The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .
In the question ,
it is given that ,
the differential equation is
y'' + 9y + 5y³ = Cos(10t) ...equation(1)
y(0) = 0, y'(0) = 1
for y = 0 , the differential equation is
y''(0) + 9y(0) + 5{y(0)}³ = Cos90)
y''(0) + 9 + 5 = 1 ;
y''(0) = 1.
differentiating equation(1) with respect to "t" , we have
y''' + 9y' + 15y²y' = -10Sin(10t)
y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)
y'''(0) + 9 + 0 = 0
y'''(0) = -9
The Taylor series is given by
y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....
Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have
y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....
= t + t²/2 - 3/2.t³ + ...
Therefore , the first three terms are t , t²/2 , -3/2.t³ .
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Lance Industries borrowed $130,000. The company plans to set up a sinking fund that will repay the loan at the end of 18 years. Assume a 6% interest rate compounded semiannually. What amount must Lance Industries pay into the fund each period? (Round your answer to the nearest cent.)
The amount must Lance Industries pay into the fund each period is $2,054.49
Define Sinking Funds
A fund set aside to cover a certain future expense is known as a sinking fund. The sinking fund can be thought of as an annuity if equal contributions are made on a regular basis; its value will rise until it is sufficient to pay the future expense.
Given,
Lance Industries borrowed = $130,000
Time = 18 years
Interest rate = 6%
The future value is,
FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )
PMT = payment fund semiannually.
i = 6% or 0.06
m = 2 (semiannually will be 2 times per year)
n = 18 * 2 = 36 periods
FV₃₆ = $130,000
Now, plug in the values in formula
FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )
130,000 = PMT ( (1 + 0.06/2)³⁶ - 1 ) / (0.06/2) )
130,000 = PMT ( (1.03)³⁶ - 1 ) / (0.03) )
PMT = 130,000 * ( 0.03 / (1.03)³⁶ - 1 ) )
= $2,054.49
Hence, the amount must Lance Industries pay into the fund each period is $2,054.49.
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In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°, what is the value of x?
A: 35
B: 37
C: 44
D: 71
The required simplified value of the x is given as 5.
Given that,
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x + 5 = 180
5x = 175
x = 35
Thus, the required simplified value of the x is given as 5.
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A cement mix calls for 2 cups of water and 1 1/4 pounds of mix to make five large tiles stick to the ground, Yolanda has plenty of water but only 4 3/8 pounds of mix. How many large tiles (including parts of a tile) can she stick to the ground? You MUST think conceptually and illustrate your thinking with a model. Do NOT use proportional reasoning.
175/26 large tiles can she stick to the ground.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A cement mix calls for 2 cups of water and [tex]1\frac{1}{4}[/tex] pounds of mix to make five large tiles stick to the ground,
2+ [tex]1\frac{1}{4}[/tex]=5
2+5/4
13/4
Which means 13/4 is needed for 5 large tiles.
Yolanda has plenty of water but only [tex]4\frac{3}{8}[/tex] pounds of mix
We need to find how many large tiles can she stick to the ground.
Let x be the number of tiles.
[tex]4\frac{3}{8}[/tex] =35/8
So
(13/4)/5=(35/8)/x
Apply cross multiplication
13/4x=35/8×5
13/4x=175/8
x=175/8×4/13
x=700/104=350/52=175/26
Hence, 175/26 large tiles can she stick to the ground.
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Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at end of the 12th year, the company invests $8,000 at end of each year at 5% compounded annually. The amount of the original loan was
Multiple Choice
$127,337.01
$70,905.60
$127,636.80
$70,950.60
The required future value of the annuity is $127,336.80.
Jones Company borrowed money that must be paid back in 12 years. To ensure that the debt is repaid by the end of the 12th year, the corporation invests $8,000 at the end of each year at a rate of 5% compounded yearly.
Compute the future value of the annuity as follows:
Future value = Annuity - FVIFA
FVIFA is taken from the table, and substitutes the value of the annuity in the above formula
Future value = $8,000 × 15.9171
Apply the multiplication operation, and we get
Future value = $127,336.80
Therefore, the required future value of the annuity is $127,336.80.
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I need help with this problem
Step-by-step explanation:
of the following is the correct arrangement of the following atoms in order of DECREASING first ionization energy?
O>Te>Se>Po
Po>Te>Se>O
O>Se>Te>Po
Po>Se>Te>O
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true?
A) The survey results are invalid because it’s impossible to word questions about politics without creating bias.
B) The survey results are invalid because only surveys conducted by phone are free from bias.
C) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money.
D) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
E) Since the survey was sent to randomly-selected households, it should be free of bias.
Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.
What is politics?
Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.
Given,
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.
We have to find the correct statement about the survey from the given options;
Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.
The correct statement about the survey is option c;
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where is root 19??????
Answer:
4.358
Step-by-step explanation:
sqrt(19) = 4.358
If the VO2 max test scores were normally distributed with a mean, median, and mode of 44ml/kg/min and standard deviation of 8, which of the following would be true. a.We should expect 16% of college students to score at least 36 on the VO2max test. b. We should expect 50% of college students to score 44 on the VO2max test. c. We should expect 84% of college students to score at least 36 on the VO2max test. d. We should expect at least 68% college students to score 36 on the VO2max test.
The VO2max test resulted by z score should result in a minimum score of 36 for 84% of college students.
To find the answer, we will use the z-score formula:
z = (x - μ)/σ
We will use the given values for the mean (μ = 44), the standard deviation (σ = 8), and the value we are looking for (x = 36).
z = (36 - 44) / 8
z = -1
We can then look up the percentage of values equal to or below -1 on the standard normal distribution table. This value is 84%. Therefore, we should expect 84% of college students to score at least 36 on the VO2max test.
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Find the Maclaurin series for f(x) = xe^2x and its radius of convergence. Use only the definition of a Maclaurin series.
The Maclaurin Series of xe²ˣ: x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
Given that,
f(x) = xe^2x
Taylor series of function f(x) at a is defined as:
f(x) = f(a) + f'(a)/1!/(x-a) +f''(a)/2! (x-a)² +....
Maclaurin series of Function F(x) is a Taylor series of Function f(x) at: a=0
f(x) = f(0) + f'(0)/1! /(x) +f''(0)/2!/ (x)² +....
Apply the Maclaurin Formula
= 0 +d/dx (xe²ˣ)(0)/1! x + d²/dx² (xe²ˣ)(0)/2! x² +....
Evaluate the derivatives :
= 0 + 1/1! x + 4/2! x² + 12/3! x³ + ...
Refine :
= x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
So, the Maclaurin series for f(x) = xe^2x is x + 2x² + 2x³+ 4/3x⁴+ 2/3x⁵ +....
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choose r for a qualification for a member of the house of representatives, s for a qualification for a senator, or b for both.
Qualifications for members of house of representatives and senate
r ;- Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
s ;- Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
Given,
The House of Representatives is the lower body of the United States Congress, and the United States Senate is its upper chamber. The United States' national bicameral legislature is made up of them all. Washington DC
Then,
Qualification for a member of the house of representatives, r ;-
Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
Qualification for a senator, s ;-
Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
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The differential treatment of individuals or groups without reference to behavior, qualifications, or other legal factors, resulting in a difference in outcome, is known as discrimination. Discrimination can occur based on various factors such as race, gender, age, religion, disability, or nationality.
There are different forms of discrimination, including: 1. Direct discrimination: This occurs when someone is treated less favorably because of a specific characteristic or attribute. For example, if an employer refuses to hire someone solely based on their gender, it would be considered direct discrimination. 2. Indirect discrimination: This happens when a seemingly neutral policy, criterion, or practice puts individuals with a particular characteristic at a disadvantage. For instance, if a job requires a height requirement that disproportionately affects a certain racial group, it would be considered indirect discrimination.
3. Systemic discrimination: This refers to discrimination that is built into the structures, policies, and practices of an organization or society. It may be unintentional but still leads to unequal outcomes. An example is when certain communities consistently receive lower funding for education compared to others, leading to systemic disadvantages for students in those areas.
Discrimination can have negative impacts on individuals and society as a whole, perpetuating inequality and hindering social progress. It is important to promote equality, fairness, and inclusivity to create a just and equitable society.
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what is the result of the following boolean expression, if x equals 5, y equals 3, and z equals 8? not (x < y or z > x) and y < z
False Reason:...This is false if (x=5) (y=3). and denotes the requirement that both be true.
This is true: (z=8) > (x=5) The entire statement is false because it relies on the and condition rather than the OR condition.
What is an example of a Boolean expression?
A Boolean expression(named for mathematician George Boole) is an articulation that assesses to one or the other valid or misleading. Let's take a look at some examples from common speech: Pink is my favorite color. valid • I'm anxious about PC programming. False This book is a laugh-out-loud good read.
Which three Boolean expressions are there?
There are three fundamental Boolean operators: What's more, OR, and NOT.
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DUE SOON!!! NEED HELP ON THESE TWO QUESTIONS PLEASE!
DUE SOON AND I DONT UNDERSTAND IT!
MANY THANKS!
WILL GET 100 POINTS! PLEASE HELP!!
The restrictions for x and y are given as follows:
3. x ∈ W, y ∈ W.
5. x ∈ W, y ∈ W.
What are the restrictions?To obtain the restrictions, the first step is classifying the variables as either discrete or continuous, as follows:
Discrete variables are countable values, that can assume only whole or integer values, that is, they do not assume decimal values.Continuous variables can assume decimal values, hence they are real values.In this problem, the variables are both resumed as follows:
Number of tickets sold in the Super Bowl.
The possible values are given as follows:
0, 1, 2, ...
Which are countable values, hence discrete, and that also cannot assume negative values, hence they belong to the whole set and not the integer set, thus the restrictions are:
x ∈ W, y ∈ W.
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NO LINKS!!
f(x)= (x^2 + x - 12)/(x^2 + 6x + 9)
Discuss the behavior of f near any excluded x-values/
a. f(x) --> -∞ as x --> 3^+ and as x--> 4^-, f(x) --> ∞ as x --> 4^+ and as x --> 3^-
b. f(x) --> ∞ as x --> 4^+ and as x --> 4^-
c. f(x) --> -∞ as 4^+ and as x --> 4^-, f(x) --> ∞ as 3^+ and as x --> 3^-
d. f(x) --> -∞ as x --> 3^+ and as x --> 3^-, f(x) --> ∞ as x --> -4^+ and as x --> -4^-
e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-
Answer:
e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-
Step-by-step explanation:
You want to know the behavior of f(x)= (x^2 + x - 12)/(x^2 + 6x + 9) near any excluded x-values.
DomainThe function can be factored as ...
[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}=\dfrac{(x+4)(x-3)}{(x+3)^2}[/tex]
The excluded values are values of x where the denominator is zero. The only excluded value is x = -3. (eliminates all answer choices except E)
Asymptotic behaviorAt either side of x = -3, the sign of the numerator is negative and the sign of the denominator is positive. That makes f(3-) < 0 and f(3+) < 0.
f(x) will never approach +∞, but f(x) approaches -∞ as x nears -3 from either direction.
Answer:
[tex]\textsf{e)} \quad f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}[/tex]
Factor the numerator:
[tex]\implies x^2+x-12[/tex]
[tex]\implies x^2+4x-3x-12[/tex]
[tex]\implies x(x+4)-3(x+4)[/tex]
[tex]\implies (x-3)(x+4)[/tex]
Factor the denominator:
[tex]\implies x^2+6x+9[/tex]
[tex]\implies x^2+3x+3x+9[/tex]
[tex]\implies x(x+3)+3(x+3)[/tex]
[tex]\implies (x+3)(x+3)[/tex]
[tex]\implies (x+3)^2[/tex]
Therefore, the rational function is:
[tex]f(x)=\dfrac{(x-3)(x+4)}{(x+3)^2}[/tex]
As the degree of the numerator is equal to the degree of the denominator, there is a horizontal asymptote at y = 1.
A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.
[tex]\implies (x+3)^2=0[/tex]
[tex]\implies x+3=0[/tex]
[tex]\implies x=-3[/tex]
Therefore, there is a vertical asymptote at x = -3.
As there is a vertical asymptote at x = -3, the excluded x-value is x = -3.
As x approaches x = -3 from both sides, the numerator of the rational function approaches -6 and the denominator approaches a very small positive number. Therefore, the function approaches a very large negative number.
Therefore, the end behaviour of the function as it approaches the excluded value is:
[tex]f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]mathematics and statistics teacher rex boggs, from australia, weighed the bar of soap in his shower stall before showering in the morning. the data on day and soap weight (in grams) appear in the table. (notice that he forgot to weigh the soap on some days!) here are the data.
As per the concept of linear regression, the equation of the data is y = 133.1807 − 6.3096x.
The term linear regression means to determine the character and strength of the association between a dependent variable and a series of other independent variables.
Here we have given that mathematics and statistics teacher rex boggs, from Australia, weighed the bar of soap in his shower stall before showering in the morning. And the data on day and soap weight (in grams) appear in the table.
Here we need to find the linear regression equation that represents the given situation.
Based on the concept of linear regression, we know the the general formula for the regression is written as,
=> y = a + bx
FRom the given data, we have identified the value of the functions as,
a = 133.1807
b = -6.3096
r² = 0.9962
r = -0.9981
When we apply these values on the formula, then we get the equation as,
Then it implies the regression line is,
=> ŷ = a + bx = 133.18076.3096x
here a represents the day and y represents the weight in grams.
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all the edges of a cube are expanding at a rate of 4 in. per second. how fast is the volume changing when each edge is 10in. long?
The rate at which the volume of the cube is changing is 1200 in³/seconds.
What is volume?Volume is the space occupied by a solid object.
To calculate the rate at which the volume of the cube is changing, we use the formula below.
Formula:
dV/dt = (dL/dt)×(dV/dL)................ Equation 1Where:
dV/dt = Rate at which the volume of the cube is changing dL/dt = Rate at which the edge of the cube is expandingdV/dL = Change in the volume of the cube with respect to the edge.From the question,
Given:
dL/dt = 4 in. per secondsL = 10 inIf, the volume of a cube is V = L³,
Then,
dV/dL = 3L² = (3×10²) = 300 in²Substitute these values into equation 1
dV/dt = 4×300dV/dt = 1200 in³/secondsHence, the rate at which the volume is changing is 1200 in³/seconds.
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assume that a and b are positive integers. for each statement below, determine whether the statement is true or false, and indicate your answer in the appropriate box
Given Statement (a!)b = ab! is false becuase it is not appropriate to represent factorial like this.
What is Factorial?
In mathematics, the term "Factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point. Thus, factorial seven is denoted by the symbol 7!, which stands for 1*2*3*4*5*6*7. Factorial 0 is equivalent to 1 by definition.
(a!)*b = ab!
this depends on the value of a and b.
I'm not sure if the phrase "ab!" means to multiply a by b and then compute the factorial of the resulting product, as in (ab)!, or to compute the factorial of b first and then multiply this by a, as in a(b!). Either way, the assertion is false.
Given Question is incomplete Complete Question here:
assume that a and b are positive integers. for each statement below, determine whether the statement is true or false, and indicate your answer in the appropriate box (a!)b = ab!
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When you are doing a survey of the time it takes for a person to run 100m, which unit would you use?
When you are doing a survey of the time it takes for a person to run 100m, the unit that you would you use is seconds.
What is unit?A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.
A unit is any standard that is used to compare measurements. Unit conversions allow measurements of a property to be converted from one unit to another, such as centimeters to inches.
In this case, time is measured in seconds.
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In Norway last year, the lowest temperature was −15°C. In Norway last year, the highest temperature was 42°C greater than the lowest temperature. Work out the highest temperature in Norway last year
Answer:
27°
Step-by-step explanation:
Let h = highest temperature
h = -15 + 42
h = 27°
Function A is represented by the equation y= 2x+1. Function B is a linear function that goes through the points shown in the table. X 1 3 4 6 3 11 15 23 Which statement correctly compares the rates of change of the two functions?
A. the rate of change of function a is 1
The rat of change of function b is 4
B. the rate of change of function a is 2
the rate of change of function b is 8
C. the rate of change of function a is 1
the rate of change of function b is 8
D. the rate of change of function a is 2
the rate of change of function b is 4
The rate of change of the linear function A is 2, and the one of function B is 4, then the correct option is D.
Which statement correctly compares the rates of change?A general linear function is written as:
y = a*x + b
Where a is the rate of change and b is the y-intercept.
In this case, we know that function A is:
y = 2x + 1
Then the rate of change is 2, and the y-intecept is 1.
We also know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the rate of change of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
In the case of function B we have the table:
x: 1 3 4 6
y: 3 11 15 23
We can use any two points on the table, if we use the first two ones:
(1, 3) and (3, 11) we will get:
a = (11 - 3)/(3 - 1) = 8/2 = 4
The rate of change of function B is 4, then the correct statement is the one in option D.
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find the future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly. (round your answer to the nearest cent.) $
The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..
The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.
P = PMT× ((1+r)ⁿ −1)/r
where:
P---> Future value of an annuity stream
PMT---->Dollar amount of each annuity payment
r -->Interest rate (also known as discount rate)
n--->Number of periods in which payments will be
We have given that
Present value for an Annuity = $200
compounded rate , r = 13%
but compounded quarterly, then, r = 13%/4
= 0.13/4 = 0.325
Number of years , n = 2 + 1/2 = 5/2
then change into quarterly, n = 5/2 × 4 = 10
Future value formula ,
F.V = PMT ( (1+i)ⁿ - 1)/r
=> Future value = 200((1+0.325)^10/0.325)
=> F.V = 10263.734
Hence, the future value of an annuity is $10263.734..
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Find an equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5.
Equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
What is Ellipse?An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Given,
center −3, 5,
Major axis of length 8
Endpoint of minor axis 0, 5.
Standard form of equation for an ellipse with vertical major axis:
(x-h)²/b²+(y-k)²/a²=1, a>b
(h,k)=(x,y) coordinates of center.
(-3, 5) are coordinates of centre
given length of vertical major axis:=8=2a=4
a=4
a²=16
Length of minor axis=b=5
b²=25
Hence, equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
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The stock of WAL-MAT pays a dividend of $.88. The stock opened at $18.25 and closed at $18.33. The stock yield is:
Multiple Choice
4.8%
4.2%
4.1%
The stock yield for the stocks will be 4.8%. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
To get the stock to yield use this formula - annual dividend / current stock price or share price
Substitute the dividend of $.88 and the closing price of $18.33 to the formula above. Divide and simplify.
Stock yield = .88 / 18.33
Stock yield = 0.0480 x 100
Stock yield = 4.8%
Therefore, the stock yield for the stocks will be 4.8%. The correct option is A.
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find the indefinite integral using integration by parts with the given choices of u and dv. x2 ln(x) dx;
Indefinite integral using integration by parts from x2 ln(x) dx is
[tex]\frac{1}{3}[/tex] [tex]X^{3\\}[/tex] (ln(x) - [tex]\frac{1}{3}[/tex]) + C
The given choice of u and dv
∫ [tex]x^{2} ln(x) dx[/tex]
we can use the formula
∫ u dv = uv - ∫ v du
Then split the component
u = [tex]ln(x)[/tex] du = [tex]\frac{1}{x}[/tex][tex]dx[/tex]
dv = [tex]x^{2}[/tex] v = [tex]\frac{1}{3}x^{3}[/tex]
∫ u dv = uv - ∫ v du
∫ [tex]x^{2} ln(x) dx[/tex] = ln(x) [tex]\frac{1}{3}x^{3}[/tex] - ∫ [tex]\frac{1}{3}x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx
= [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3}[/tex] [tex]\frac{1}{x}[/tex] dx
= [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{3} . x^{-1}[/tex] dx
= [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] ∫ [tex]x^{2}[/tex] dx ----> ∫ [tex]x^{2}[/tex] dx = [tex]\frac{1}{3} x^{3} + C[/tex]
= [tex]\frac{1}{3}x^{3}[/tex] ln(x) - [tex]\frac{1}{3}[/tex] [tex]\frac{1}{3} x^{3} + C[/tex]
= [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]
Therefore Indefinite integral using integration by parts
∫ [tex]x^{2} ln(x) dx[/tex] is [tex]\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C[/tex]
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Let P (t) represent the amount of _ certain drq milligrams; that = he bloodstream time hou? The rate at which the= drug leaves the bloodstream proportional to the amount of the drug bloodstream: The amount of the drug in the bloodstream can be modeled by # KP ; where constant and- time; hours At time 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour Which of the following an expression for P (t) P (t) = 500 0.23t P (t) = 500 4t P (t) = s0e 0.23 P (t) = e-02x + 499
As proportional relationship, the amount decreasing at a rate milligrams per hour expression P(t) = 500 + e⁻⁰²ˣ
Proportional relationship:
In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.
Given,
Here we have the rate at which the= drug leaves the bloodstream proportional to the amount of the drug bloodstream: The amount of the drug in the bloodstream can be modeled by K; where constant and- time; hours At time 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.
Here we need to find the expression.
While we looking into the given question, we have identified the following details,
=> Bloodstream = 500 milligrams
Here they state that the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.
So, the expression for this proportional relationship is written as,
=> P(t) = 500 + e⁻⁰²ˣ
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The price of a gift plus 14% delivery charge comes to a total cost of $19.38. What was the price of the gift?
Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity.
Answer:
1.14x = 19.38
$17
Step-by-step explanation:
Let the price before delivery charge = x.
The charge is 14%, so it is 14% of x, or 0.14x.
The original price plus charge is x + 0.14x, or 1.14x.
1.14x = 19.38
x = 19.38/1.14
x = 17
The price is $17
If I earn 100% more than you, then you must earn 50% less than me
Please help. I tried and couldn’t solve it
Using the law of cosines, the measure of the angles are
α ≈ 127°
β ≈ 28°
γ ≈ 25°
Law of Cosines: Calculating the angles in a triangleFrom the question, we are to solve the triangle.
To solve the triangle, we will determine the value of the unknown angles.
Using the law of cosines, we can write that
cosα = (b² + c² - a²)/2bc
From the given information,
a = 34
b = 20
c = 18
Thus,
cosα = (20² + 18² - 34²)/2(20)(18)
cosα = -432/720
cosα = -0.6
α = cos⁻¹(-0.6)
α = 126.8699°
α ≈ 127°
Calculating angle β
cosβ = (a² + c² - b²)/2ac
cosβ = (34² + 18² - 20²)/2(34)(18)
cosβ = 1080/1224
β = cos⁻¹(1080/1224)
β = 28.0724°
β ≈ 28°
To determine angle γ
α + β + γ = 180° (Sum of angles in a triangle)
127° + 28° + γ = 180°
155 ° + γ = 180°
γ = 180° - 155°
γ ≈ 25°
Hence,
α ≈ 127°
β ≈ 28°
γ ≈ 25°
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Suppose that survey is planned to estimate the proportion of population that is left-handed The sample data will be used to form confidence interval: Which one of the following combinations of sample size and confidence leve will give the widest interval? n E 500, confidence level 909 n = 1,000, confidence level 909 n = 500, confidence level 959 n = 1,000, confidence level 959 Explain why this sample size and confidence level will give the widest interval: The Select-- sample size and Select- confidence level will both tend to increase the width of the confidence interval:
The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.
In this question, we have been given the combinations of sample size and confidence level.
We need to select a combinations of sample size and confidence level that will give the widest interval.
We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.
As we know increasing the confidence will increase the margin of error which results in a wider interval.
But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.
This means, for the widest interval we need to select a high confidence interval and small sample size.
Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.
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How long does it take to finish A Christmas Carol?; How many stages are in A Christmas Carol?; How did Scrooge change from the beginning to the end?; What is the time and place of A Christmas Carol?
Average one hour 45 minutes time is taken to read A Chirstmas Carol Novel.
There is total five chapters in this novel. In the ed of of beginning, Scrooge has completely transformed into a charitable, altruistic man. A chirstmas Carol is at a time when the British were investigating and reassessing past Christmas
traditions and place is Washington.
A Christmas Carol:The average reader will spend 1 hour 4 minutes reading this book at 250 WPM (words per minute). A Christmas Carol is set in London during the Victorian era. The events of the story take place on Christmas Eve at Ebenezer's Scrooge home, where various events are shown by three visiting spirits. Charles Dickens wrote A Christmas Carol at a time when he was very critical of his writing and the world around him.
Dickens wrote A Christmas Carol at a time when the British were investigating and reassessing past Christmas traditions, including carols, and more recent practices such as Christmas cards and Christmas trees. He was influenced by his own adolescent experiences and by other writers' Christmas stories, such as Washington in his Irving and Douglas in his Jerold.
The book is divided into his five chapters, which Dickens entitled "Staves".
By the end of the novel, Scrooge has completely transformed into a charitable, altruistic man, rather than a misanthrope. This concept becomes apparent when you say, "I'm light as a feather, happy as an angel, and so baby." Scrooge changed his attitude and behavior.
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Fill in the missing digits to find the base 2 representation of 59.
To find the base 2 representation of 59, we need to express 59 as a sum of powers of 2.
The powers of 2 are: 1, 2, 4, 8, 16, 32, 64, 128, etc.
The largest power of 2 that is less than or equal to 59 is 32. The next largest power of 2 is 16. The largest power of 2 that is less than or equal to the remaining value (59 - 32 = 27) is 16. The largest power of 2 that is less than or equal to the remaining value (27 - 16 = 11) is 8. The largest power of 2 that is less than or equal to the remaining value (11 - 8 = 3) is 2. The largest power of 2 that is less than or equal to the remaining value (3 - 2 = 1) is 1.
The base 2 representation of 59 is therefore:
32 + 16 + 8 + 2 + 1
which can be written as:
111011
Therefore, the base 2 representation of 59 is 111011.
Answer:
0111011
Step-by-step explanation:
By doing L.C.M of 59 by 2 only
__2__[_59__
__2__{_29__ ----->remainder=1
__2__{__14__ ----->remainder=1
__2__{__7___----->remainder=0
__2__{__3___----->remainder=1
__2__{__1___------>remainder=1
__2__{__0__------->remainder=1
__2__{__0__------->remainder=0
answer: 0111011
