If f and h are inverses of one another, then we have
h(f(x)) = x
Differentiating both sides using the chain rule gives
h'(f(x)) • f'(x) = 1
Let f(x) = -1. Then it would follow that
h'(-1) = 1/f'(x)
for the value of x such that f(x) = -1. This result is known as the inverse function theorem.
Solve for x such that f(x) = -1 :
2x³ - 3x = -1
2x³ - 3x + 1 = 0
By inspection, x = 1 is a solution, since 2 - 3 + 1 = 0. So x - 1 is a factor of the left side; polynomial division yields a factorization of
(x - 1) (2x² + 2x - 1) = 0
and using the quadratic formula, we find three solutions,
x = 1, x = (-1 - √3)/2, x = (-1 + √3)/2
Since there's more than one solution here, this means f(x) is not one-to-one and thus has no inverse in the strict sense of the term.
We can however restrict the domain of f(x) to a subset over which it can be inverted. Using the fact that polynomials are monotonic over intervals between their extrema, we find the critical points of f(x) :
f'(x) = 6x² - 3 = 0 ⇒ x² = 1/2 ⇒ x = ± 1/√2
Check the sign of the second derivative at each critical point:
f''(x) = 12x
• f''(-1/√2) = -12/√2 < 0 ⇒ x = -1/√2 is a local maximum
• f''(1/√2) = 12/√2 > 0 ⇒ x = 1/√2 is a local minimum
Now we have a few choices of how to define the inverse of f(x).
• If we restrict the domain of f(x) to the interval (-∞, -1/√2), then f(x) = -1 when x = (-1 - √3)/2. Then by the inverse function theorem,
f((-1 - √3)/2) = -1 ⇒ h'(-1) = 1/f'((-1 - √3)/2) = (-1 + √3)/6
• If we instead restrict the domain to (-1/√2, 1/√2), then f(x) = -1 when x = (-1 + √3)/2. Then
f((-1 + √3)/2) = -1 ⇒ h'(-1) = 1/f'((-1 + √3)/2) = (-1 - √3)/6
• Otherwise, if we restrict to (1/√2, ∞), then f(x) = -1 when x = 1. Then
f(1) = -1 ⇒ h'(-1) = 1/f'(1) = 1/3
A 40 N box is pushed 5 m up a ramp. The angle of the ramp is 37° above the horizontal. The applied force is parallel to the ramp and opposed by a frictional force of 10.0 N. Find the net increase in potential energy by the crate.
The net increase in potential energy by the crate is negative 49.4 Joules. That is, ΔP.E = - 49.4 J
Given that a 40N box is pushed 5 m up a ramp. The angle of the ramp is 37° above the horizontal.
We can find the height h of the ramp with the equation below;
h = 5sin 37
h = 3.009 m
Mass of the box = 40/9.8 = 4.082 kg
The maximum energy attained = mgh
Maximum Energy = 4.082 x 9.8 x 3.009
E = 120.36 J
The maximum K.E = Maximum P.E
1/2m[tex]U^{2}[/tex] = 120.36
m[tex]U^{2}[/tex] = 240.72
[tex]U^{2}[/tex] = 240.72 / 4.082
[tex]U^{2}[/tex] = 58.97
U = [tex]\sqrt{58.97}[/tex]
U = 7.7 m/s
We can find the acceleration by using third equation of motion
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2aS
Since the box is going to rest, V = 0, and acceleration will be negative
0 = 7.7^2 - 2 x a x 5
10a = 59.29
a = 59.29/10
a = 5.93 m/[tex]s^{2}[/tex]s^2
The applied force F = ma
F = 4.082 x 5.93
F = 24.2 N
Given also that the applied force is parallel to the ramp and opposed by a frictional force of 10.0 N. The net increase in potential energy by the crate will be
ΔP.E = Net work done
ΔP.E = Net force x distance
ΔP.E = (24.2 - 10 - 40sin37) x 5
ΔP.E = - 9.87 x 5
ΔP.E = - 49.4 J
Therefore, The net increase in potential energy by the crate is negative 49.4 Joules.
Learn more about Potential energy here: https://brainly.com/question/25791834
a crocodile ate my shoes
Answer: Spiderman
Explanation: The raccoon man said so
Which of the following best explains the changes on the map between 1644 and 1800?
Answer: It incorporated many diverse cultural groups
Explanation:
im almost done with high school and I want to go to a college in texas where the love of my life lives. anyone got any suggestions for good colleges there???
Answer:
Trinity University in San Antonio is nice, just know that if you walk around downtown San Antonio (really anywhere in Texas) either carry pepper spray and or other self defense mechanisms and/or walk with a man you trust (that applies only if you are a woman, sadly)
I was there visiting Trinity and it's nice, really nice gyms and stuff, cool food court, other stuff too, but i was walking downtown with MY PARENTS on either side of me and a scary guy came up and cut us off and was making crude comments toward me and was advancing on us. so guys in big cities are bold a-holes.
It seems like going to school in texas would mean out-of-state tuition for you, so apply for any and all scholarships that you can.
Explanation:
What are the arithmetic operators?give an example using at least one arithmetic operator and at least two values
Answer:
I don't know
Explanation:
how do i find the limiting reactant
In ΔABC, ∠B is a right angle, AB = 30, and sec A = 5/3. Find the value of csc C in fraction and in decimal form.
I will mark brainliest if you are correct!
sec(A) = 5/3 ⇒ cos(A) = 3/5
Angles A and C are complimentary (they sum to 90°), so
sin(C) = cos(A) = 3/5
since sin(90° - x) = cos(x) for all x, and in turn
csc(C) = 1/sin(C) = 5/3
TRUE atau FALSE:
Singapura mempelopori balapan malam F1 pertama
Answer:
true
Explanation:
urgent!
Which of the following becomes
disrupted when we don't feel
self-control?
A. anxiety
B. internal circadian rhythm
C. relational processes
D. personal reality
Self-control could be defined as the conscious ability to regulate impulses voluntarily, if we don't feel self-control relational processes becomes disrupted.
Self-control is the ability to regulate emotions, thoughts and behaviors effectively in different situations.
A person with self-control can manage their emotions and regulate her behavior, copes with setbacks with serenity, has patience and understanding in relational processes.Lack of self-control affects the ability to establish and maintain positive and rewarding relationships with diverse individuals and groups through communication, social commitment, and teamwork.Therefore, we can conclude that self-control allows to regulate emotions, thoughts and behaviors, giving the possibility of choosing actions and reactions to stimuli, with the aim of achieving a greater personal and relational balance.
Learn more about self-control here: https://brainly.com/question/12787425
What are the benefits that can help the body in doing physical exercise? essay
Answer:
a essay a
Explanation:
List the molecules of the “energy investment phase” in order starting from Glucose?
Answer:
Energy investment phase. Glucose is first converted to fructose-1,6-bisphosphate in a series of steps that use up two ATP. Then, unstable fructose-1,6-bisphosphate splits in two, forming two three-carbon molecules called DHAP and glyceraldehyde-3-phosphae.
Explanation:
hope it helps you
which factor contributes least to the rate at which a stream deposits sediment?
Solution
To determine the angle of the velocity, we use the following equation.
Tan θ = Vertical velocity ÷ Horizontal velocity
As the particle moves from its initial position to its final position, its vertical velocity decreases at the rate of 9.8 m/s each second. During this time its horizontal velocity is constant. To determine the time when the angle is 45˚, we need to determine the object’s vertical velocity at this angle. Let’s determine the vertical and horizontal components of its initial velocity.
Vertical = 50 × sin 60˚, Horizontal = 50 × cos 60˚ = 25 m/s
Since horizontal velocity is constant, let’s put 25 m/s and 45˚ into the tangent equation.
Tan 45 = Vertical velocity ÷ 25
Vertical velocity = 25 m/s
To determine the time for the vertical velocity to decrease from its initial value to 25 m/s, use the following equation.
vf = vi – a × t
a = 9.8
25 = 50 × sin 60˚ – 9.8 × t
t = (25 – 50 × sin 60˚) ÷ -9.8
This is approximately 1.83 seconds.
The economy has been sluggish in recent months with slow economic growth. Explain the policies that the Federal Reserve could use to improve the economy.(1 point)
The Federal Reserve stops purchasing treasuries and securities, and then issues new reverse repurchase agreements. The short-term profits and decrease in the money supply cause a decrease in interest rates and increased lending.
The Federal Reserve sells treasuries back to banks and issues new reverse repurchase agreements. The decrease in the money supply increases interest rates, which increases lending.
The Federal Reserve purchases treasuries and securities and also issues new repurchase agreements. The increase in the money supply and decrease in interest rates result in more lending and risk.
The Federal Reserve purchases treasuries and securities, and also issues new repurchase agreements. The increase in the money supply increases interest rates and inflation, which spurs economic growth.
The policy that the Federal Reserve could use to improve the economy are;
C: The Federal Reserve purchases treasuries and securities and also issues new repurchase agreements. The increase in the money supply and decrease in interest rates result in more lending and risk.
The Federal Reserve which is the US Central Bank has 2 major roles which are:
To find a way to work to achieve low level of unemploymentTo maintain stable prices all through the economy.Now, when there is recession which is slow economic growth, unemployment level increases, and prices may drop in a process called deflation.
The Federal Reserve could take the following steps to arrest the slide in economic growth;
Open market operations; In this system, the federal reserves can lower interest rates by buying debt securities on the open market which is traded in return for newly created bank credit. This means the federal reserve purchases mostly Treasury securities in its normal open market operations. Lower capital requirementsDiscount LendingThus, the correct answer is option C.
Read more about recession at; https://brainly.com/question/3578090
Answer: C: The Federal Reserve purchases treasuries and securities and also issues new repurchase agreements. The increase in the money supply and decrease in interest rates result in more lending and risk.
Hope this helps :)
EZ COLLEGE QUESTION:Which of the following people would be most appropriate to ask for a letter of recommendation to accompany your college application?:
A.the coach of your seventh grade soccer team
B.the minister of your local church who has known you for 10 years
C.the neighborhood family for whom you babysit on a regular basis
D.the friend you made at a two-week YMCA camp last summer
The minister of your local church who has known you for 10 years would be most appropriate to ask for a letter of recommendation. A letter of recommendation can help to obtain a job or college application.
A letter of recommendation is a document used to validate the work, specific skills, and/or academic performance of an individual.
These letters (letters of recommendation) are generally requested by a superior for obtaining a job or college opportunity.
The letters of recommendation can be helpful for adding extra merit to a job/college application.
Learn more about letters of recommendation here:
https://brainly.com/question/10281132
20 POINTS!!!!
Which of the following statements BEST describes the position of the United States following World War II?
The United States should set up and control democratic governments in allied European countries.
Promoting democracies in European countries is the best way for the United States to combat the spread of communism.
The United States should not be expected to provide financial aid to countries struggling to rebuild after the war.
It is not the United States' responsibility to provide aid to states that have resisted communist takeovers.
The United States should focus attention on Western Europe only.
What composition of rigid motions maps ΔPQR to ΔXZY?
A. T<1, 3> ◦ r(270°, O)
B. Rx = 0 ◦ T<0, 2>
C. T<6, 2> ◦ Rx = −2
D. Ry = −2 ◦ T<6, 0>
Answer:
reflection across x=1, translation up 2
units
Step-by-step explanation:
The order of vertices PQR is
clockwise, and the order of XZY
is counterclockwise. This means a
reflection is involved. The longest and
shortest sides are at the left and bottom
of APQR, and at the right and bottom
of AXZY, indicating the reflection is
left-right, not up-down.
Line x=1 contains the midpoints of
segments PX, QZ, and RY, so that is a
suitable line of reflection. Once APQR
is reflected over that line, it needs to be
translated upward 2 units to coincide
with AXZY.
The motions are ...
.
reflection over x=1
translation up 2
.
The motions could also be ...
reflection over y, translation right 2 and
up 2.
ANSWER
The composition of rigid motions maps ΔPQR to ΔXZY is T<6, 2> ◦ Rx = −2. The correct option is C.
What are rigid motion maps?In rigid motion, the position or orientation of the entire set changes without affecting the separation between the line segments. A triangle, for instance, can turn or slide but not extend or squeeze.
PQR's vertices are in clockwise and XZY's are in a counterclockwise sequence. This indicates that a reflection is necessary. The reflection is left-right, not up-down, as evidenced by the longest and shortest sides being on the left and bottom of A PQR, and on the right and bottom of AXZY, respectively.
The midpoints of the segments PX, QZ, and RY are on line x=1, making it a viable line of reflection. To match with AXZY, APQR must be translated upward 2 units after crossing that line.
Therefore, the correct option is C. T<6, 2> ◦ Rx = −2.
To learn more about rigid motion maps, refer to the link:
https://brainly.com/question/23415649
#SPJ5
The question is incomplete. Your most probably complete question is given below:
The image is added.
Explain ONE way in which European practices affected the environment in the Americas in the period c. 1450-c. 1750.
A way through which European practices affected the environment in the Americas during this period was that colonization ruptured the ecosystem.
It should be noted that during this period, colonization ruptured the ecosystem. It brought in new organisms while others were eliminated.
Also, the Europeans brought many diseases with them. This decimated the population of the Native Americans. Therefore, new plants were planted by the Native Americans as medicines.
Learn more about the Europeans on:
https://brainly.com/question/24877599
A 0.2 kg baseball with a speed of 48 m/s is struck by a bat. The ball rebounds and travels in the opposite direction at 52 m/s. The ball was in contact with the bat for only 2 ms. Find the magnitude of the force of the bat on the ball.
The magnitude of the force of the bat on the ball is 10000 N
From the question given above, the following data were obtained:
Mass (m) = 0.2 KgInitial velocity (u) = 48 m/sFinal velocity (v) = 52 m/sTime (t) = 2 ms = 2×10¯³ sForce (F) =?The magnitude of the force can be obtained as follow:
F = m(v + u) / t
F = 0.2 (52 + 48) / 2×10¯³
F = (0.2 × 100) / 2×10¯³
F = 20 / 2×10¯³
F = 10000 N
Thus, the magnitude of the force is 10000 N
Learn more about change in momentum:
https://brainly.com/question/21124361
How many years is it in college for both botany, cooking, and mechanic's together?
Answer:
It can take anywhere from 6 years to 10 years. Depends on the university.
In most unis:
Botany - 4 years
Culinary school - 4 years
Mechanical trade - 2 years
Hope that helps
what centrifugal force lead to the Rwandan civil war
Answer:
The Hutus and Tutsis. Also known as the Rwandian Genocide
Explanation:
For Mendel’s studies, why was it important that his subjects, pea plants, could reproduce quickly and produce many offspring?
Substance abuse does all of the
following, with the exception of
which?
A. alters perception
B. diminishes self-esteem
C. causes physical harm
D. extreme withdraw symptoms
Answer:
D
Explanation:
how would most Spanish speaker ask the school principal for his or her office telephone number
Answer:
Disculpe director, ¿podria darme el número de teléfono de su oficina?
Explanation:
Tu créeme
A particle moves along a curve with position function s(t) = t/2 - cos(t) for [tex]0\leq t\leq 2\pi . Find the max velocity of the particle and the time it reaches this velocity.
Answer:
t/2 = 5/5 squared
Explanation:
So basically you find out all the functions, add it up and then you will have the max velocity of the particle. To find out the time you find the mean.
Before you begin, access the accompanying document in PDF or word-processing format. For practice purposes, set a timer when you are ready to begin. You will have 55 minutes to complete the synthesis essay.
Often used to define the culture, philosophy, society, and politics of the country, education has long been considered a cornerstone of the United States. Despite this, great disagreement exists about what that education should entail and accomplish.
Carefully read the following seven sources, including the introductory information for each source. Then, synthesize information from three of the sources in a coherent, well-developed essay that develops your position on a primary purpose of education today.
Answer:
It won't let me comment but did you ever figure this out? I am on the same assignment and struggling.
Explanation:
The student takes an example of XCl2, the chloride salt of metal X, and mixes it with 100.0 mL of distilled water to form a saturated solution. The value of K_sp for XCL2 is 4.0 x 10^-12 at 298 K.
Write the balanced equation for the change that occurs when solid XCL2 dissolves in water.
The balanced equation is written as follows; XCl2 ⇄ X^+(aq) + 2Cl^-(aq).
The solubility product is an equilibrium constant that describes the solubility of a substance in water. The higher the value of the equilibrium constant, the more soluble the substance is in water.
For the salt XCl2, its solubility in water is shown by the balanced equation written as follows; XCl2 ⇄ X^+(aq) + 2Cl^-(aq).
Learn more about solubility product:https://brainly.com/question/857770
Jemma purchased six scratch-off lottery tickets and won $25 on the fifth ticket. Which kind of reinforcement schedule does this exemplify? Continuous reinforcement Fixed-ratio reinforcement Variable-ratio reinforcement Fixed-interval reinforcement Variable-interval reinforcement
Answer:
Variable-ratio reinforcement
Explanation:
The kind of reinforcement schedule this exemplifies is variable-ratio reinforcement. The correct option is c.
What is variable-ratio reinforcement?A variable ratio schedule is a reinforcement schedule in which a behavior is reinforced after a random number of responses. This type of schedule produces high, consistent response rates. It is a sort of partial reinforcement in which only a subset of responses are reinforced and no definite pattern exists.
Organisms persevere in reacting in the belief that the next reaction will be the one required to earn reinforcement. A variable-ratio schedule is a partial reinforcement schedule in operant conditioning, in which a response is reinforced after an unknown number of responses.
Therefore, the correct option is c, Variable-ratio reinforcement.
To learn more about variable-ratio reinforcement, refer to the link:
https://brainly.com/question/15702305
#SPJ2
Explain ONE historical situation in the period 1450-1750, other than the one illustrated in the passage, in which states experienced environmental impact.
During the period 1450-1750, are the environmental impact on the soil erosion are the transfer of the diseases.
What is environmental?
The term "environmental" refers to the surrounds on Earth. The environment is made up of both living and non-living entities. The influence of the environment on human life Plants, fisheries, animals, woods, and microorganisms are examples of biotic factors in the environment. Water, land, rocks, air, and other abiotic components are examples.
The movement of cattle and animals from one region to another, notably from the eastern to western hemispheres, had a significant environmental impact in the Americas. The animals brought west overgrazed, causing land degradation and disease transmission.
As a result, during the period 1450-1750, are the environmental impact on the soil erosion are the transfer of the diseases.
Learn more about on environmental, here:
https://brainly.com/question/21976584
#SPJ2
John notices Jimmy taking $5 from the cash register at the end of the night. Jimmy says that the company owes him for making him work three Friday nights in a row. Jimmy also asks John not to tell anyone. John’s ethical duty is to ______. a. Stay loyal to Jimmy and not turn him in b. Forget the incident because it doesn’t involve him c. Ask Jimmy for half the money not to tell d. Turn Jimmy in despite his protests Please select the best answer from the choices provided A B C D
Answer:
Explanation:
super subjective, but i assume they want D
John’s ethical duty is to turn Jimmy in despite his protests, hence option D is correct.
What is work Ethics?Work Ethics are a set of standards, values, and moral with which employees executes their duties e,g Integrity.
In this case, if John does not turn Jimmy in, he will be an accomplice which is unethical also.
Learn more about work Ethics here:
https://brainly.com/question/12156293
#SPJ2
I NEED THIS PLEASE 4x4