The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is
x sin⁻¹x + √(1 - x²) + C.
Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as
x sin⁻¹x + √(1 - x²) + C.
where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.
Integral of Sin Reverse proof by integration by parts :
The formula for integration by parts is ∫f(x)g(x)dx = f(x) ∫g(x)dx - ∫[d(f(x) ) /dx×∫g(x) dx] sin⁻¹x can be written as sin⁻¹x = sin⁻¹x.1.f(x) = sin⁻¹x, g(x) = 1
d(sin⁻¹x)/dx = 1/√(1 - x²)
Using these equations and facts,
∫sin⁻¹x dx = ∫sin⁻¹x.1 dx
= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx
= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx
= x sin⁻¹x - ∫x/√(1 - x²) dx
= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]
= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx
= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}
= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C
= x sin⁻¹x + (1 - x²)1/2 + C
= x sin⁻¹x + √(1 - x²) + C
Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.
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Can you tell me the
Measure of
Answer:
please tell us what you need help with
Step-by-step explanation:
you did not include a number
Answer: what
Step-by-step explanation:
i really need help plsss help me
The linear equation that represents the total cost of the gas will be y = 15.7x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The cost of two gallons of gas is $31.40. Then the rate (slope) is given as,
m = $31.40 / 2
m = $15.7 for each gallon
Let 'x' be the number of gallons of gas and 'y' be the total cost. Then the equation is given as,
y = 15.7x
The linear equation that represents the total cost of the gas will be y = 15.7x.
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Beth bought 16 tickets to a movie, where adult tickets cost $8.00 and senior citizen
tickets cost $5.00. She spent a total of $120. Create a system of equations to determine
the number of adult tickets and the number of senior citizen tickets that Beth
purchased?
A system of equations that determines the number of adult tickets and the number of senior citizen tickets that Beth purchased is x + y = 16
8x + 5y = 120.
What is a system of an equation?
A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one with two equations and two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
Here, we have
Given: Beth bought 16 tickets to a movie, where adult tickets cost $8.00 and senior citizen tickets cost $5.00. She spent a total of $120.
We let adult tickets be x and
let senior citizens' tickets be y.
x + y = 16....(1)
8x + 5y = 120...(2)
From equation(1)
x = 16 - y
we put the value of x in equation(2) and we get
= 8(16 - y) + 5y = 120
= 128 - 8y + 5y = 120
= 3y = 8
y = 8/3
Now, we put the value of y in equation(1) and we get
x = 16-8/3
x = 40/3
Hence, a system of equations that determines the number of adult tickets and the number of senior citizen tickets that Beth purchased is x + y = 16
8x + 5y = 120.
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Sam and ben are grading english tests. Sam grades 6 6 tests in 24 24 minutes and ben grades 5 5 tests in 20 20 minutes. At these rates, what is the total number of tests they can grade in 3 3 hours? enter the answer in the box.
The total number of tests graded by them in 180 minutes (3 hours) will be 90 tests.
Sam ,
6 tests in 24 mins
Therefore ,
1 test in 24/6 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Ben,
5 tests in 20 mins
Therefore ,
1 test in 20/5 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Therefore at the end of 180 mins
they would have graded 45 + 45 = 90 tests.
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.
In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers.
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Use the following sample to estimate the population proportion of red automobiles in the United States.
A.19%
B.20%
C.21%
D.22%
The population proportion of red automobiles in the United States exists 22 %.
What is meant by proportion?An analysis of two numbers in terms of their proportion. A ratio is said to be directly proportional to another if two sets of given numbers are increasing or decreasing in the same ratio.
The proportion of red automobiles in the United States(P) is given by:
P = [Number of red automobiles / Number of automobiles in US ]× 100
According to the table
Number of red automobiles = 32 + 29 + 23
Number of red automobiles = 84
Number of automobiles
= 32 + 29 + 23 + 18 + 36 + 25 + 4 + 17 + 11 + 25 + 26 + 39 + 10 + 46 + 33
Number of automobiles = 374
put the values into the equation
P = [Number of red automobiles / Number of automobiles in US ] × 100
substitute the values in the above equation, we get
P = [84 Cars / 374 Cars] × 100
simplifying the above equation, we get
Proportional = 0.2245 × 100
Proportional = 22.45
Proportional = 22 percentage
Therefore, the correct answer is option D. 22 %.
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x and y are declared as integer variables.
You are given the following expression:
x >= y
Which of these expressions is the opposite of the above expression and has valid syntax?
-x <= y
- x =< y
- There's not enough information to determine this.
- x == y
- x < y
- x =< y is the expression and acceptable syntax.
Explain about the expression?
A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.
A term may be a number, a variable, a product of two or more variables, or a combination of both. A single phrase or a set of terms can make up an algebraic expression. The two terms in the formula 4x + y, for instance, are 4x and y.
Algebra's associative, commutative, and distributive characteristics are the ones that are most frequently utilized to make algebraic expressions simpler.
The converse of the expression and having proper syntax is
= x >= y.
= -x <= y
=- x =< y
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If there is inverse variation and y = 3 y = 3 when x = 24 x = 24 , find x x when y = 18 y = 18 . x = 1 x = 4 x = − 1 x = − 6
SHOW WORK FOR BRAINLIST AND HEARTS!
The value of the function h(x) = -3(x - 1) + 4 when x is -5 is 19.
How to find the value of the function?It is important to note that a function is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, the function is given a :
h(x) = -3(x - 1) + 4
When x = -5. This will be:
h(-5) = -3(-5 - 1) + 4
= -3(-6) + 1
= 18 + 1
= 19
The value is 19.
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describe the relationship between the variables in terms of direction (positive or negative slope), form (a straight line or a curve), and strength (how much the points deviate from a straight line).
The relationship between the variables in terms of direction form and strength.
Given :
the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.
The straight line form with variables is :
y = mx + b is a straight line equation
here x and y are variables
m = slope
b = y - intercept
example :
y = 3x + 3
m = + 3 is a positive slope
y = -2x + 4
here
m = - 2 is a negative slope
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In the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 30%.
How to calculate the percentage?From the information given, in the the first week of July, a record 1060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 348 fewer people went to the pool than in the third week
The total number of people at the end of the week will be:
= 1060 - 100 + 130 - 348
= 742
The percentage decrease will be:
Decrease / Original value × 100
= (1060 - 742) / 1060 × 100
= 30%
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The average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{\$1583.9 per day}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The table with the information}[/tex]
Find: [tex]\textsf{The average daily balance of Elliott's account for the month of June}[/tex]
Solution: In order to get the average daily balance, we need to use a formula where we have a weighted balance for each day. For example, out of the 30 days in June, 9 of the days there was $1223 in the account, for 5 days there was $1223 + $615 in the account, for 7 days there was $1223 + $615 - $63 in the account, and for the last 9 days there was $1223 + $615 - $63 - $120 in the account. This all happened over 30 days and to translate this to an equation it will look something like the following.
Convert to equation and simplify
[tex]\frac{(1223\ *\ 9)\ +\ (1223\ +\ 615)\ *\ 5\ +\ (1223\ +\ 615\ -\ 63)\ *\ 7\ +\ (1223\ +\ 615\ -\ 63\ -\ 120)\ *\ 9}{30\ days}[/tex][tex]\frac{(11007)\ +\ (9190)\ +\ (12425)\ +\ (14895)}{30\ days}[/tex][tex]\frac{(47517)}{30\ days}[/tex][tex]\textsf{1583.9 per day}[/tex]Therefore, the final answer would be that the average daily balance of Elliott's account for the month of June would be $1583.9 per day.
examine the linear relationships. linear equation a: y=45xy=45x linear equation b is represented by this graph.
The correct option 1. the slope of Equation A is steeper because 4/5 is bigger than 2/5.
Explain the term slope of the line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (variation in y divided by change in x).The format of a linear function is as follows:
y = ax + b
That where:
The rate of change is represented by the slope, or a.The function is steeper the higher the slope:Given by: Linear equation A
y = 4/5 x.
Points (0, 2) and pass through linear equation B. (5, 4).
Given that changes in y divided by change in x determines the slope between two points, we have that:
m = (4 - 2)/(5 - 0)
m = 2/5
Equation A is steeper as it contains a higher slope, so the appropriate response is:
Due to the fact that 4/5 is greater than 2/5, Equation A has a steeper slope.
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The complete question is-
Linear equation A: y=45x
Linear equation B is represented by this graph.
A line that passes through points (0, 2) and (5, 4).
Which statement is entirely correct?
Equation A has a steeper slope, because 4/5 is greater than 2/5.Equation A has a steeper slope, because 4 fifths is greater thanEquation B has a steeper slope, because 4/5 is greater than 2/5.Equation B has a steeper slope, because 4 fifths is greater thanEquation A has a steeper slope, because 5/2 is greater than 4/5.Equation A has a steeper slope, because 5 halves is greater thanEquation B has a steeper slope, because 5/2 is greater than 4/5.Which equation could be represented by the number line?
Answer:
B
Step-by-step explanation:
if kenneth has 11 dimes and nickels in his pocket, and they have a combined value of 80 cents, how many of each coin does he have?
Answer: let d=# of dimes
let n= # of nickels
n+d=11
5n+10d=80
5d+25
5 dimes and 6 nickels
What is the length of AB
Answer: 11.5 maybe ? {sorry if its wrong]
Step-by-step explanation:
Emma and Jane were playing soccer in their backyard, and Emma kicked the ball to
Jane. The curve of the ball's path can be represented by
d=-16t² + 32t + 9, where d is the distance of the ball from Emma and t is
the time (in seconds). Find how long it takes the ball to reach Jane.
4
It takes 4 seconds for the ball to reach Jane.
It takes 2.25 seconds for the ball to reach Jane.
It could take 2.25 seconds or 0.25 seconds.
It could take 4 seconds or 3.25 seconds.
it takes 2.25 seconds
oh, and it's 18 seconds for the next question assuming we had the same test.
How do you write 0.112 as a fraction?
Answer:
112/1000
Step-by-step explanation:
Just put 1 under decimal point and just add as many zeros as digits after that
Write the complex number 8/1+i in standard form?
Answer: 8 + i
Step-by-step explanation:
The complex number 8/1+i can be written in standard form as 8 + i. In standard form, a complex number is written as a+bi, where a is the real part and bi is the imaginary part. In this case, the real part is 8 and the imaginary part is i. Therefore, the standard form of the complex number 8/1+i is 8 + i.
Answer: 4-4i
Step-by-step explanation:
[tex]\displaystyle\\\frac{8}{1+i} =\\\\\frac{8(1-i)}{(1+i)(1-i)}=\\\\\frac{8(1-i)}{1^2-i^2} =\\\\\frac{8(1-i)}{1-(\sqrt{-1})^2 }=\\\\\frac{8(1-i)}{1-(-1)}=\\\\\frac{8(1-i)}{1+1} =\\\\\frac{8(1-i)}{2} =\\\\4(1-i)=\\\\4-4i[/tex]
Karen has a bag containing 423 rubber ducks.
If Karen gives 30 rubber ducks to every person she meets, then she will have enough for _____ people and she will have _____ extra ducks left over.
Answer:
karen will have enough for 14 people, and she will have 3 extra ducks left over
Step-by-step explanation:
divide 423 by 30
423/30 = 14
14 times 30 is 420, so subtract 420 from the total number of rubber ducks
423 - 420 = 3
so, karen will have enough for 14 people and 3 ducks will be left over !!
Answer:
Karen we'll have enough for 14 people and have 3 ducks left over.
60 POINTS ANSWER FOR BRAINLIST AND PROVIDE THE GRATH!! Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day. Draw a graph to represent
this situation.
Answer: He needs 9 days to complete all his overdue assignments and if this is happening to you sry I feel your pain. Just vibing to k-pop while having a mental breakdown doesn't sound bad until you feel it :(
Step-by-step explanation:
Well, he has 36 overdue assignments, and if he completes 4 overdue assignments each day you need 9 days to complete all his overdue assignments.
36 divide 4 = 9 days
How do you simplify and make the decimal 0.225 into a fraction?
Step-by-step explanation:
a finite decimal number into a fraction is very easy.
remember what the different positions after the decimal point are worth :
tenths, hundredths, thousandths, tenthousandths, hundredthousandths, ...
0.225 covers thousandths.
how many ?
well, 225, of course.
so,
0.225 = 225/1000 = 9/40 × 25/25 = 9/40
In the diagram below, \overline{EF}
EF
is parallel to \overline{BC}
BC
. If DC=27DC=27, EF=27.5EF=27.5, and BC=49.5BC=49.5, find the length of \overline{DF}
DF
. Figures are not necessarily drawn to scale.
)
Applying the AA similarity theorem, the length of DF is: 15 units.
What is the AA Similarity Theorem?When two angles in one triangle are congruent to the corresponding two angles in another triangle, both are said to be similar to one another. This means that, the corresponding sides of these two triangles would be proportional or have the same ratio.
In the image attached bellow, triangle DEF and triangle DBC are similar to each other because they have two pairs of corresponding angles that are congruent which are:
<DFE ≅ <DCB [right angles are equal]
<EDF ≅ <BDC [reflexive property of congruence]
Therefore, their corresponding sides will have equal ratios such as:
DC/DF = BC/EF
Substitute:
27/DF = 49.5/27.5
Cross multiply:
DF = (27.5 * 27) / 49.5
DF = 15
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in a world atlas study, 10% of people have blue eye color. lane decided to observe 44 people and she concluded 7 people had blue eyes. calculate the z-score.
Therefore the value of the z score comes out to be Z = 1.1261
what is z score?Simply expressed, a z-score (sometimes called a standard score) gives you a sense of how distant from the mean a data point is. Technically, however, it's a calculation of how far a raw score deviates from or exceeds the population mean.
The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviation. The mean and population standard deviation must be known in order to use a z-score.
Here,
In a World Atlas study, 10% of people have blue eye color. Lane decided to observe 44 people and she concluded 7 people had blue eyes. Calculating the z-score
Given that :
Sample size (n) = 44
Number of people with blue eyes (x) = 7
Proportion (p) = 10% = 0.1
Using the relation :
Z = (p" - p) / [tex]\sqrt{\frac{pq}{n} }[/tex]
Since : q = 1 - p = 1 - 0.1 = 0.9
p" = x / n = 7/ 44
p"= 0.15909
pq = 0.1 * 0.9 = 0.09
Hence,
Z = (0.15909- 0.1) / [tex]\sqrt{\frac{0.09}{44} }[/tex]
Z = 0.0509 / 0.0452
Z = 1.1261
Therefore the value of the z score comes out to be
Z = 1.1261
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Find the equation for a polynomial f(x) that satisfies the following:
Degree 3
Zero at x=−1
Zero at x=−4
Zero at x=−1
y-intercept of (0,8)
f(x)=
The polynomial with the given degree and zeros is:
y = 2*(x + 1)²*(x + 4)
How to find the equation of the polynomial?A polynomial of degree N with the zeros {x₁, x₂, ...} and a leading coefficient a can be written as:
y = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Here we know that the degree is 3, and the zeros are {-1, -4, -1}
Then we can write the polynomial as:
y = a*(x + 1)*(x + 4)*(x + 1)
y = a*(x + 1)²*(x + 4)
We also know that the polynomial passes through (0, 8), replacing these values we will get:
8 = a*(0 + 1)²^*(0 + 4)
8 = a*1*4
8/4 = a
2 = a
The polynomial is:
y = 2*(x + 1)²*(x + 4)
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In 2014, 100 trees were planted by the people in Cherry Hill. The table below shows the number of trees planted of each type.
Trees Planted
Tree Number of Trees
Oak 45
Maple 17
Palm 28
Pine 10
Which circle graph correctly shows the information from the table?
Answer:
where is your circle graph
Step-by-step explanation:
i need the graph in order to solve this
How do you write 0.54 in percent?
Step-by-step explanation:
as percent means per 100
So we can say 0.54 or 54100 is the same as 54%.
hope understand
today b is 3 times older than a. in 5 years b will be 2 times older than a. how old are a and b today?
If we substitute a = 5 into the equation 3a = 15, we get b = 15.
Therefore, a = 5 and b = 15.
We are given that b is 3 times older than a, so b = 3a.
We are also told that in 5 years b will be 2 times older than a, so b = 2(a + 5).
We can set 3a = 2(a + 5) and solve for a.
3a = 2a + 10
2a = 10
a = 5
Therefore, a = 5 and b = 3a = 15.
We know that today, b is 3 times older than a. This means that b = 3a. We can use this equation to help us solve the problem.
We know that in 5 years' time, b will be 2 times older than a. This means that in 5 years, b = 2(a + 5). We can use this equation to help us solve for a and b.
We can set the two equations equal to each other, 3a = 2(a + 5). We can then solve for a, which gives us a = 5.
We can then substitute this value into either of the equations to find the value of b. If we substitute a = 5 into the equation 3a = 15, we get b = 15.
Therefore, a = 5 and b = 15.
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bookword code G06 calculate length of AD
Edpuzzle Fractions Equivalent
A) The decimal 2.256 in expanded form and word form are respectively; 2 + 0.2 + 0.05 + 0.006; Two and three hundred fifty six one - thousandths
B) The decimal 24.09 in expanded form and word form are respectively; 20 + 4 + 0 + 0.09; Twenty four and 9 one - hundredths.
How to write decimals in expanded form?The expanded form used when writing decimals is the mathematical expression that shows the sum of the values of each digit in the given number.
A) We are given the decimal 2.256
Thus, in expanded form, the given decimal can be expressed as;
2 + (2/10) + (5/100) + (6/1000)
= 2 + 0.2 + 0.05 + 0.006
In word form, we can write the decimal as;
Two and three hundred fifty six one - thousandths
B) We are given the decimal 24.09
Thus, in expanded form, the given decimal can be expressed as;
20 + 4 + (0/10) + (9/100)
= 20 + 4 + 0 + 0.09
In word form, we can write the decimal as;
Twenty four and 9 one - hundredths.
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The purchase price of a large 4K LED TV, including finance charges, was $1230. A down payment of $300 was made, and the remainder was paid in 12 equal monthly installments. Find the monthly payment.
The monthly installment is $ 77.5. We have to divide the annual rate by 12 to find monthly installments.The number of equated monthly installment is equal to the number of month in the repayment tenure.
What is finance purchase charges?
A purchase finance charge is a fee applied to purchase a credit account like a credit card .This typically takes the form of an interest charge, although some accounts have may other terms.
How do we made monthly installment?The installment is generally in equal month payments that include interest and portion of the principle.We schedule to be created by the lender detailing payment throughout the loan duration.
By solving :
1230=300+12 x
1230-300=12 x
x= $ 77.5 monthly payment
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