The value of the indefinite integral [tex]\int [z^2 + \frac{1}{(1-z)^8}]dz[/tex] will be [tex][ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c[/tex].
Given that:
[tex]\begin{aligned} I &= \int \left [z^2 + \dfrac{1}{(1-z)^8}\right] dz \end{aligned}[/tex]
The indefinite integral, also known as an antiderivative, represents the family of functions whose derivative is equal to the given function. It is denoted by the symbol ∫.
Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
Let 1 - z = u, then -dz = du and 1 - u = z. Then we have
[tex]\begin{aligned} I &= -\int \left [(1-u)^2 + \dfrac{1}{u^8}\right] du\\I &= \left [ \dfrac{(1-u)^3}{3} - \dfrac{1}{7u^7}\right] + c \\I &= \left [ \dfrac{(z)^3}{3} - \dfrac{1}{7(1-z)^7}\right ] + c\end{aligned}[/tex]
The value of the indefinite integral [tex]\int [z^2 + \frac{1}{(1-z)^8}]dz[/tex] will be [tex][ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c[/tex].
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What is the length of WY?
The length of WY is 4.9.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
From two triangles the proportional sides are
11.1/5.55=8/4=9.8/WY
2=2=9.8/WY
So 2=9.8/WY
WY=9.8/2
WY=4.9
Hence, the length of WY is 4.9.
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27.3=3/4y
y=?
Can you please help me?
Answer: 36.4
Step-by-step explanation:
27.3= (3/4)y
divide both sides by 3/4 to isolate the y
27.3/(3/4)= 36.4
To double-check, plug in 36.4 to y; should get you 27.3
If co A = 1/2 then what i the poitive value of co 1/2 B,in implet radical form with a rational denominator?
The answer is cos(B/2) = 2√5 / 5
Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]
Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:
Regarding applying the cosine half-angle formula:
cos²(B/2) = (1 + cos B) / 2
put value of cos B =3/5 (given)
cos²(B/2) = (1 + 3/5) / 2
on simplifying
cos²(B/2) = (8/5) / 2
cos²(B/2) = 4/5
on taking under root we get
cos(B/2) = 2/√5
use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5
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Hello! help quick thank you
The expressions for (h - g)(x) and (h . g)(x) are -x - 8 and (x - 5)(2x + 3)
While the function (h + g) (-1) is -5
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
g (x) = 2x+3
h(x) = x - 5
This means that
(h - g)(x) = x - 5 - 2x - 3
Evaluate
(h - g)(x) = -x - 8
Also, we have
(h . g)(x) = (x - 5)(2x + 3)
Lastly, we have
(h + g)(-1) = (x - 5) + (2x + 3)
So, we have the following equation
(h + g)(-1) = ((-1) - 5) + (2(-1) + 3)
Evaluate
(h + g)(-1) = -5
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three point charges are located at the corners of an equilateral triangle
At the four corners of an equilateral triangle are three point charges.
Due to the fact that three charges do not cancel one another out with Colombian force, the system can never reach equilibrium.
A subatomic particle's electric charge causes it to experience a force when it is in an electric and magnetic field.
What does the phrase "charge" actually mean?Electric charge is the property of matter that causes it to experience a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges. Energy is created by charge movement.
The most frequent charge carriers for positive and negative electric charges, respectively, are protons and electrons. The coulomb (C) is the standard unit of electric charge used by the International System of Units (ISO) (SI).
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Complete question -
Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic force are acting
By what percent is the population increasing/decreasing?
Angle bisectors split the sides of a triangle into a1, a2, b1, b2, c1, and c2. a1 = 11/3 a2= 22/3 b1 = 143/12. Find the perimeter
The perimeter of the triangle which has a bisector that splits a triangle into 6 sides would be = 47½
What is a bisector?A bisector is defined as the line that divides a shape into two equal parts.
The perimeter of triangle is the sum total of all the sides of the triangle. That is;
perimeter = a1 + a2 + b1 + b2 + c1 + c2
But the value of only 3 sides which is exactly half of the perimeter where given;
= 11/3+22/3+153/12
= 44+ 88+ 153/12
= 285/12
Therefore perimeter
= 285/12 + 285/12
= 570/12
= 47½
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let a = r − {1} and define f : a → a by f (x) = x x − 1 for all x ∈ a. (a) prove that f is bijective. (b) determine f −1. (c) determine f ◦ f ◦ f
(b) The value of f^(-1) is g.
(c) The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).
According to the question
(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).
Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.
Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.
Therefore, f is bijective.
(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.
Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.
Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.
Therefore, f^(-1) = g.
(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.
Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).
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Health and safety guidelines set the highest sound intensity level in the workplace to 90. 0 db. One workshop with 32 similar machines produces a sound intensity level of 92. 0 db. How many of them must be shut down to bring the workshop into compliance with the guidelines?.
The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.
A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.
Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.
It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.
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B-1. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places. )
The value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
The value of the test statistic in this case is the percentage of drivers under the age of 18 who still use a cell phone while driving. The test statistic is calculated using the following formula:
Test Statistic = (Number of Drivers under 18 using Cell Phone)/ (Total Number of Drivers under 18) x 100
For this case, the test statistic is calculated as follows:
Test Statistic = (150/200) x 100 = 75.00
Therefore, the value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
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Someone help me plss
The value of y when x = 45 using the given table is; y = (6/√2) + 4
How to solve function tables?The equation that represents the table is;
y = a cos x° + b
At x = 0, y = 10. Thus;
10 = acos 0 + b
cos 0 = 1
Thus;
10 = a + b ------(1)
At x = 60, y = 7
Thus;
7 = a cos 60° + b
cos 60 = 0.5
Thus;
7 = 0.5a + b -----(2)
Subtract eq 2 from eq 1 to get;
3 = 0.5a
a = 3/0.5
a = 6
b = 10 - 6
b = 4
Thus, the equation is;
y = 6cos x° + 4
At x = 45. we have;
y = 6cos 45° + 4
y = (6/√2) + 4
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find the 20th term of the A.p 3,6,9
Answer:
60
Step-by-step explanation:
1=3
2=6
3=9
The relation is Y=3X
Y20 = 3X20=60
Write an equation for a parabola that has a vertex at (2, 3), focus at (2,5), and directrix at y = 1.
f(x) = (x - 2)² +3
f(x) = 2(x - 5)² + 2
f(x)=(x-3)² + 2
f(x) = 2(x - 3)² + 1
Solve the system by substitution. -3x+3=y -x+3y=29
Answer: x = −2, y= 9
Step-by-step explanation:
Solving for X
-3x+3=y
-x+3y=29
Plug the top equation into the bottom one
-x+3(-3x+3)=29
Distribute
-x - 9x + 9 = 29
combine like terms
-10x + 9 = 29
-10x = 20
Divide the x
x = -2
Solving for Y:
Plug the value x into any of the equations'
-3(-2) + 3 = y
Distribute
6 + 3 = y
y = 9
To check if that is right, plug x into the other equation
-(-2) + 3y = 29
Distribute and combine like terms
2 + 3 y = 29
3y = 27
y = 9
M is located at ( -7 , -6 ) on coordinate plane . point p is located 5 units from m . point P has the same x coordinate as point m.
The possible locations of point P are (-7, -1) and (-7, -11)
How to determine the location of point P?From the question, we have the following parameters that can be used in our computation:
M = (-7, -6)
Also, we have"
P = 5 units from M
And
P = same x coordinate as point m.
This means that
P = (-7, y)
5 units from (-7, -6) is calculated as
(-7, -6 + 5) and (-7, -6 - 5)
Evaluate
(-7, -1) and (-7, -11)
Hence, the possible location is (-7, -1) and (-7, -11)
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WILL MARK BRAINIEST!!!
An artist is creating various sizes of stained-glass pieces to fit over windows that have a ratio 3:2 between the height and width. That means that the height of the glass portion can be represented as 3x and the width can be represented as 2x. The wooden trim adds 7 inches to the width and 8 inches to the height.
A: Using the length and width of the window what is the area of the glass portion? Show and explain your work.
B: What is the length and width, of the window and the pane? Show and explain your work.
C: Using the length and width you calculated from Part B, what is the area of the window and the pane? Show and explain your work.
D: What is the area of just the wooden pane? Show and explain work.
A. The area of the glass portion is 6x². B. Length of window and pane is 3x + 8 inches, and Width is 2x + 7 inches. C. Area of the window and pane is 6x² + 23x + 56. D. Area of the wooden pane is 23x + 56 inches².
A: The area of the glass portion can be found by multiplying the length and width of the glass.
Given that the height of the glass portion can be represented as 3x and the width can be represented as 2x, we have:
Area of glass portion = 3x × 2x = 6x²
B: To find the length and width of the window and the pane, we must add the wooden trim to the height and width of the glass portion. The wooden trim adds 7 inches to the width and 8 inches to the height, so we have:
Length of window and pane = 3x + 8 = 3x + 8 inches
Width of window and pane = 2x + 7 = 2x + 7 inches
C: Using the length and width from Part B, we can calculate the area of the window and the pane by multiplying the length and width:
Area of window and pane = (3x + 8) × (2x + 7) = 6x² + 23x + 56
D: To find the area of just the wooden pane, we subtract the area of the glass portion from the area of the window and the pane:
Area of wooden pane = Area of window and pane - Area of glass portion = 6x² + 23x + 56 - 6x² = 23x + 56 inches²
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Help and show work pls I’ll mark brainlist
f(x) = x + 4. q(x) = 12x1
Solve for: 1(g(-3))
The value of the composite function f(g(-3) is -32
What is the value of h(1)?From the question, we have the following parameters that can be used in our computation:
f(x) = x + 4. q(x) = 12x
The above are individual functions
This means that
f(g(x)) = 12x + 4
For f(g(-3)), we have
f(g(x)) = 12 * -3 + 4
Evaluate
f(g(x)) = -32
Hence, the value of the composite function is -32
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Two year ago, a car wa valued at $24,000. Thi year, the value of the car i $23,160. What wa the percent decreae in the value of the car?
A car was worth $24,000 two years ago. The automobile is worth $23,160 this year. 3.5% of the value of the car has decreased.
How to calculate percent?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage. An enormous, red percentage symbol with a black outline. If you multiply two percentages that are fractions of 100 or decimals, you can find the percentage of another percentage. Calculating, for instance, 50% of 40% results in (50/100) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%. As we can see, it provides us with the exact same response as the first approach: 2/5 as a percentage equals 40%. A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed.24,000 - 23,160 = 840
840/24,000 = 0.035
Simplifying the above equation, we get,
0.035 = 3.5%
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
What is the domain of the relation?
{−3, −2, −1, 0, 1, 2, 4}
{−3, 0, 1, 4}
{−2, −1, 0, 1, 4}
{−3, −1, 0, 2, 4}
The correct option representing the domain of the relation is given as follows:
{−3, −1, 0, 2, 4}
How to obtain the domain of the relation?The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, representing the number of years.
The values of x are the values of x for which there is a dot, hence they are given as follows:
x = -3.x = -1.x = 0.x = 2.x = 4.Meaning that the fourth option represents the correct option.
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a boat travling at an average speed of 30 miles per hour. how far will the boat travle in 2 seconds
Answer:
The boat traveling at 30 miles per hour will travel 30 * (2/3600) = 0.05 miles in 2 seconds.
Step-by-step explanation:
Here's a step-by-step explanation to find the distance traveled by the boat in 2 seconds:
Start with the speed of the boat, which is given as 30 miles per hour.
To find the distance traveled in 2 seconds, we need to convert the speed from miles per hour to miles per second.
To convert from miles per hour to miles per second, divide the speed by 3600 (since there are 3600 seconds in an hour).
30 / 3600 = 0.008333333 (miles per second)
Multiply the speed in miles per second by the time in seconds to find the distance traveled.
0.008333333 * 2 = 0.016666666 miles
So the boat will travel 0.016666666 miles in 2 seconds, or approximately 0.05 miles.
the accurate scale drawing shows a car and a lamp post
the car is a real width of 1.5 metres
find an estimate for the real height, in meters of the lamp post
An estimate of the real height of the lamp post is 9m.
What is the estimate of the real height?The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm
here, we have,
Scale = length of the lamp post / height of the car
10.8 / 1.8 = 6
Now, multiply the scale by the width of the car.
The real height of the lamp post = 6 x 1.5 = 9m
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Nvm I’ll just fail lol
Answer: probably greater than 3 1/2 inches, since bumper stickers are usually wider than they are tall
Step-by-step explanation:
Andre ran 5 1/2 laps of a track in 8 minutes at a constant speed. It took Andre x minutes to run each lap. Select all the equations that represent this equation
Here, we don't know the exact values for the speed or the lap length, so we need to use symbols in the equation i.e., x= 8 / (5.5 / lap length × speed ).
There are a couple of ways to approach this problem, but one common method is to use the formula: distance = speed x time.
To find the time it took Andre to run each lap, we need to find the distance he covered in 8 minutes and then divide that by the number of laps. Here are the equations:
1. Distance = 5.5 laps x lap length
2. Distance = speed x 8 minutes
3. x = (5.5 x lap length) / (speed x 8)
4. x = 8 / (5.5 / lap length x speed)
Note that we don't know the exact values for the speed or the lap length, so we need to use symbols in the equations.
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Which quantity is proportional to 8⁄12?
Check all that are true.
16⁄36
12⁄16
24⁄36
2⁄3
18⁄24
The quantities that are proportional to 8⁄12 are 24 / 36 and 2 / 3.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that the fraction is 8 / 12. The equivalent expression will be calculated as:-
8 / 12 = 2 / 3
16⁄36 = 4 / 9
12⁄16 = 3 / 4
24⁄36 = 2 / 3
2⁄3 = 2 / 3
18⁄24 = 3 / 4
The equivalent expressions will be 8 / 12 = 24 / 36 = 2 / 3.
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60 is 5 times as great as 12 write the equation
5x = 60
Step-by-step explanation:Let x be the value of 12. Then, 5 times as great as 12 is 5x.
So, the equation can be written as:
5x = 60
If you wish to undo this:To isolate x, we can divide both sides of the equation by 5:
x = 60/5
⬇️
x = 12
Find the sum of the interior angles and the measure interior angle for the given regular Polyguns round to the nearest tenif needed A 12-gon 102-gon 90-gon 36-gon
The sum of interior angle in 12-gon is 1800°, in 102-gon is 18000°, in 90-gon is 15840° and 36-gon is 6120° and measure of interior angle in 12-gon is 150°, in 102-gon is 176.5°, in 90-gon is 176° and 36-gon is 170°
What do you mean by polygon?A polygon is a two-dimensional geometric shape consisting of straight lines and having three or more sides. The sides of a polygon are line segments that connect its vertices, or corners, and the vertices are where the sides meet. The most common types of polyggon include triangles, squares, rectangles, and hexagons. There are also many types of irregular polygon, which have sides of different lengths or angles, as well as regular polygon, which have equal sides and equal interior angles.
The sum of the interior angles and the measure of the interior angle of a regular polygon can be found using the formula:
Sum of interior angles = (n-2) * 180°
Measure of interior angle = Sum of interior angles / n
Where n is the number of sides of the polygon.
For a 12-gon:
Sum of interior angles = (12-2) * 180° = 1800°
Measure of interior angle = 1800° / 12 = 150°
For a 102-gon:
Sum of interior angles = (102-2) * 180° = 18000°
Measure of interior angle = 18000° / 102 = 176.5°
For a 90-gon:
Sum of interior angles = (90-2) * 180° = 15840°
Measure of interior angle = 15840° / 90 = 176°
For a 36-gon:
Sum of interior angles = (36-2) * 180° = 6120°
Measure of interior angle = 6120° / 36 = 170°
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Solve the equation for x.
−0.24x − 16.4 = 1.96
x = −60.2
x = 60.2
x = −76.5
x = 76.5
Answer:
254
Step-by-step explanation:
i think it is correct
Answer:
-76.5
Step-by-step explanation:
see image attached for sol
Which of the following functions are solutions of the differential equation y″−4y′−21y=0? A. y(x)=e7xy(x)=e7x
B. y(x)=0y(x)=0
C. y(x)=exy(x)=ex
D. y(x)=e−3xy(x)=e−3x
E. y(x)=e−xy(x)=e−x
F. y(x)=−3xy(x)=−3x
G. y(x)=7xy(x)=7x
The functions that are solutions of the differential equation y" - 4y' -21y = 0 is -Option E: y(x) = [tex]e^{-3x}[/tex] Option F: y(x) = [tex]e^{7x}[/tex]
Differential equation definitionA differential equation is any equation that has one or more terms and one or more derivatives of the dependent variable with respect to the independent variable.
The given differential equation is y" - 4y' -21 = 0
This can be written as characteristic equation -
m² - 4m - 21 = 0
m² - 7m + 3m - 21 = 0
m(m - 7) + 3(m - 7) = 0
(m + 3)(m - 7) = 0
m = -3 and m = 7
The general solution is given by
[tex]y = (C1 + xC2)e^{-3x}[/tex]
[tex]y = C1 e^{-3x} + C2 xe^{-3x}[/tex]
[tex]y = (C1 + xC2)e^{7x}[/tex]
[tex]y = C1 e^{7x} + C2 xe^{7x}[/tex]
So, now the solutions are y = [tex]e^{-3x}[/tex], [tex]y = xe^{-3x}[/tex], [tex]y = e^{7x}[/tex]and [tex]y = xe^{7x}.[/tex]
Therefore, the solutions are y = [tex]e^{-3x}[/tex] and [tex]y = e^{7x}[/tex]
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Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?
Answer:
Below
Step-by-step explanation:
Her base salary (500) for the week PLUS her comission (.3 * 1575)
totals 972.50 dollars
a matrix consisting entirely of zeros is called a
A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.
It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.
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