium, iodine, gold, aluminium, and cobalt.
In a stable atom the expected number of proton, neutron, and electron are present while in an unstable atom or radioactive atom, there are more than the expected number of neutrons or protons, such that the internal energy of the nucleus is excessive and more than the binding energy, which can lead to radioactive decay.
I need the ans for this question QUICK PLEASE!!!
Answers
Explanation:
A) 1.05
B) 1.33
C) 1.16
D) 0.62
All units in cm
What is a tomato
Fruit
Root
Stem
None of these
Answers
Bella makes the 6.1m distance to her food bowl in 8.8 seconds what is her average velocity
Answers
To find the average velocity, you must divide the distance by the change in time, which should look like v=d/t
Here is how you set up the equation-
v=6.1/8.8
Once you divide 6.1 meters by 8.8 seconds, you should get a number that looks like 0.69318182.... however, I just rounded it to 0.693 meters per second. You can round it to whatever you like.
Hope this helped! If you have any questions about what I mentioned in my answer or explanation, feel free to comment on my answer and I’ll try to get back to you!
30. A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?
Answers
Answer:84 generations
Explanation:
A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD? Approximately 84 generation.
a dog walks 12 meters to the west and then 16 meters back to the east
Answers
Answer:
Explanation:
4 meters east
A jet engine pushes air at high velocity toward the rear of the plane. Thrust is created moving the plane forward. Which statement is correct about the amount of force the air pushes the engine forward with?
The air pushes the engine with an equal force in the opposite direction. The air pushes the engine with a much smaller force in the same direction.
The air pushes the engine with an equal force in the same direction. The air pushes the engine with a much smaller force in the opposite direction.
Answers
Whenever force is used there is an opposite yet equal affect.
Calculate velocity of a plane flying 1800 miles North East in 4.5 hours
Answers
Answer:
400
Explanation:
We divide time (4.5 hours) and speed (1800 miles)
1800÷45=400
How might error analysis help scientists identify and quantify the
causes and effects of uncertainties in measured data? Why is it
important to perform multiple trials in an experiment?
Answers
Answer: For producing the error free results of an experiment that identification and quantification of effects of uncertainties are important.
Explanation:
The error analysis is necessary to detect the uncertainties in the measured data or results of the experiment to ensure the validity and acceptability of the results. The errors can be avoided by increasing the precision and accuracy of the measuring instruments. The other factors like changes in the variables of the experiment can also contribute to the errors in the experiment.
It is necessary to perform the multiple trails in an experiment to assure that the results of the experiment are consistent with every trial.
difference between fundamental unit and derived unit (any two)
grade 8 question
Answers
Answer:
fundamental units are those units that are independent to other units where as derived units are derived from fundamental units . there are altogether 7 fundamental units where as there are more than seven derived units..
Answer:
[tex] \boxed{ \sf{see \: below}}[/tex]
Explanation:
[tex]\underline{ \sf{fundamental \: unit}}[/tex]
[tex] \star[/tex] This is the unit of a fundamental quantity.
[tex] \star[/tex] This unit is independent of other units.
[tex] \star[/tex] There are only seven fundamental units. They are metre , kilogram , second , Kelvin , ampere , candela and mole.
[tex] \underline{ \sf{derived \: unit}}[/tex]
[tex] \star[/tex] This is the unit of a derived Quantity.
[tex] \star[/tex] This unit is obtained from fundamental units.
[tex] \star[/tex] It is formed in many types using seven fundamental units. They are Newton , Pascal , Joule , Watt , Hertz , Ohm etc.
Hope I helped!
Best regards! :D
The circus dog in the picture below is balancing a ball on his nose. The ball has __________ energy right now, but when he drops the ball it will have __________ energy.
Answers
Right now the ball only has potential energy but when the ball falls that will be converted into kinetic energy because it is moving. BTW Im 14 in 9th grade ya'll should know this.
Answer:
potential; kinetic
Explanation:
the diagram shows a ray of light being reflected by a plane mirror and one angle is 60 degrees.what will be the measure of its angle of incidence and angle of reflection?
Answers
Answer:
when the light is reflected from a surface the angles of incident is always equal to the angles of reflected where both angles are measures from the path of the light to the normal to the surface at the point at which light stricks the surface . this equality is known as the law of reflection .
Since the angle of reflection is 60 degrees, the angle of incidence is also 60 degrees.
What are the laws of reflection?The laws of reflection describe the behavior of light when it is reflected off a smooth surface, such as a plane mirror. There are two laws of reflection:
1. The angle of incidence is equal to the angle of reflection: When a light ray strikes a surface, the angle between the incoming ray and the surface (the angle of incidence) is equal to the angle between the reflected ray and the surface (the angle of reflection). This law holds true for all angles of incidence.
2. The incident ray, the reflected ray, and the normal to the surface all lie in the same plane: The normal is an imaginary line perpendicular to the surface at the point where the ray strikes the surface. The incident ray is the incoming ray of light, and the reflected ray is the ray that bounces off the surface. Both of these rays, along with the normal, all lie in the same plane.
These laws can be used to predict the path of reflected light and to determine the position and size of an image formed by a plane mirror. The angle of incidence and angle of reflection can be measured using a protractor, and the normal can be found by drawing a line perpendicular to the surface at the point of incidence.
Here in the Question,
According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r), which means:
i = r
The angle of incidence = Angle of reflection = 60 degrees.
Therefore, The angle of incidence is also 60 degrees since the angle of reflection is 60 degrees.
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Which equation can be used to solve for acceleration?
Answers
Answer:
The answer's A
Explanation:
Have a good day! :)
Option A is correct. the equation that can be used to solve the acceleration is expressed as [tex]t = \frac{\triangle V}{a}[/tex]
Acceleration is defined as the change in velocity of a body with respect to time. Mathematically;
[tex]a=\frac{\triangle V}{t}[/tex] where:
[tex]\triangle V[/tex] is the change in velocityt is the time takenMaking the time "t" the subject of the formula:
[tex]t = \frac{\triangle V}{a}[/tex]
Hence the equation that can be used to solve the acceleration is expressed as [tex]t = \frac{\triangle V}{a}[/tex]
Learn more here: https://brainly.com/question/24175401
what do understand by the efficiency of a machine? By using a block and tackel a man can raise a load of 720 N by an effort of 180 N.Find the mechanical advantage of the method.
Answers
Answer:
Efficiency of a machine is how well the machine works and what the machine is capable of doing.
Mechanical advantage=Load/Effort.
720/180=4
Why does the first raindrop decide to drop down to the field?
Answers
Answer:
good question lol
Explanation:
The raindrop wants to help in any way it can. The raindrop believes it can water the field by itself.
Answer:
The first raindrop decided to drop down to the field to cheer up the farmer a little bit.
i need help with this one 2 if you guys don’t mind
Answers
4 is 0.47 liters
5 is 4 cm
6 is 23 mm
7 is 53 m
8 is 1800 mg
9 is 31.07 mi
Hope I’m helping ya
The microwave oven was invented in 1945 when some experiments with radar equipment failed and melted some nearby chocolate instead. The scientists realized there were other applications for this energy source. What is an example of.
Answers
Answer: Creative Thinking.
Explanation: Creative thinking this is a special ability possessed by individuals to see things differently or I’m a different dimension, and find new ways of solving problems. The fact it’s Creative thinking skills doesnt mean it’s for only 'creative types' like musicians. Everyone can also be a beneficiary of creative thinking from time to time. Just like in the case of the scientist above who saw an invention from his failed experiment.
Answer:
good thinking
Explanation:
gave the person above me brainy
The major changes in the state of the universe that occurred immediately after the Big Bang were in ______ and ______.
Answers
calculate the pressure of water in a well if the depth of water is 10m
Answers
p=d×h×g
p=1000×10×10
:.:p=100000 pa
Explanation:
p=Liquid pressure
d=Density
h=Height
g=acceleration due to gravity
T H A N K Y O U ! !
________________ is a scientific field and job that involves taking our scientific understanding of the natural world and using it to invent, design, and build things to solve problems and achieve practical goals.
Column 1
Column
Civil Engineer
Engineering
KIP
Column
Civil Engineer
Engineering
KIP
Answers
Answer:
civil engineering is the correct answer.