The solution to the given composite functions are;
f(g(x)) = √(x² + 1) + 8
g(f(x)) = [√(x) + 8]² + 1
How to solve composite functions?
Composite functions are usually formed when one function is used as the input of another function.
We are given the functions;
f(x) = √(x) + 8
g(x) = x² + 1
1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;
f(g(x)) = √(x² + 1) + 8
2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1
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If A flips n+1 and B flips n fair coins, show that theprobability that A gets more heads than B is ½.
.
(Hint: Condition on which player has more heads after each hasflipped n coins.)
If n is zero, Player A has one coin and Player B has none. B will always have 0 heads. There is a 50% chance that Player A has one head, and a 50% probability that Player A also has one head.
If they had the same number of coins, they would most likely obtain the same number of heads, and each person has an equal chance of getting more heads than the other player (the chance is less than 1/2).
If we give player A one more coin than player B, player A has a 50% probability of winning (if that extra coin comes out heads) which is the sample space.
There is a 50% probability that the coin will not provide an advantage (it come out tails). As a result, player A has a 50% probability of getting more heads than player B which is the required outcome.
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.
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*the data set `normtemp` (**usingr**) contains measurements of 130 healthy, randomly selected individuals. the variable `temperature` contains normal body temperature. does the data appear to come from a normal distribution? if so, perform a $t$-test to see if the commonly assumed value of 98.6 degrees fahrenheit is correct. (studies have suggested that 98.2 degrees fahrenheit is more accurate.)*
A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.
library(UsingR)
attach(normtemp)
print(normtemp)
hist(normtemp$temperature)
shapiro.test(normtemp$temperature)
qqnorm(normtemp$temperature)
qqline(normtemp$temperature)
We can observe that the data follows a normal distribution from the histogram and q plot.
The points in the q plot fall on a straight line and correspond to a normal distribution.
P-value = 0.2332, P>0.05, from the Shapiro test
hence, we fail to reject null htpothesis.
On accepting the null hypothesis we get to know that the data follows normal distribution.
The output for the given code will be ,
data: normtemp$temperature
t = 1527.9, df = 129, p-value < 2.2e-16
alternative hypothesis: true mean ≠0
90 percent confidence interval:
98.14269 98.35577
sample estimates:
mean of x
98.24923
Therefore , we can conclude that ,
The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.
98.6 is not included in the 90% confidence interval.
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Rosemary works two part-time jobs while attending college. During the day she works at the college bookstore and earns $8.25 per hour. In the evening she delivers pizza for Papa Gino's, earning $9.25 per hour. If Rosemary earned $247 last week from working a total of 28 hours, find how many hours she worked at Papa Gino's last week.
Answer: 16 hours
Step-by-step explanation:
We will write a system of equations to help us solve. Let x be equal to the number of hours worked at the college bookstore, and y be equal to the number of hours worked at Papa Gino's.
First, we will write an equation for the money earned. Then, we will write one for the hours worked.
8.25x + 9.25y = 247
x + y = 28
Now, we will will substitute the second equation into the first and solve for the hours worked at Papa Gino's last week, equal to y.
x + y = 28 ➜ x = -y + 28
8.25x + 9.25y = 247
8.25(-y + 28) + 9.25y = 247
-8.25y + 231 + 9.25y = 247
y + 231 = 247
y = 16
Rosemary worked 16 hours at Papa Gino's last week.
A ball rolls down a hill. It starts with velocity of 2 m/s After 2 seconds, the ball has a velocity of 12 m/s What is the acceleration of the ball?
The acceleration of the ball is 5 ms2.
What is acceleration?
Acceleration is the rate at which an object's velocity with respect to time changes. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration.
The acceleration of the car in its present direction of motion is referred to as a linear acceleration (or tangential acceleration in circular motions), and the passengers on board feel a force pressing them back into their seats as a result.
The acceleration that is used to change direction is referred to as radial acceleration (or centripetal acceleration in circular travels), and the reaction that the passengers feel is a centrifugal force.
Therefore, The acceleration of the ball is 5 ms2.
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Throughout your life, you will need to adapt your budget to respond to changes in your income and expenses. Now, it is time to practice making changes to a budget.
4. Change your previous budget to reflect these new factors. (10 points)
• Your school announced that you will not have to pay for a bus pass to get to classes, because a new school program will cover this expense for all students.
• You just found out that your books will cost more than you had expected. You will now need to spend an additional $100 on books in October.
• You got an unexpected raise at work; you will now be making $650 each month.
• Make sure that you are still meeting your overall goal of saving $100 by the end of October.
To change your budget to reflect these new factors, we need to update the budget to reflect the changes in income and expenses. Here is an updated version of the budget, showing the changes:
Income:
• Salary: $650 (increased by $100 due to unexpected raise)
Expenses:
• Rent: $400 (unchanged)
• Food: $200 (unchanged)
• Entertainment: $100 (unchanged)
• Books: $100 (increased by $100 due to unexpected cost)
• Bus pass: $0 (no longer needed due to school program)
Total expenses: $700 (unchanged)
Savings:
• Savings goal: $100 (unchanged)
Total income: $650
Total expenses: $700
Total savings: -$50 (decreased by $50 due to increase in expenses)
As you can see, even with the unexpected raise in income, the overall goal of saving $100 by the end of October is not being met. To reach this goal, you will need to find ways to reduce your expenses or increase your income. Some possible options for doing this might include cutting back on entertainment expenses, finding a cheaper source of books, or looking for additional ways to earn money, such as taking on a part-time job or freelance work. By making these changes to your budget, you can ensure that you are able to meet your savings goal and manage your finances effectively.
On the coordinate plane, point K is located at (3, -2) and point L is located at (x, 6). The
distance between points K and L is 10 units.
Graph one possible point L on the coordinate plane.
All of the points along the y-axis are located in the region of the coordinate plane that is equally distant from the coordinates a(-3 2) and b(3, 2).
Find the coordinate plane by what method?The x-axis, a horizontal number line, and the y-axis, a vertical number line, cross to create a coordinate plane. The coordinate plane's origin is where the two axes—plural for "axes"—vertically intersect.
What is an illustration of a coordinate plane?Each point on a coordinate plane will have an x coordinate and a y coordinate, which are stated as (x, y). For instance, the coordinate (3,2) has a y-coordinate of 2, an x-coordinate of 3, and a coordinate in between.
Here,
Given: K(3, -2) and (x, 6).
Thus ,distance between points K and L is 10 units.
Thus,
=> 10 = [tex]\sqrt{(3-x)^{2}-(-2-6)^{2} }[/tex]
=> 10 = [tex]\sqrt{9+x^{2} -6x+64\\[/tex]
=> 100 = 73 +[tex]x^{2}[/tex] -6x
=> 27 =[tex]x^{2}[/tex] -6x
=>[tex]x^{2}[/tex]-6x-27=0
=>x(x-9)+3(x-9)
=>x=-3 , x=9
Thus, x comes out to be x =-3.
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In an analysis of variance, differences caused by treatment effects contribute to which of the following variances? both between treatments variance and within-treatments variance between treatments variance but not within treatments variance within-treatments variance but not between treatments variance neither between treatments variance nor within-treatments variance
The analysis of variance compares the differences between treatments to determine the variance attributed to treatment effects, not the variance within treatments.
An analysis of variance (ANOVA) is a statistical technique used to compare the means of two or more groups. This technique is used to determine the variance attributed to differences between treatments. The variance between treatments is the variance between the group means of the different treatments, while the variance within treatments is the variability of the data within each treatment group. In an ANOVA, only the variance between treatments is considered to be caused by the treatment effect. This is because the within-treatment variance is assumed to be caused by random sampling error, which is independent of the treatment. Thus, in an ANOVA, only the between treatments variance is attributed to treatment effects, while the within-treatment variance is not. This allows the analyst to better understand and explain the differences between treatments.
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13. A contractor is building a new subdivision. A rectangular piece of land for a new
house and yard is 60 feet wide. The length of the land is longer than the width by a
distance of n feet. Which equation represents the area of the land?
Answer:
Area = (60 + n) * 60 = 3600 + 60n
Step-by-step explanation:
The length of the land is 60 + n feet. The area of the land is the product of the length and width, so the equation representing the area of the land is:
Area = (60 + n) * 60 = 3600 + 60n
This equation represents the area of the land in square feet.
A study tested the effects of sleep deprivation and alcohol consumption on reaction time. Which of the following would be considered responsible for the interaction effect of this study? a. reaction time b. how sleep deprivation and alcohol consumption react together on the participant's reaction time
c. the results for only alcohol consumption d. the results for only sleep deprivation
Alcohol consumption is responsible for the interaction effects of this study as alcohol consume is independent variable and sleep deprivation is dependent on it.
what is interaction effect?An interaction effects express the activity of a variable on the results of a particular research survey. Research study is conducted based on some elements. The elements can be dependent or independent. whenever the activities of independent elements react on large scale over the dependent elements' interaction effects are occurred.
What is reaction time?Reaction time means the time required to achieve an expected results from a particular experiment as well as research study.
Let the above study was conducted by researcher to assess the bad result of alcohol consumption on human body. The study had two major components, one is the level of alcohol consumption and the other is how it effects on sleep. Sleep deprivation is increased or decreased depends on the level of alcohol taken by someone. The effects of alcohol on human body cannot be appeared just after it is taken. It has particular reaction time for achieving expected outcome. The reaction time is not similar for each human body. The study also revealed variances of interaction effects on different body.
hence, there is intimate relationship between sleep deprivation and alcohol consumption.
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Alcohol consumption is responsible for the interaction effects of this study as alcohol consumption is the independent variable and sleep deprivation is dependent on it.
What is reaction time?
Reaction time means the time required to achieve expected results from a particular experiment as well as a research study.
Let the above study was conducted by researchers to assess the bad result of alcohol consumption on the human body. The study had two major components, one is the level of alcohol consumption and the other is how it affects sleep. Sleep deprivation is increased or decreased depending on the level of alcohol taken by someone. The effects of alcohol on the human body cannot appear just after it is taken. It has a particular reaction time for achieving the expected outcome. The reaction time is not similar for each human body. The study also revealed variances of interaction effects on different bodies.
hence, there is an intimate relationship between sleep deprivation and alcohol consumption.
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Please use the Standard Normal Table (link on the first page of the quiz) to find the following probabilities.
1. P(Z < -0.42) =
2. P(z > -1.25) =
3. P(z ≥ 2.13) =
4. P(z≤ 1.94) =
5. P(-0.38 < z < 1.48) =
Using the Standard Normal Table, probabilities are:
1) P(Z < 0.42) = 0.3372
2) P( Z > -1.25) = 0.89443
3) P( Z ≥ 2.13) = 0.1667
Define standard normal table.A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table. It is also known as the unit normal table or the Z table. The standard normal distribution table is a collection of regions from the standard normal distribution, also referred to as a bell curve, and it shows the size of the region beneath the bell curve and to the left of a particular z-score to illustrate probabilities of occurrence in a specific population.
Given,
Using the Standard Normal Table,
Probabilities are:
1) P(Z < 0.42) = 0.3372
2) P( Z > -1.25) = 0.89443
3) P( Z ≥ 2.13) = 0.1667
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True or false
is every rectangle is a rhombus?
Every rectangle with four congruent sides is a square?
Every rhombus is a parallelogram?
Every quadrilateral is a rhombus?
Answer- false, true, true, and false
Step-by-step explanation:
No, rectangle is not always a rhombus because in rectangle two opposite sides are equal in length, and all the angles in rectangle is right angled but it is not necessary in rhombus.
All rectangles are squares. False! A square has ALL sides equal, but a rectangle only has opposite sides equal. All trapezoids have only one pair of parallel sides.
A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.
If you have a quadrilateral with two pairs of parallel sides, you do not necessarily have a rhombus;
Propose a molecular formula that fits the following data: (a) A hydrocarbon \left(C_{x} H_{y}\right)(CxHy) with a molecular ion peak at m/z = 66. (b) A compound that absorbs IR radiation at 1720 \mathrm{cm}^{-1}1720cm −1 and exhibits a molecular ion peak at m/z = 70.
C₁₂H₁₂BrO₁N₁ is the molecular formula that fits the following data A hydrocarbon \left(C_{x} H_{y}\right)(CxHy) with a molecular ion peak at m/z = 66.
An analytical technique used to measure the mass to charge ratio of the ions is known as mass spectrometry. This is one of the best technique used to analyse the structure of a molecule. It is used in a a lot of applications such as carbon dating, food contamination detection, isotope detection, protein identification etc.
We have given that,
molecular ion at 265 m/z
another ion seen at 267 m/z
their ratio is 1:1
C₁₃H₉Cl₂ON₁ in this in here Cl have two isotopes that are
36 and 37 but m/z is not equal to 265
in here C₁₂H₁₂BrO₁N₁ Br have two isotopes
Br-79, Br-81 and m/z equals to 256 and 257
so the molecular formula is therefore C₁₂H₁₂BrO₁N₁
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PLEASE ANS ASAP
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOKKKKKKKKKKKKKKKKKKKKKKKK
100 POINTS
BRAINLIEST IF POSSIBLE
a) The minimum number of hikers that could have walked between 6 miles and 17 miles is of: 9.
b) The maximum number of hikers that could have walked between 6 miles and 17 miles is of: 19.
How to obtain the amounts?The amounts are obtained by the frequency table given in the image, which shows the number of times that each range was observed.
The minimum number in the desired range will be obtained when:
The 2 hikers in the interval 5 < x < 10 walk less than 6 miles.The 8 hikers in the interval 15 < 20 < 20 walk more than 17 miles.Hence the minimum number is of 9, which is the number of people in the range 10-15.
The maximum number in the desired range will be obtained when:
The 2 hikers in the interval 5 < x < 10 walk more than 6 miles.The 8 hikers in the interval 15 < 20 < 20 walk less than 17 miles.Then the maximum number is calculate as follows:
2 + 9 + 8 = 19 hikers.
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V=150cm3 when B=25cm2 and h=18cm.
Identify hwhen V=48cm3 and B=24cm2.
The height of the similar solid is equal to 3 / 2 centimeters.
How to determine the dimension of similar solid by direct and inverse variation
In this problem we find the case of two similar solids. Dimensionally speaking, the volume is equally to the following equivalence:
[V] = [A] × [L]
Where:
[L] - Length variable, in centimeters.[A] - Area variable, in square centimeters. [V] - Volume variable, in cubic centimeters.The volume is directly proportional to the area (B), in square centimeters, and the height of the solid (h), in centimeters:
V ∝ B · h
V = k · B · h
Where k is the proportionality constant, no unit.
We can eliminate this constant by using the following relationship:
V' / (B' · h') = V / (B · h)
If we know that V' = 150 cm³, B' = 25 cm², h = 18 cm, V = 48 cm³ and B = 24 cm², then the height of the solid is:
(150 cm³) / [(25 cm²) · (18 cm)] = (48 cm³) / [(24 cm²) · h]
1 / 3 = 1 / (2 · h)
2 / 3 = 1 / h
h = 3 / 2 cm
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select each of the equations that represent a line segment between the points (1,5) and (3,13). a. x
On solving the provided question the equation of line segment is [tex]3y = x+11 OR y = 1/3x + 11/3[/tex]
What is equation?An equation in algebra is a condition on a variable. Only for a certain value of the variable does it satisfy. This indicates that the equation 2x - 5 = 13 can only be met when x = 9. Polynomial equations and linear equations are two significant kinds of equations that are taken into account in algebra. One-variable polynomial equations can be expressed as P(x) = 0, where P is a polynomial and ax + b = 0 is the standard form for linear equations. Here, the variables a and b are used.
Let y=m x + c be the slope intercept form of the equation.
Here, the slope m and the y-intercept c are unknown.
What is known is that this goes through (x 1, y 1) and (x 2, y 2), two coordinate pairs.
Consequently, we have three equations.
[tex]y=mx+c.........1\\ y1=mx1+c....2\\ y2=mx2+c ......3[/tex]
now let's delete m and c using these.
subtracting (2) from (1), we get [tex](y-y1)=m(x-x1) ......(4)[/tex]
and subtracting (2) from (3), we get[tex](y-2-y1)=m(x2-x1) ......(5)[/tex]
[tex]\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} \\\\\frac{y-3}{4-3} = \frac{x+2}{1+2} \\\\y-3 = \frac{x+2}{3}\\ 3y-9 = x+2\\3y = x+11\\OR\\y = 1/3x + 11/3[/tex]
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The quotient of 5 and a number, k ? Write the algebraic expression
Answer: [tex]\frac{5}{k}[/tex]
Step-by-step explanation:
To write an algebraic expression that represents this situation, we need to know that a quotient will involve division.
We will write the quotient of 5 and a number, k. also written as 5 divided by k, as;
[tex]\displaystyle \frac{5}{k}[/tex]
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The algebraic expression is - [tex]\frac{5}{k}[/tex]
If one number is divided by another number, the answer obtained is called the quotient.
In mathematics, a number that divides another number is called a divisor.
The number which is to be divided by the divisor is called a dividend.
In arithmetic, if we divide one integer by another, the 'leftover' portion is called the remainder.
In this case, 5 is the dividend, and k is the divisor, which is representing an unknown number.
We can not get an actual number, but we can use an algebraic equation to express the quotient as follows:
The quotient of 5 and k = [tex]\frac{5}{k}[/tex]
The algebraic expression is - [tex]\frac{5}{k}[/tex]
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The cost of a new home is $90,000 and the bank requires a 8.8% down payment.
What is the amount that will need to be borrowed from the bank after the down payment is paid?
The mortgage amount will be____.
To find the amount of the down payment, we need to multiply the cost of the home by the down payment percentage: $90,000 * 8.8% = $7,920.
This means that the total amount that will need to be borrowed from the bank is $90,000 - $7,920 = $82,080.
The mortgage amount will be $82,080. This is the amount that will need to be borrowed from the bank after the down payment of $7,920 is paid. The down payment is calculated by multiplying the cost of the home by the required down payment percentage: $90,000 * 8.8% = $7,920. The mortgage amount is then calculated by subtracting the down payment from the cost of the home: $90,000 - $7,920 = $82,080.
George buys 7 pairs of pants and uses a discount of $11 off. He spends $73 total. What is p, the cost of each pair of pants?
Answer:
$12 is the cost of each pair of pants
Step-by-step explanation:
First we need to know the price with no discount first: $11 + $73 = $84
The we take the real price of the pants to divide to the 7 pairs: $84 ÷ 7 = $12
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Solve for
x. Round to the nearest tenth, if necessary.
ø= 20°
Adj = 24
Hyp = x
Cos ø = Adj/Hyp
Hyp = Adj/ Cos ø
x = 24/ cos 20
x= 24/0.9397
x= 25.5 to the nearest tenth
Please help will mark brainly
Answer: >
i might be wrong tho
Step-by-step explanation:
x=(-12,0)
y=(0,6)
m=6/-12
m=-1/2
slope is positive
m=1/2
y=1/2x+6
shade is to the right
y>1/2x+6
When a logistic regression coefficient is negative, the exponentiated coefficient, i.e. the EXP(B), will always be less than one.
True or False
Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level. Positive coefficients show that the event is more likely to occur at the reference level than at that level of the predictor.
What is Positive coefficients?Positive coefficients indicate that the event is more likely to occur at that predictor level than it is at the reference level for the factor.
Positive coefficients indicate that the event has a higher probability of happening at the reference level than at the predictor level.
The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.
To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.
However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.
Hence, Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level.
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You are running a special for the holiday season during the morning rush
hours. You have sold a total of 40 doughnuts and coffee in the morning rush
hours. You charged $4 per doughnut and $6 per coffee and the total sales were
$180. Determine the total number of coffee (c) and doughnuts (d) sold.
Answer:
40 donuts
10 Coffees
Step-by-step explanation:
d+c=40
4d+6c=180
-4d-4c=-160
+4d +6c +180
2C=20
C=10
d+10=40
d=30
IF POSSSIBLE INSERT A DIGIT TO make 13_0 divisible by 6
YAnswer: Yes
Step-by-step explanation: 425 / 5.000
Resultados de traducción
Resultados de traducción
You only have to verify that it is divisible by 2 and by 3. Since it ends in zero (which is an even number) it is divisible by 2. Then it only remains for it to be divisible by 3 and for this the sum of its digits must be a multiple of 3. Therefore, if x is the missing number, we have that 1+3+x+0 must be a multiple of 3. It would suffice, for example, to take x =2 (there are more possibilities as you can see). So one possibility is the number 1320
Answer:
Possible digits are 2, 5 or 8-------------------------------------
Divisibility rule by 6:
It must be an even number and sum of digits must be multiple of 3.The number 13 x 0 is even number as ends with zero and the sum of its digits is:
1 + 3 + x + 0 = 4 + xThe x is between 0 and 9.
Possible values of x to make x + 4 a multiple of 3:
x = 2, then the number is 1320 ⇒ 1320/6 = 220x = 5, then the number is 1350 ⇒ 1350/6 = 225x = 8, then the number is 1380 ⇒ 1380/6 = 230
Write the ratio in fractional notation in lowest terms 9 nickels to 3 dollars?
Answer:
3:1
Step-by-step explanation:
divide by 3 both sides
I don’t understand number 2
Answer:
They're asking you to plug in the x values for x. for example the first x in the table is "-6" so you will replace the x in 1/3(-6)^2 and the Y answer would be 12.
1/3 x (-6)^2 which is 36.
1/3 x 36= 12.
and you'll basically do that for each value. I hope that helps.
In how may ways can the letters of the word 'SEMESTER' be arranged such that at least two vowels are together. Show ALL your work step by step to get credit. Final answers MUST be provided in decimal form
In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.
Arrangement in probability
A number of topics like statistics and probability are closely interrelated to the topic of permutation and combination. Permutation and combination is about making arrangements and making selections on the basic of certain formulas.Given that:
In SEMESTER there are 8 letters.
Which include 3 vowels (E) and 5 consonants (S, M, T , R )
Take 3 vowels as one letter, we have 6 letters
arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways
Number of words = 6! × 1!
= 6 × 5 × 4 × 3 × 2 × 1
= 720 ways
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the base area of the rectangular prism is 28 square meters. It the height of the prism is 14 meters what is the total volume of the prism,
Answer:
Step-by-step explanation:
28 x 14 equals 392 so the answer is 392
research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers. (meaning, they help students understand the value of fractions and how the size of these numbers relates to the whole numbers that students already know.)
The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.
What is meant by pedagogical tool?
In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.
Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.
While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.
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as we learned in class, an important component of non-linear least squares is the jacobian matrix, the set of partial derivatives with respect to parameters at each data point. in def calc jacobian(x,p), you will need to implement the calculation of the jacobian matrix for the function: where 'a' is the first parameter (p[0,0]), 'b' is the second (p[1,0]), an so on...
The set of partial derivatives with respect to parameters at each data point.
def calc_jacobian(x, p):
jacobian = np.zeros([len(x), len(p)])
for i in range(len(x)):
for j in range(len(p)):
jacobian[i][j] = (2 * p[j] * x[i]**j)
return jacobian
What is partial derivatives?Partial derivatives are a type of derivative in calculus that are used to measure the rate of change of a function with respect to a single independent variable, while holding the other variables constant. They are denoted with a symbol called a partial derivative operator, which is a curved d with a line over it. Partial derivatives are used to calculate derivatives in multivariable functions and to find the maximum or minimum points of a function. Partial derivatives can also be used to analyze the behavior of functions near a point, or to solve equations involving multiple variables.
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A particle moves on a circle of radius 9 cm, centered at the origin, in the xy-plane (x and y measured in centimeters). It starts at the point (0, 9) and moves counterclockwise, going once around the circle in 6 seconds. Write a parameterization for the particle's motion. x (t) = What is the particle's speed? Speed =
It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).Explanation:
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.
Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.
Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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