Using formula Work done against gravity,
The work done by person against the gravity is 5880 J .
Work done against gravity:
The work done in lifting an object against gravity becomes the potential energy of the object-earth system. The change in gravitational potential energy Δ P.Eg is Δ P.Eg = mgh, where h is the increase in altitude and g is the acceleration due to gravity.
Mathematically, work done against gravity is given by,
W = Fg×d×cosθ
where, Fg --->force of gravity = weight = m×g
m --> mass
g --> gravity
d---> displacement
θ--> angle between force and displacement
we have given that
g = 9.8 m/s²
d = displacement = height = 2×4 = 8m
θ =angle between force and displacement = 180°
Combined mass = 75 kg
So, W = 75×9.8×8×cos 180°
W = -5880 J
Hence, the required work done is -5880J.
To learn more about Work done against gravity,
refer:
https://brainly.com/question/1851977
#SPJ4
Complete question:
A spiral staircase in a building is in the shape of a helix of radius 5 meters Between two floors of the building; the stairs make one full revolution and climb by 4 meters A person carries a bag " of groceries up two floors The combined mass of the person and the groceries is 75 kg and the gravitational force is 75g downward, where g 9.8 m/sec? is the acceleration due to gravity: Calculate the work done by the person against gravity in joules. Enter an exact answer.
sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 if he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
The service life that appear to be out of control is 0.0456 as per the given sample service life.
What is meant by sample standard deviation?The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.
The sample standard deviation (s) is the square root of the sample variance and a measure of the deviation from expected values.
It is given that,
Rationale:
UCL=520
LCL=480
Mean [tex]\bar{x}[/tex]=500
The standard deviation of sample([tex]S_{n}[/tex])=11.55
Z(for UCL)=(UCL-Mean)/[tex]S_{n}[/tex]
=(520-500)/10
=2
Similarly, Z(for LCL)=(LCL-Mean)/[tex]S_{n}[/tex]
==(480=500)/10
=-2
Now, by using the z table for finding the confidence level between the Z value of -2 and 2.
Therefore, confidence level=0.4772+0.4772
=0.9544
Risk(alpha)=1-confidence level
=1-0.9544
=0.0456
The service life that appear to be out of control is 0.0456 as per the given sample service life.
To know more about sample standard deviation, visit:
https://brainly.com/question/24277447
#SPJ4
What is a paragraph proof of Theorem 3 8?.
Perpendicular lines (or segments) really structure four right points, regardless of whether only one of the right points is set apart with a case.
Let m and n be lines that converge line a. Let m be perpendicular to a. This implies that every one 4 of the points framed by the convergence of m and an are 90°.
Allow n to be opposite to a. This implies that every one 4 of the points framed by the convergence of n and an are likewise 90°.
Since the points are all consistent, this implies that the equivalent side inside points (between lines m and n) are harmonious. In the event that two same-side inside points are harmonious, the lines are equal. In a direction plane, two particular nonvertical lines are equal if and provided that they have a similar slant. Any two vertical lines are equal.
To learn more about lines and segments,
https://brainly.com/question/25727583
#SPJ4
Factor completly
(x-5)^2-16
instructor number of failures prof. a 13 prof. b 0 prof. c 11 prof. d 16 what are the .95 (5 percent risk of type i error) upper and lower control limits for the p-chart?
The Average proportional failure of the instructors is 0.10
From the question we are told that
Sample size 100
Instructor Number of Failures
Prof. A 13
Prof. B 0
Prof. C 11
Prof. D 16
Confidence level= 0.95
From Z table
Z=1.96
Generally proportion for failure is mathematically given as
proportion of failure = number of failure/ sample size
Prof A
Pa = 13/100
Pa = 0.13
Prof B
Pb = 0/100 = 0
Prof c
Pc = 11/100 = 0.11
Prof D
Pd = 16/100 = 0.16
Average proportional failure = (0.13 + 0.16 + 0.11 +0)/4 = 0.10
Therefore the Range is 0.0412 to 0.1588
Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options
Therefore, the Average proportional failure of the instructors is 0.10
To learn more about proportionality refer here
https://brainly.com/question/12242745
#SPJ4
Suppose that 17 inches of wire costs 51 cents. At the same rate, how many inches of wire can be bought for 42 cents?
Computing a one-sample t test is appropriate when
-Participants are assigned to only one group
-The population variance is unknown
-Participants are observed one time
-All of the above
Computing a one-sample t-test is appropriate when d) all of the above
A statistical hypothesis test called the one-sample t-test is used to examine whether an unknown population mean differs from a given value. The test is applicable to continuous data. When doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.
When performing a one-sample t-test, the data should be collected at random from a population that is generally healthy. When each participant is put into a single group and is present on time, it is suitable. Additionally, it is suitable when the population variance is unknown.
Read more about t-tests on:
https://brainly.com/question/20216196
#SPJ4
which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials
None of the options are commutative for the given binary operations.
Define the term commutative property?According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. With addition and multiplication, the principle is true, but not for division or subtraction.commutative property:
a*b = b*a
* is any binary operation.
Consider option a: subtraction of integers
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Option b: . division of nonzero real numbers
Let a = 2, b = 3
a/b = b/ a (commutative property)
But
2/3 ≠ 3/2 not commutative
Option c. function composition of polynomials.
Let polynomial be a - b
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Thus, none of the options are commutative for the given binary operations.
To know more about the commutative property, here
https://brainly.com/question/2542910
#SPJ4
How many of an acute triangle's angles are less than 90 degrees?.
In an acute triangle, all the three angles are less than 90°.
How do triangles work?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to a total of 180 degrees.The definition of an acute triangle?
When all three of the triangle's internal angles are acute, the triangle is said to be acute. Triangles with sharp angles are also known as acute triangles. Acute triangles can have different side lengths, but their interior angles can never exceed 90 degrees.Learn more about acute triangle
brainly.com/question/1311149
#SPJ4
a bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles. you randomly select one marble from the bag. what is the probability that you select a gold marble? write your answer as a reduced fraction. p (gold marble)
After solving, the probability that we select a gold marble is 2/31.
In the given question,
A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.
So, Total marbles = 2+8+21
Total marbles = 31
As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.
We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is
P(G) = Total number of gold marble/Total marbles
P(G) = 2/31
Hence, the probability that we select a gold marble is 2/31.
To learn more about probability link is here
brainly.com/question/11234923
#SPJ4
suppose the p-value of a hypothesis test was 0.02 and the level of significance (alpha) was 0.05. what is the correct decision?
Answer Desisonw 2
Step-by-step explanation:
List the potential rational zeros of the polynomial function. Do not attempt to find the zeros.
f(x) = 7x4 - 5x3 + x2 - x + 1
Choose the answer below that lists the potential rational zeros.
A. -1,1, -7,7, -5,5, -1/7,1/7, -1/5,1/5
B. -1,1, -1/7,1/7, -1/5,1/5
C. -1,1, -7,7
D. -1,1, -1/7,1/7
Answer:
D. -1,1, -1/7,1/7
Step-by-step explanation:
Use all the factors of the leading coefficient, 7. And also, all the factors of the constant, 1.
Put the factors of the constant on top (numerator). Put the factors of the leading coefficient on the bottom (denominator).
+- 1/1 and +- 1/7
Simplifying:
-1, 1, -1/7, 1/7
That's it. Just list of possibilities of the rational zeroes.
at 95% confidence, how large a sample should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion? assume that past data are not available for developing a planning value for
For a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.
It is given to us that -
There is 95% confidence
The margin of error is 0.04
We have to do the estimation of the population proportion.
We know that in case of unknown population proportion, we can assume that the value of population proportion can be regarded as 0.5.
It is known that the formula of sample size is given by -
[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }[/tex] ----- (1)
where,
n = sample size
Z = critical value of Z-value
p = population proportion
E = margin of error
Also, we know that for a 95% confidence interval, Z = 1.960
From the given information, we have
p = 0.5
and E = 0.04
Substituting the values in equation (1), we have
[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }\\= > n = \frac{(1.960)^{2}*0.5(1-0.5) }{(0.04)^{2} }\\= > n = \frac{3.8416*0.25}{0.0016}\\ = > n = 600.25[/tex]
Since this is the value of minimum sample size, rounding up, we have the sample size as 601.
Therefore, for a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.
To learn more about population sample size visit https://brainly.com/question/14100967
#SPJ4
Given a collection of paired sample data, the between the two variables, x and y. y = bo + b1x algebraically describes the relationship between x and y. Given a collection of paired sample data, the between the two variables, x and y. ỹ = bo+bqx algebraically describes the relationship between x and y.
The answer is regression equation.
What is regression equation?
The regression of y on x is that the algebraic expression of the regression lines. it's accustomed predict the values of the variable quantity from the given values of freelance variables.
Main Body:
When there is a relation between 2 variables , regression equation is used to describe the relation .
Hence regression equation is the result.
The actual question is like:
Given a collection of paired sample data, the ____________________ y with caret=b0+b1x algebraically describes the relationship between the two variables, x and y.
to know more about regression equation click on the link below
https://brainly.com/question/26843436
#SPJ4
An empty bowl weighted 3. 4 pound julian added water that weighted 5. 12 pound and a fih that weighted 0. 7 pound. What i the total weight the bowl including the water and fih
Total weight the bowl including the water and fih is 9.22 pound
What does math add mean?
To add is to integrate or bring two things together. The ability to add more than two numbers is then taught to students by building on this understanding. The foundational concept for understanding more complex operations like multiplication and division in higher grades is addition.
Given that :
An empty bowl weighted = 3.4 pound
A water that weighted = 5.12 pound
A fih that weighted = 0.7 pound
Total weight = A bowl + water + fih = 3.4 + 5.12 + 0.7 = 9.22 pound
Learn more about adding
https://brainly.com/question/24536701
#SPJ4
Why do we use graphing?.
each tile in the model represents 1/4. How many titles make a group of 3/4
Answer:
3 tiles
because 1/4+1/4+1/4=3/4
I hope this helps you!
a 20,000 m3 waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river. the inflow to the pond has a flow rate of q
Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L
What is unitary method?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.Consider your square as being composed of smaller unit squares.The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.According to our question-
Qin = 4 000m3/day
Cin = 25mg/L
V = 20 000m3
k = 0.25/day
Find: Count = ?
outStarting from the mass balance equation for steady state 0 = QCin - QCount - kCountV
manipulate the equation to get:
\(Count=Cin(Q/Q+kV)\)
Then simple plug in your givens:
Count = (25mg/L)((4000m3/day)/(4000m3/day + 0.25/day(20000m3))
Count = 11mg/L
Hence, Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L.
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
the monthly utility bills in a city are normally distributed with a mean of $70 and a standard deviation of $8. find the monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75. do not round and do not include the $ sign.
The monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75 is 64
Z-score gives you an idea of how far from the mean a data point is.
it’s a measure of how many standard deviations below or above the population mean a raw score is. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).
The basic z score formula for a sample is:
z = (x – μ) / σ
According of the question,
Monthly utility bills in a city follows normal distribution
Mean of the monthly utility bills in a city : μ = $70
A standard deviation of monthly utility bills in a city : σ = $8
Z-score of utility bill = -0.75
z - score = x - μ / σ
=> - 0.75 = x - 70 / 8
=> -6 = x - 70
=> x = 70 - 6
=> x = 64
Hence , the x-value is 64
To know more about z-score here
https://brainly.com/question/15016913
#SPJ4
Given that D( x ) = 2 x , select all of the following that are true statements.
D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3
The true statements are:
D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).D(x) is a direct variation.x is the dependent variable.D(x) is a function.How to determine the true statements?The function is given as D(x) = 2x
The function D(x) is a linear function, and it is also a proportional function
Proportional functions represent direct variation
This means that (b) and (e) are true
Also set x = 5, 6 and -2
D(5) = 2 x 5 = 10
D(6) = 2 x 6 = 12
D(-2) = 2 x -2 = -4
This means that (a) is true
Lastly, the function D(x) is dependent on x for its value
This means that x is the dependent variable.
Read more about linear functions at
brainly.com/question/2030026
#SPJ1
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).
If W(t) denotes the sumo wrestler's weight then the Function's formula will be w(t) = 5.5t + 79.5
Function formula: This relationship is often represented as y = f(x), or "f of x," and y and x are related in such a way that there is a unique value of y for every x; consequently, f(x) cannot have multiple values for the same x.
if we take y = mx + b,
the slope, m = 5.5, we need to find b,
at x = 11 and y = 14
14 = (5.5) (11) + b
b = 79.5
We plug in the qualities for x, y, and m. Then, we rearrange and deduct 60.5 from the two sides.
This makes the equation,
y = 5.5x + 79.5
or we can write as
w(t) = 5.5t + 79.5
know more about functions formula here: https://brainly.com/question/20345338
#SPJ4
(complete question)
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).
Write the function's formula.
W(t)=?
you are given the following total market values for an index over a five-year period. assuming the index starts at 1,000, calculate the index value each year.
The index value for 5 years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, Year 5: 1,414.74 as it starts at 1000 index points.
What is percent?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Here,
Market value of the stocks:
Year 1: 2,645 million
Year 2: 2,957 million
Year 3: 3,318 million
Year 4: 3,193 million
Year 5: 3,742 million
Value of Index in 5 years:
Year 1: 1,000
Year 2: 1,117.96
Year 3: 1,254.44
Year 4: 1,207.18
Year 5: 1,414.74
Calculations:
Year 1: 2,645 million / 2,645 million × 1,000 = 1,000.00
Year 2: 2,957 million / 2,645 million × 1,000 = 1,117.96
Year 3: 3,318 million / 2,645 million × 1,000 = 1,254.44
Year 4: 3,193 million / 2,645 million × 1,000 = 1,207.18
Year 2: 3,742 million / 2,645 million × 1,000 = 1,414.74
Since the index starts at 1,000 points, the values for the subsequent years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, and Year 5: 1,414.74.
To know more about percent,
https://brainly.com/question/29306119
#SPJ4
Which polynomials are in standard form? x2 3x 2 q3 â€"" 15q 12q2 â€"" 16 4a a2 a â€"" 2 3x4 4x3 â€"" 3x2 â€"" 1 3t3 3t2 2t 14 a3 â€"" 6a 8a2
The polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² .....a₁x + a0, where x is the variable and ai are coefficients.
In the given options, when we analyse
x2 + 3x + 2 is given in standard form that is x2 + 3x + 2
15q 12q2 is not present in standard form
3t3 + 3t2 + 2t 14 is given in standard form
Therefore, the polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14
To learn more about polynomials refer here
https://brainly.com/question/4142886
#SPJ4
Samuel and Jaon pent 3/4 of their combined earning from 100 by gift. How much do they pend? I there enough left over from Wedneday’ earning to buy a card that cot $3. 25
There is not enough money left to buy a card for $3.25 but they spend $ 5.88 to buy a gift.
What are combined earnings?
The term "Combined Earnings" refers to the total (without repetition) of (a) the aggregate (without repetition) Dividend Capacity of the Regulated Subsidiaries, (b) EBITDA, and (c) the aggregate (without repetition) tax provision, created in accordance with GAAP, for the Regulated Subsidiaries.
Here, we have
The earnings from Wednesday of Samuel and Jason are:
Samuel earnings = 12.5 x 0.40 = $5
Jason earnings = 7.1 x 0.40 = $2.84
The combined earnings from Wednesday are as follows:
Combined earnings = Samuel's earnings + Jason's earnings
Combined earnings = $5 + $ 2.84 = $ 7.84
The spended earnings are:
Spended earnings = combined earnings x ¾
Spended earnings = 7.84 x ¾ = $ 5.88
The leftover is:
Leftover = combined earnings – spended earnings
Leftover = 7.84 – 5.88 = $ 1.96
Hence, they spend $ 5.88 to buy a gift but not enough money to buy a card for $3.25.
To learn more about the combined earnings from the given link
https://brainly.com/question/25623677
#SPJ4
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount of money that Erica owes at the end of 6 years is $8,551.56.
What is the amount owed?The amount of money that has in his account would increase at a compound rate each month. Compound growth is when both the amount that was invested and the interest that has already been earned increases at each compounding time.
The formula that can be used to determine the future value with monthly compounding is:
A = P(1 + r/n)^nt
Where:
P = amount invested r = yearly interest rate = 8% / 12 = 0.67%n = number of compounding in a year t = number of yearsA = $5300 x (1 + 0.0067)^(6 x 12)
A = $5300 x 1.0067^72 = $8,551.56
To learn more about future value, please check: https://brainly.com/question/18760477
#SPJ1
area of a rectangle, measured in cm^2, is numberically equal to 4 times its perimeter, measured in cm. ratio of the rectangle's length to its width is 5:2
A rectangle's area of 28cm2 (measured in cm2) is numerically equal to 4 times the rectangle's circumference (measured in cm). The rectangle's length to width ratio is 5:2.
Given,
l/b = 5/2
l = 5b/2
area = 4 times the rectangle's perimeter,
which equals 4*2(l+b)
= 8(l+b)
= 8(5b/2 + b)
= 28b cm2.
Learn more about area here
https://brainly.com/question/27683633
#SPJ4
Present age of nick is 8 years and Jonas age is 14 years. What fraction of Jonas age represent the age of nick after 6 years? (Complete solution with data)
The fraction of Jonas age represent the age of nick after 6 years is 7/10.
Given that, present age of nick is 8 years and Jonas age is 14 years.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
After 6 years
Nick's age =14 years and Joan's age =20 years
So, the fraction =14/20
= 7/10
Therefore, the fraction of Jonas age represent the age of nick after 6 years is 7/10.
To learn more about the fraction visit:
brainly.com/question/1301963.
#SPJ1
Approximately what percentage of the almost 1,500 highway deaths in pennsylvania each year are attributed to aggressive driving?.
5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.
What is aggressive driving?Aggressive driving is defined as any behind-the-wheel exertion that, without regard for safety, puts another person( or people) and/ or property in peril.
Aggressive driving can vary from potentially dangerous conduct to serious assault.
From the data attained the percentage of the nearly 1500 highway deaths in Pennsylvania each year attributed to aggressive driving will be 50%
5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.
To know more about Percentage:
https://brainly.com/question/16797504
#SPJ4
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" 4y sec(2z). a. Find the most general solution to the associated homogeneous differential equation. Use c and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2 b. Find a particular solution to the nonhomogeneous differential equation y" +4y sec(2). c. Find the most general solution to the original nonhomogeneous differential equation. Use ci and c2 in your answer to denote arbitrary constants.
The general solution of equation y''+4y=sec(2z) is
y = c₁cos2z + c₂sin2z + [tex]\frac{cos2z}{4}[/tex] ln(cos2z) + [tex]\frac{z sin2z}{2}[/tex].
Given differential equation is,
y'' + 4y = sec(2z)
Characteristic equation of this equation is
(D²+4)=0
⇒ D² = -4
D = ±2i
Therefore the roots are imaginary.
D₁=2i ⇒ y₁ = e⁰cos2z = cos2z
D₂=-2I⇒ y₂ = e⁰sin2z = sin2z
yn= c₁cos2z + c₂sin2z
Noe to solve yp, first we need to solve Wronskian
y₁= cos2z , y₂=sin2z
y₁'= -2sin2z , y₂'=2cos2z
⇒ W = [tex]\left[\begin{array}{ccc}y1&y2\\y1'&y2'\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}cos2z&sin2z\\-2sin2z&2cos2z\\\end{array}\right][/tex]
= (cos2z)(2cos2z)-(-2sin2z)(sin2z)
= 2cos²2z + 2sin²2z
=2 (cos²2z + sin²2z)
= 2 ≠ 0
yp = - y₁[tex]\int\ {\frac{y2 g(z)}{W} } \, dz[/tex] + y₂[tex]\int\ {\frac{y1 g(z)}{W} } \, dz[/tex]
= -(cos2z)[tex]\int\ {\frac{(sin2z)(sec2z)}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{(cos2z)(sec2z)}{2} } \, dz[/tex]
= - (cos2z)[tex]\int\ {\frac{sin2z/cos2z}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{cos2z/cos2z}{2} } \, dz[/tex]
= - [tex]\frac{cos2z}{2}[/tex][tex]\int\ {tan2z} \, dz[/tex] + [tex]\frac{sin2z}{2}[/tex][tex]\int\ \,dz[/tex]
= - [tex]\frac{cos2z}{2}[/tex](-[tex]\frac{1}{2}[/tex] ln (cos2z)) + [tex]\frac{sin2z}{2}[/tex] (z)
= [tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]
Now the general equation will become
y = yn + yp
y = c₁cos2z + c₂sin2z +[tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex] .
To know more about Wronsian here
https://brainly.com/question/16930425
#SPJ4
question content area top part 1 find the arc length of the following curve on the given interval. x
The arc length of the curve is L= π^2/8
In order to get the length of the arc's curved line, an arc length formula is used (a segment of a circle). The arc length is the length of the circle's curved line, which can be expressed as a distance through the curve.
To find arc length of the curve on the given interval
X= sin t-cos t y= cos t +t sin t
0≤ t ≤ π/2
On differentiating x and y w.r.t t
dx/dt = cos t - [cos t+t (-sin t)]= cos t – cost + t sin t
dy/dt = sin t + [t cos t+sin t]= sin t+ sin t+ t cos t
So we have
dy/dt = t cost and dx/dt= t sin t
Arc length for parametric equation is given by
L= ∫_0^(π/2)▒〖√((〖dx/dt)〗^2+(〖dy/dt)〗^2 ) 〗 dt
L= ∫_0^(π/2)▒〖√((t^2 〖cos〗^2 t+t^2 〖sin〗^2 t) ) 〗 dt
L= ∫_0^(π/2)▒t dt
L= [t^2/2] (π/2)¦0 = π^2/4*1/2
L= π^2/8
Therefore the arc length of the curve is L= π^2/8
To learn more about the arc length visit
https://brainly.com/question/16403495
#SPJ4
Suppose A, B and C are square matrices.
(1) A is similar to A.
(2) If A is similar to B, then B is similar to A.
(3) If A is similar to B and if B is similar to C, then A is similar to C.
All the Options (1, 2, 3) are correct i.e., A is always similar to A. and If A is most similar to B, then we can say B is similar to A. and at last If A is most similar to B and B is also similar to C, then A must be similar to C matrix.
Properties of Similar square Matrices : Similar matrices percentage many residences and it's miles those theorems that justify the selection of the word ``similar.'' First we can display that similarity is an equivalence relation. Equivalence members of the family are essential withinside the have a look at of diverse algebras and might continually be seemed as a sort of susceptible model of equality.
Sort of alike, however now no longer pretty equal. The perception of matrices being row-equal is an instance of an equivalence relation we were operating with on account. Row-equal matrices aren't equal, however they may be lots alike. For instance, row-equal matrices have the identical rank. Formally, an equivalence relation calls for 3 situations hold: reflexive, symmetric and transitive. We will illustrate those as we show that similarity is an equivalence relation.
Learn more about square matrices visit : brainly.com/question/13179750
#SPJ4
