Suppose that y)2-4 +4. Then on any interval where the inverse function y= f-1(d exists, the derivative of y. f-1(x) with respect tox is:
Answers
Let's consider the function `f(x) = x^2-4`. Now, `y = f(x) + 4`.The inverse function of `f(x)` is `f^-1(x) = sqrt(x+4)` where `x>=-4`.Note that if we want to find the derivative of `f^-1(x)` with respect to `x`, we need to use the inverse function rule, which is given by `d/dx[f^-1(x)] = 1/f'(f^-1(x))`.Then, `f'(x) = 2x` and `f'(f^-1(x)) = 2f^-1(x)`.
Therefore, the derivative of `f^-1(x)` with respect to `x` is `d/dx[f^-1(x)] = 1/2f^-1(x)`.But we need to find the derivative of `y=f^-1(x)+4` with respect to `x`, so we use the chain rule, which gives `dy/dx = d/dx[f^-1(x)+4] = d/dx[f^-1(x)] = 1/2f^-1(x)`.So, on any interval where the inverse function `y = f^-1(x)` exists, the derivative of `y = f^-1(x) + 4` with respect to `x` is `1/2sqrt(x+4)`.Hence, the answer is "On any interval where the inverse function `y=f^-1(x)` exists, the derivative of `y=f^-1(x) + 4` with respect to `x` is `1/2sqrt(x+4)`.
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Related Questions
What is the word form for 43.22
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who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?
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René Descartes was the person who created analytic geometry and the Cartesian coordinate system
Find the magnitude of →/u.
→/u = (-4,-5).
Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth
Answers
The magnitude of a vector can be calculated using the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of its components. In this case, the vector →/u is given as (-4, -5), representing the x and y components respectively. By applying the Pythagorean theorem, we can determine the magnitude of →/u.
The magnitude (|→/u|) of a vector →/u = (x, y) can be calculated using the formula:
|→/u| = sqrt(x^2 + y^2)
In this case, →/u is given as (-4, -5), so the magnitude is:
|→/u| = sqrt((-4)^2 + (-5)^2)
Simplifying the equation:
|→/u| = sqrt(16 + 25)
|→/u| = sqrt(41)
Calculating the square root of 41, we find that the magnitude of →/u is approximately 6.40 rounded to the nearest hundredth. Therefore, |→/u| ≈ 6.40.
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consider data below 62 78 84 62 72 78 54 60 78 80, the mode is?
Answers
Answer:
The mode is 78, which appears the most times (3).
The mode of the given data 62, 78, 84, 62, 72, 78, 54, 60, 78, 80 is 78.
The mode is the data that occurs most frequently, in the data set listed below 62, 78, 84, 62, 72, 78, 54, 60, 78, 80. We can see that the number 78 appears three times, which is more than any other value in the set when we look at the data.
Note: If multiple values occur with the same highest frequency, but in this case, 78 is the only mode, the data set may have multiple modes.
Thus, the mode of 62, 78, 84, 62, 72, 78, 54, 60, 78, and 80 data set is 78.
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the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,641 miles, with a variance of 14,561,860 . what is the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct? round your answer to four decimal places.
Answers
The probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
We can use the central limit theorem to approximate the distribution of the sample mean. According to the central limit theorem, if the sample size is sufficiently large, the distribution of the sample mean will be approximately normal with a mean of 30,641 and a standard deviation of sqrt(variance/sample size).
So, we have:
mean = 30,641
variance = 14,561,860
sample size = 242
standard deviation = sqrt(variance/sample size) = sqrt(14,561,860/242) = 635.14
Now, we need to calculate the z-score corresponding to a sample mean of 31,358 miles:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
= (31,358 - 30,641) / (635.14 / sqrt(242))
= 2.43
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 2.43. The probability is approximately 0.9925.
Therefore, the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).
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what expressions are equivalent to 4×3/10
Answers
Answer:
Hop. Answer ur question the answer is 13
Step-by-step explanation:
yeah hope i helped
12/10
6/5
It’s simple by Dividing
2. Ana hace recuerdos para bodas con velas en forma de pirámide cua- drangular decoradas con semillas. a) Si un lado de la base mide 7 cm y la altura de la pirámide es de 15 cm, ¿qué volumen de cera ocupará para hacer 40 velas?
Answers
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
How do you calculate a quadrangular pyramid's volume?The volume of a pyramid with a square base can be calculated using the formula V=13s2h, where s is the length of the base's sides. A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume = (1/3) base area height, where height is the height from the base to the apex, is the basic formula for a pyramid's volume.
Given,
side = 7cm
height = 15cm
Volume = 1/3 × h × 5/2 × s
⇒ volume = 15×7 ×5/6
⇒ volume = 87.5 cm³
It will take 87.5 cm³ × 40 = 3500 cm³ volume of wax will it take to make 40 candles
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Complete Question -
Ana makes wedding favors with candles in the shape of a quadrangular pyramid decorated with seeds. a) If one side of the base measures 7 cm and the height of the pyramid is 15 cm, what volume of wax will it take to make 40 candles?
If 10^ 5, what is x?
Answers
Answer:
100,000
Step-by-step explanation:
Five employees are available to perform four jobs. The lime it takes each person to perform each job is given in Table 50. Determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs.
TABLE 50
Person
Time (hours)
Job 1
Job 2
Job 3
Job 4
1
22
18
30
18
2
18
—
27
22
3
26
20
28
28
4
16
22
—
14
5
21
—
25
28
Answers
To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.
By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.
Therefore, the optimal assignment would be:
- Person 4 for Job 1 (16 hours)
- Person 2 for Job 2 (18 hours)
- Person 1 for Job 3 (25 hours)
- Person 4 for Job 4 (14 hours)
This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.
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Eloise is creating a game for her Strategic Games option.
Her square game board will have 64 squares on the inside and a decorative border around the outside edge.
What is the length of the border?
What assumptions can you make?
Answers
64 square would suggest that sides of square are 8 “units”.
A=a^2
64=8•8
If decorative border is all around square (1 “unit”) that would make a length of a border: 8•2+10•2=16+20+36.
Good luck.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+248x+116
Answers
Answer:
Step-by-step explanation:
The rocket will hit the ground when y = 0. If you use the quadratic equation:
x = (-248±√(2482-4(-16)(116))/(2(-16))
The measures of the angles of a triangle are shown in the figure below. Solve for x. 4
Answers
A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. what is the probability that?
Answers
The probability of any one person visiting a particular station is 1/3. Since there are three people in the family, the probability that they would all visit the same station is 1/3 x 1/3 x 1/3, which is equal to 1/27.
The probability that all three members of the family visit the same station at the medical clinic is 1/27 (1/3 x 1/3 x 1/3). This is because each person has an equal chance of being assigned to any of the three stations and since there are three people in the family, the probability that they would all visit the same station is 1/3 multiplied by itself three times, which is equal to 1/27. The experiment is recording the station number for each member and since the incoming individuals are assigned to any of the three stations randomly, the probability that all three members visit the same station is 1/27.
The complete question is :
A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that all three members visit the same station?
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What is the y intercept?
Answers
Answer:
-5
Step-by-step explanation:
Again. I need help with this
Answers
Answer:
Option B.
Step-by-step explanation:
Scale factor of the image = \(\frac{\text{One side of the triangle FED}}{\text{Corresponding side of the triangleABC}}\)
= \(\frac{\text{DF}}{\text{AC}}\)
= \(\frac{3}{6}\)
= \(\frac{1}{2}\)
Coordinates of point C → (-2, 2)
Coordinates of the corresponding point C' after dilation with a scale factor \(\frac{1}{2}\),
C(-2, 2) → C'(-1, 1)
Coordinates of point C' after reflection across y-axis,
C'(-1, 1) → C"(1, 1)
Followed by the translation of 2 units downwards,
C"(1, 1) → D[1, (1 - 2)]
→ D(1, -1)
From the graph we get the same coordinates of point D as (1, -1).
Therefore, ΔABC was dilated by a scale factor of \(\frac{1}{2}\), reflected across the y-axis and moved through the translation of 2 units downwards.
a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
Answers
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
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all three angles of a triangl add up to 180 degrees. the three angles measuure 75 degrees, 10x degrees, and 5x degrees. write and solve an equation for x. then find the measure of the two unknown angles.
Answers
Answer:
elaborate more.....
Step-by-step explanation:
znnznzhzhdhsnsn
What is half of a 3/4 cup?
Answers
Answer:0.375
Step-by-step explanation:
3/4=0.75
0.75/2=0.375
(3/4)/2=0.375
Question 4
At practice, Diego does twice as many push-ups as
Noah, and also 40 jumping jacks. He does 62 exercises
in total. The equation 2x+40=62 describes this situation.
What does the variable x represent?
The number of push-ups Diego does.
The number of push-ups Noah does.
The number of jumping jacks Diego does.
The number of jumping jacks Noah does.
Answers
Answer: The number of push-ups Noah does.
Step-by-step explanation:
Diego does twice as many push-ups as
Noah (2x) and also 40 jumping jacks (+40). He does 62 exercises (=62).
It's not the amount that Diego does because Diego's amount is twice of Noah's, or twice of x. X would have to equal the number of push-ups Noah does.
ms swanson asked question how does knowing the fact 6 times 5 help us find 60 times 500 mario answerd i know 6 times 5 is 30 now all i have to do count zeros and i get 3000
Answers
Answer: See explanation
Step-by-step explanation:
Maria is incorrect as she didn't count the number of zeros properly. After knowing that 6 × 5 = 30, the question is 60×500 which means there are 3 zeros that should be added to the 30 that she got, this will have given her a value of 30,000 which is correct. She write 3000 which is 3 under thousands rather than 30,000 which is 3 under tens of thousands.
Graph the system of inequalities. Which two quadrants does the solution lie in?
Answers
Answer:
Step-by-step explanation:
y 2x=3 i really dont know
Answer:
2 and 3
Step-by-step explanation:
It lies in quadrant 2 and 3
hope the visuals help :D
Which statement correctly compares the water bills for the two neighborhoods?
Overall, water bills on Pine Road are less than those on Front Street.
Overall, water bills on Pine Road are higher than those on Front Street.
The range of water bills on Pine Road is lower than the range of water bills on Front Street.
The range of water bills on Pine Road is higher than the range of water bills on Front Street.
Answers
The statement that correctly compares the water bills for the two neighborhood is D. The range of water bills on Pine Road is higher than the range of water bills on Front Street.
How to explain the informationThe minimum water bill on Pine Road is $100, while the maximum is $250.
The minimum water bill on Front Street is $100, while the maximum is $225.
Therefore, the range of water bills on Pine Road (250 - 100 = 150) is higher than the range of water bills on Front Street (225 - 100 = 125).
The other statements are not correct. The overall water bills on Pine Road and Front Street are about the same. There are more homes on Front Street with water bills above $225, but there are also more homes on Pine Road with water bills below $150.
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Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 residents from two different neighborhoods are displayed in the histograms. 2 histograms. A histogram titled Pine Road Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. A histogram titled Front Street Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 5; 125 to 150, 7; 150 to 175, 8; 175 to 200, 5; 200 to 225, 8; 225 to 250, 7. Which statement correctly compares the water bills for the two neighborhoods? Overall, water bills on Pine Road are less than those on Front Street. Overall, water bills on Pine Road are higher than those on Front Street. The range of water bills on Pine Road is lower than the range of water bills on Front Street. The range of water bills on Pine Road is higher than the range of water bills on Front Street.
Which fraction is equivalent to 2/3 a 4/9 b18/21. C6/8 d 16/24
Answers
Answer:
your answer is D. 16/24
Step-by-step explanation:
mark brainliest if you could please! good luck!
Answer:
D. 16/24
Step-by-step explanation:
the 2 and 3 need to be multiplied by the same number for it to be equivalent.
16/2 = 8
24/3 = 8
So 16/24 is equivalent to 2/3.
Given
mZAOC is a straight angle.
mZBOC = 6x + 29°
mZAOB = 3x + 124°
Find mZBOC:
O
с
A
Answers
Answer:
47°
Step-by-step explanation:
Given that m<BOC = 6x + 29, m<AOB = 3x + 124, and m<AOC is a straight angle, therefore, m<AOC = 180°.
m<BOC +m<AOB = 180°
6x + 29 + 3x + 124 = 180
Solve for x
6x + 3x + 29 + 124 = 180
9x + 153 = 180
Subtract both sides by 153
9x = 180 - 153
9x = 27
Divide both sides by 9
x = 3
m<BOC = 6x + 29
Plug in the value of x
m<BOC = 6(3) + 29
m<BOC = 18 + 29 = 47°
PLEASE HELP!!!!
i need help on all of these but if you only have 1 answer that’s still great
Answers
Answer:
n = -6
x = -7
n = 27
Step-by-step explanation:
Question 1
-3n - n + 12 = 36
First we get all the variables to one side using subtraction property of equality.
-3n - n + 12 (-12) = 36 (-12)
-4n = 24
divide by the coefficient of n to isolate the variable
-4n/-4 = 24/-4
n = -6
Question 2
-2x - 3x - 15 = 20
-5x - 15 = 20
-5x = 35
x = -7
Question 3
3 + n/9 = 6
Isolate the n variable
n/9 = 6 - 3
multiply by 9
n = 27
Answer:
1. n = -6
2. x = -7
3. n = 27
√2, √3, √4 are _______ numbers.
Answers
Answer:
Step-by-step explanation:
√2, √3 are irrational numbers.
√4 = 2 is not irrational.
Write a ratio and a percent for the shaded area.
6/100 - 60%
6/10 - 60%
12/20 - 60%
36/100 - 36%
Answers
What is the value of X?
Answers
Answer:
16
Step-by-step explanation:
AB = BC
32\(\sqrt{2}\) = \(\sqrt{2 *AB^{2} } \\ => AB = 32 = BC\\x= BC/2 => x = 32/ 2 = 16\)
How do you turn -2x+10y=2 into slope intercept form?How do you turn 5x-25y=3 into slope intercept form?
Answers
EXPLANATION
In order to turn -2x + 10y = 2 into slope-intercept form:
First, as we know, the generic slope-intercept form is:
y= mx + b
where m is the slope and b is the y-intercept
Going back to our equation:
-2x + 10y = 2
Adding +2x to both sides:
-2x + 2x + 10y = 2 + 2x
Adding similar terms:
10y = 2 + 2x
Dividing both sides by 10:
10y/10 = 2/10 + 2x/10
Simplifying:
y = 1/5 + x/5 --> Slope-intercept form
T/F: if two angles are vertical angles, then they are congruent (have equal measures).
Answers
Answer:
True
Right angles measure 90° . So each vertical angle = 90° and hence they are equal
Step-by-step explanation: