The integral of f (z) around the positively oriented circle |z|
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3
What is integral?In mathematics, an integral lends numerical values to functions to represent notions like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
With the exception of the point where z = z, where f(z) is analytic within and on C, let C be the smooth, simple closed curve except at z =z , then ,
[tex]\int\limits^_ {} \,[/tex] f(z) dz = 2πi [ res f(z)] z = [tex]z_{1}[/tex]
here f(z) is singular at z = -1,
res [tex]f(z)_{z = -1}[/tex] = [tex]\lim_{z\to \-1} z+1 f(z)_[/tex]
[tex]\lim_{z\to \-1}[/tex] [tex]z^{3}[/tex](1-3z)/(1+2[tex]z^{4}[/tex])
when z = -1 then f(z) = -4/3
Therefore [tex]\int\limits^_ {} \,[/tex]f(z) dz = 2πi (-4/3)
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3.
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What is the geometric mean of 7 and 12? 09.5
02/21
04√21
Answer:
9.16
Step-by-step explanation:
formula for Geometric mean is
b = √a × √c
a = 7 and c = 12
b = √ 7×12
b = √84
b = 9.16
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6(3w-4y) please help
Answer:
18w-24y
Step-by-step explanation:
distribute
6(3w-4y)
18w-24y
Lupe says that the product
of 4 and any number is even.
Does her statement make
sense? Explain.
Answer:
I'm not to sure what the answer is
Lupe's statement seems quite fair
When multiplied by 4, any number's pair
An even product will be produced
By this rule, we are not reduced
For example, take the number 6
Multiply it by 4, and what do you get?
The answer is 24, a multiple of 2
This confirms Lupe's statement is true
In conclusion, Lupe's statement rings true
It makes perfect sense, through and through
The product of 4 and any number
Will always be an even number.
Select the correct answer.
Which list orders the angles of triangle ABC from smallest to largest measure?
B
OA.
B.
O C.
OD.
130
180
ZA, ZC, ZB
ZC, ZA, ZB
ZB, ZC, ZA
ZA, 2B, 2C
120
Answer:
<B, <C, <A
Step-by-step explanation:
The order from smallest to largest angle is the same as the order from shortest to longest opposite side.
Sides from shortest to longest:
120, 130, 180
Angles from smallest to largest:
<B, <C, <A
Which two values of x are roots of the polynomial below?
x^2+ 5x + 9
The two values of x that are roots of the polynomial are:
x = -5 + i√11/2
x = -5 - i√11/2
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² + 5x + 9 = 0
It is in the form of ax² + bx + c
a = 1
b = 5
c = 9
Using the determinant.
x = -b ± √(b² - 4ac) / 2a
x = -5 ± √(25 - 36) / 2
x = -5 ± √-11 / 2
x = -5 ± i√11/2
Where i = √-1
Thus,
The roots of the polynomial are:
x = -5 + i√11/2 and x = -5 - i√11/2
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One number is 5 more than twice another and their sum is 23. Find the numbers.
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
One number is 5 more than twice another and their sum is 23.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
y = 2x + 5 ...1
x + y = 23 ...2
From equations 1 and 2, then we have
x + 2x + 5 = 23
3x + 5 = 23
3x = 23 - 5
3x = 18
x = 6
Then the value of the variable 'y' will be given as,
6 + y = 23
y = 23 - 6
y = 17
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
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Which of the following terms are equivalent to the slope in a proportional relationship? Select all that apply.
a.) Constant Rate of Change
b.) origin
c.) Change in y / Change in x
d.) rise/run
e.) inverse
Answer:
a.) Constant Rate of Change - yes
b.) origin - yes
c.) Change in y / Change in x - yes
d.) rise/run - yes
e.) inverse - Not apply
What is the difference between rate of change and slope coefficient?
The terms rate of change, gradient, slope coefficient, and rise over run are all equivalent to the slope in a proportional relationship. The slope of a line describes the rate at which a variable changes in relation to another variable. Rate of change is the same concept, but it is more general and can be applied to any relationship, not just linear. Gradient is another term for the slope of a line, which is the change in one variable compared to the change in another variable. Slope coefficient is a mathematical term for the slope of a line, which is the ratio of the vertical change to the horizontal change. Rise over run is another term for the slope of a line, which describes the rate of change by measuring the vertical change (rise) over the horizontal change (run). All of these terms describe the same concept, which is the rate of change in a proportional relationship.
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Please help with question 1.
Answer:
reflection over the y-axistranslation left 4, down 3Step-by-step explanation:
You want two transformations that will map segment AB to segment A"B", where the points are A(1, 1), B(5, 3), A"(-5, -2), B"(-9, 0).
ReflectionWe notice that the difference B-A is (5 -1, 3 -1) = (4, 2), and the difference B"-A" is (-9 -(-5), 0 -(-2)) = (-4, 2). These values have the same magnitudes, so we know no dilation is involved. The sign of the x direction of the segment has been reversed, which means the segment has been reflected horizontally. (B" is left of A", where B is right of A.)
Reflection over any vertical line will do, but the simplest is reflection over the y-axis.
The first transformation can be reflection over the y-axis.
TranslationThe reflected line segment will be ...
(x, y) ⇒ (-x, y)
A(1, 1) ⇒ A'(-1, 1)
B(5, 3) ⇒ B'(-5, 3)
The value that must be added to A' to move it to A" is ...
A" -A' = (-5, -2) -(-1, 1) = (-5 -(-1), -2-1) = (-4, -3) . . . . . . left 4, down 3
Similarly, the value that must be added to B' to move it to B" is ...
B" -B' = (-9, 0) -(-5, 3) = (-9 -(-5), 0 -3) = (-4, -3) . . . . . . left 4, down 3
That is, the entire segment A'B' can be moved to A"B" by a translation left 4 and down 3.
The second transformation can be translation left 4 and down 3.
__
Additional comment
The translation left could be accomplished by reflection over the line x = -2 instead of the y-axis.
The movement of the line segment could be accomplished in one transformation by rotation 126.87° clockwise about the point (-1.25, -2). The exact angle is arctan(-4/3) in the second quadrant.
Shana makes a 3 gallon batch of lemonade. Each 1 gallon batch requires 2.5 pints of fresh lemon juice. How many cups of lemon juice will Shana need for 3 batches?
There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
What is the probability of getting an even number or a 1?
The probability of getting an even number or a 1 is 11/20
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given that there are 20 cards numbers 1,2... 20.
A card is randomly drawn.
We have to find the probability of drawing either 1 or even card.
P(drawing even card) = no of even cards/total cards = 10/20= 0.5
P(drawing one) = no of 1's/total cards = 1/20 = 0.05
P(drawing both one and even card) = 0 (since impossible)
Hence P(drawing even or one) =0.5+0.05-0
=0.55
= 11/20
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Find the area of the figure. (Sides meet at right angles.)
7 in
2 in
5 in
8 in
4 in
5 in
2 in
7 in
Answer:
36
Step-by-step explanation:
27 km equals about how many miles?
27 kilometers to miles
1 kilometer = 0.621371 miles
27 kilometers * 0.621371 miles = [tex]\fbox{16.777 miles}[/tex]
Brody runs a farm stand that sells strawberries and grapes. Each pound of strawberries sells for $2.50 and each pound of grapes sells for $2. Brody made $160 from selling a total of 72 pounds of strawberries and grapes. Graphically solve a system of equations in order to determine the number of pounds of strawberries sold, x,x, and the number of pounds of grapes sold, yy.
The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given that the selling price of strawberries each pound = $2.50,
The selling price of grapes each pound = $2
The total earning = $160
Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,
x = y + 12 and 2.50x + 2y= 160
Solve the equation by substitution method;
x = 32 and y = 20
Therefore, the number of pounds of strawberries sold is 32
the number of pounds of grapes sold is 20.
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this is serious pls help ASAPPPPPPPPPPPPPPPPPPPPPP its due in 25 mins
Answer:
14,641
Step-by-step explanation:
11^4 = 11 × 11 × 11 × 11 = 121 × 11 × 11 = 1331 × 11 = 14,641
Answer:
14,641
Step-by-step explanation:
10^4 = 10000
11^4 > 10 ^4 so A is the answer
10. en Vision STEM Sound travels in
waves. In dry air at 20° Celsius, sound
travels about 343 meters in one second
How many meters will sound travel in
7 seconds?
In 2401 meters will sound travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.
Define distance.The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line. Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Given
Speed = 343 m
Time = 7 seconds
For distance,
Distance = Time × Speed
Distance = 343 × 7
Distance = 2401
In 2401 meters sound will travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.
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FOR BRAINLIEST Jada's pet turtle walked 10 feet, and then half that length again. b, C. d. Jada's baby brother walked 3 feet, and then half that length again.
Jadas hamster walked 4.5 feet and then half length That again
Jadas robot walked 1 foot then half that length again
a person walked x feet then half that length again
Answer:
a walked x feet then half that length again-step explanation:
Consider the two expressions 6x^3 + 9x^2 + 4x + 7 and 3x^2 + 2 + 6x^3 + 6x^2 + 4x + 5.
a) Show that the two expressions represent equal numbers when x=10.
b) Explain why these two expressions do not represent equal numbers when x = -3/2.
c) Show that these two expressions represent equal numbers for all x other than x = -3/2.
When x = 10 the equations are equal and when x gets any value the two equations are equal.
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.
When x = 10 the equation becomes
6x³ + 9x² + 4x + 7
6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
Both the equations are equal when x = 10
When x = -3/2 the equation becomes
6x³ + 9x² + 4x + 7
6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
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You are shown TUV below whose measure is 76°. Draw an angle bisector of
LTUV by clicking a dragging a ray out from the vertex at U.
Click and drag to draw a ray from the yellow dot.
To redraw, click and drag from the yellow dot again.
m/TUV = 76⁰
The bisector of the angle TUV is attached below.
What is an angle?
In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The steps to draw a bisector of an angle:
1) Cross both rays with an arc. Place the compass point at the vertex of the angle after opening it to any width. Swing the compass so the pencil creates an arc that spans the angle's two rays.
2) Make a vertical arc inside. Place the compass such that the point is at the spot where the first ray and the first arc connect. Swing the compass to create an arc that fits inside the angle.
3) To intersect the first interior arc, draw a second interior arc. Move the point to the spot where the first arc crosses the second ray without altering the compass's breadth. Draw an internal arc by swinging the compass and intersecting it with the initial interior arc you drew.
4) From the vertex to the spot where the arcs meet, draw a line. To make sure the line is exact, use a straightedge. This line cuts the angle in half.
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Here are yesterday's high temperatures (in Fahrenheit) in 13 U.S. cities.
50, 51, 55, 55, 59, 59, 64, 67, 67, 74, 77, 78, 80
Notice that the temperatures are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answer:
To find the five-number summary for a set of data, we need to find the minimum, first quartile, median, third quartile, and maximum of the data. To find the interquartile range, we subtract the first quartile from the third quartile.
The minimum temperature in the list is 50 degrees Fahrenheit. The maximum temperature is 80 degrees Fahrenheit. To find the median, we need to first find the middle value in the list. Since there are 13 temperatures in the list, the middle value is the seventh temperature, which is 64 degrees Fahrenheit.
To find the first and third quartiles, we need to divide the list into two halves at the median. The first half of the list contains the first six temperatures, and the second half contains the last six temperatures. The median of the first half of the list is the average of the third and fourth temperatures, which is 55 degrees Fahrenheit. The median of the second half of the list is the average of the sixth and seventh temperatures, which is 61.5 degrees Fahrenheit.
Therefore, the five-number summary for this data set is:
Minimum: 50
Lower quartile: 55
Median: 64
Upper quartile: 61.5
Maximum: 80
The interquartile range is the difference between the upper and lower quartiles, which is 61.5 - 55 = 6.5.
use implicit differeniation to find dy/dx x^2+xy+y^2+1=0
The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given,
x² + xy + y² + 1 = 0
Take the first derivative on both sides with respect to x as,
d/dx(x² + xy + y² + 1) = d/dx(0)
2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0
2x + x(dy/dx) + y + 2y (dy/dx) = 0
2x + y + dy/dx(x + 2y) = 0
Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".
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Sarah made a floral arrangement with 60% roses. If there were a total of 25 flowers in the arrangement, how many roses?
Answer:
Step-by-step explanation:
turn percentage into decimal :
60/100 = 0.6
Then times it by how many flowers there are :
0.6×25 = 15
And your answer should be 15.
First person to answer gets a Brainilest!!!Solve this math questions of the picture.
Answer: S wanted points I
Step-by-step explanation:
I need help with my math homework
A = {red, blue, green, yellow, orange} B = {pink, blue, purple, yellow, green} Find A ⋂ B.
According to the given sets, A ⋂ B = {blue, green, yellow}.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A ⋂ B:
A set called an intersection B has components that are found in both sets A and B.
The intersection of sets A and B is shown by the symbol, which is interpreted as "An intersection B" and written as A⋂B.
The set of components shared by all sets is the intersection of two or more sets.
So, we have:
A = {red, blue, green, yellow, orange}
B = {pink, blue, purple, yellow, green}
A ⋂ B which means common elements:
A ⋂ B = {blue, green, yellow}
Therefore, according to the given sets, A ⋂ B = {blue, green, yellow}.
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Help please, what is the slope and y intercept
slpoe is -1/2 and y-intercept is 2
If the perimeter of a trapezium is 68cm, its non -parallel sides are equal to 12cm each and its altitude is 4cm. The area of the trapezium is
Answer:
88 cm²
Step-by-step explanation:
Area of trapezium = [tex]\frac{1}{2}[/tex](a + b)h
12 * 2 = 24
68 -24 = 44
44 is (a + b) as they are the sum of the parallel sides of the trapezium.
h (altitude) = 4
[tex]\frac{1}{2}[/tex](44)(4) = 88 cm²
Answer:
88 cm², hope it helps.
5) An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the central angle made by the knife measures 120°, what is the diameter of the plate? Show all work.
6) If the area of a circumscribed square is 324 square feet, then
The diameter of the plate. show all work. will be 9.24 inches. The diameter is double of the hypotenuse.
What is the diameter?
A diameter is a line that travels through the center of an object and intersects the circumference at opposing ends. It measures twice as long as the object's radius.
The radius of the circle becomes the hypotenuse when a right triangle is formed by joining the edge of the knife to the center of the circle and the center of the knife to the center of the circle.
With the help of the trigonometric function, the value of the hypotenuse is found as;
sin60 = 8/h
h = 4.62 inches
The diameter of the plate is double the hypotenuse in the given figure;
D = 2 X h
D = 2 X 4.6
D = 9.8
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Ivanna is draining an aquarium. The graph shows the amount of water (in liters) in the aquarium versus time (in minutes).
(a) At what time does the amount of water in the aquarium reach 0 liters?
minutes
(b) Choose the statement that best describes how the time and amount of water are related. Then fill in the blank.
As time increases, the amount of water in the aquarium decreases.
At what rate is the amount of water decreasing?
liters per minute
As time increases, the amount of water in the aquarium increases.
At what rate is the amount of water increasing?
liters per minute
A linear function gives us the following:
a) At 0 seconds, there are 300 liters of water in the aquarium.
b) The amount of water is losing volume at a rate of 60 liters per minute as time goes on.
Given,
Linear function;-
Modeling a linear function involves:
y = ax + b
That where:
The rate of change, or a, is the slope, or how much y changes when x changes by one.B is the y-intercept, which is also known as the function's starting point and is the value of y at x = 0.The y-intercept in this problem is 300, hence 300 liters of water are present in the tank at 0 seconds.
The quantity drops by 60 liters each minute, so:
Water is losing volume at a rate of 60 liters per minute as time goes on.
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Which number line models the expression 1/8-(-3/4) ?
Answer: 7/8
Step-by-step explanation:
what is the slope of the line
Answer:
a) 9/5
Step-by-step explanation:
Formula we use,
→ Slope (m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-16 - 2)/(-10 - 0)
→ m = (-18)/(-10)
→ m = 18/10
→ [ m = 9/5 ]
Hence, the slope is 9/5.