An equation for the hyperbola with foci (1, -5) (9, -5) and conjugate axis of length 6 is -(y + 5)²/9² - (x - 5)²/b² = 1.
How to determine the equation of the hyperbola?Mathematically, the standard form of the equation of a hyperbola is represented by this mathematical expression:
(y - k)²/a² - (x - h)²/b² = 1
Where:
a represents the semi-major axis.b represents the semi-minor axis.h and k represents the center.y and x represents the point.From the information provided above, we have the following parameters about the equation of this hyperbola:
Center (h, k) = (5, -5).
Also, the vertices is given by:
2c = -5 - (-5)
2c = -5 + 5
c = 0
Since the conjugate axis has a length of 6, we have:
2b = 6
b = 6/2
b = 3
Therefore, the value of a is given by:
c² = a² + b²
a² = c² - b²
a² = 0² - 3²
a = 0 - 9
a = -9.
So, the equation of this hyperbola is as follows;
-(y + 5)²/9² - (x - 5)²/b² = 1
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the mean number of cars sold by each salesman at kovak motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). ben polamalu only sold 6 cars last month. which statement is true?
The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. The statement which true is B) Ben's sales were not unusual last month.
ABOUT MEAN IN MATHThe mean is one of the important formulas in mathematics. Another term for the mean is the average. The mean is a calculation that is studied further in statistics.
Calculating the mean is a basic math skill. The mean is a calculation that can be calculated using a simple formula. Usually, the mean is a formula that is used in conjunction with other statistical formulas such as the mode and median.
In everyday life, the mean is a calculation that is often used. An example of using the mean is to find out the average income of employees in an office.
Your question is incomplete but most probably your full question was:
The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. which statement is true?
A) Ben's sales were unusual last month.
B) Ben's sales were not unusual last month.
C) Ben's sales were not unusual this month.
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What is 15 meters to feet?
Answer: It is approximately 49.2126 or 49, for short.
Step-by-step explanation:
For a more approximate result, multiply the length value by 3.281
49.21 feet or 15 meters are the same.
What is the length of a mile in meters?This is due to the fact that 1,609.344 meters, or one mile, are equivalent.The Hollywood Sign is comparable in height to it. Aproximately 15 meters tall is The Hollywood Sign. (Also known as Hollywoodland Sign) The Hollywood Sign has 15 m-tall white letters that are each individual.The average person can anticipate to walk a mile in 15 to 22 minutes, according to data from a 2019 study spanning five decades. The Centers for Disease Control and Prevention estimate that people typically walk between 2.5 and 4 mph.49.21 feet or 15 meters are the same.The Hollywood Sign is comparable in height to it. Aproximately 15 meters tall is The Hollywood Sign.To learn more about meters refer to:
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According to vsepr theory, if there are five electron domains in the valence shell of an atom, they will be arranged in a(n) __________ geometry.
According to VSEPR (Valence Shell Electron Pair Repulsion) theory, the electron domains around an atom will arrange themselves in a trigonal bipyramidal geometry based on the number of domains in the valence shell.
If there are five electron domains in the valence shell, they will be arranged in a trigonal bipyramidal geometry. In this geometry, the five domains occupy the positions of three axial domains (120 degrees apart) and two equatorial domains (90 degrees apart). This arrangement minimizes the repulsion between the electron domains, leading to a more stable molecule.
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In triangle QRS the measure of angle RSQ is 117°, and the measure of angle QRS is 23°.
What is the measure of angle SQR in degrees?
Answer:
the angle of SQR = 40°
Step-by-step explanation:
in any triangle, the sum of all angles will be equal to 180°
by adding RSQ and QRS you get 140°
180°-140°=40°
The measurement of angle ∠SQR is 40 degrees
We are given that triangle QRS the measure of angle RSQ is 117°, and the measure of angle QRS is 23°.
Since we know that in any triangle, the sum of all angles will be equal to 180°
To find the total angle of any polygon, use the formula = 180(n-2)
The "n" is number of sides a polygon have. Triangle has 3 sides.
Hence,substitute as n=3 in the formula above.
Total angle in a triangle =180(3-2)= 180(1)
= 180 degrees
∠QRS+∠RSQ+∠SQR=180°
180°-140°=40°
The angle SQR= 40°
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What is the Formula of Sum of Cubes of n Natural Numbers?
The formula for the sum of cubes of the first n natural numbers is:
(1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2
What is the formula of sum of cubes?The sum of cubes of the first n natural numbers is the sum of cubes of the numbers 1, 2, 3, ..., n.To find the formula, we can start by using the formula for the sum of the first n natural numbers: (1 + 2 + 3 + ... + n) = n(n+1)/2.We can then cube this expression: (n(n+1)/2)^3 = n^3(n+1)^3/8.Expanding the cube on the right side, we get: n^3(n+1)^3/8 = n^3(n^3 + 3n^2 + 3n + 1)/8.Combining like terms and simplifying, we get the final result: (1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2.This formula can be used to efficiently calculate the sum of cubes of any set of natural numbers, without having to sum the cubes individually.To learn more about natural numbers refer:
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Alfred borrowed $10,400 at a fixed annual interest rate of 3%. The amount he owes, A, can
The required amount Alfred owes is given as $10712 for a year.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Let the amount owes be x,
According to the question,
x = 10400 + 3% of 10400
x = 10400 + 312
x = 10712
Thus, the required amount Alfred owes is given as $10712 for a year.
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what is the slope that goes through the points (-1,4) and (14,-2)
The slope is:
-2/5Work/explanation:
To find the slope, I use the slope formula
[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m = slope.
Plug in the data
[tex]\sf{m=\dfrac{-2-4}{14-(-1)}[/tex]
Simplify
[tex]\sf{m=\dfrac{-6}{14+1}}[/tex]
Simplify the denominator
[tex]\sf{m=-\dfrac{6}{15}}[/tex]
Finally, reduce the fraction to its lowest terms.
[tex]\sf{m=-\dfrac{2}{5}}[/tex]
Hence, the slope is -2/5.Laine correctly factor expreion 16. 5 a - 77. 2 b 36 and give two poible anwer Laine could have written
The two possible answer is 3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36 .
Laine could just just used another common number to write it down as,
LCM(165, 36, 72) = 3960
Prime factorization of the numbers:
165 = 3 × 5 × 11
36 = 2 × 2 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
LCM(165, 36, 72)
= 2 × 2 × 2 × 3 × 3 × 5 × 11
= 3960
GCD(165, 36, 72) = 3
So we get three as a common multiple of them so after removing 3 common from them we can write 16.5a - 7.2b + 36 as
3(5.5a - 2.4b + 12)
Hence, The two possible answer is 3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36.
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A farmer sells 6.9 kilograms of apples and pears at the farmer's market.
1/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
1.725
Step-by-step explanation:
1/4 or .25 multiplied by the total of 6.9
It costs a small production company a fixed cost of $2,600 for props and costumes plus
$140 for each performance to put on plays at area schools. For each performance, the
company earns $400. Let x represent the number of performances and let y represent
the amount of dollars of expenses or income. Then the two equations graphed below
represent the expenses and income earned by the production company. How many
performances must the company put on in order to break even?
The number of performances which the company must put on in order to break even is equal to 10 performances.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by the ordered pair (10, 4,000).
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Find k such that x(t)=3^t is a solution of the differential equation dx/dt = kx
The value of k such the the solution of differential equation of dx/dt = kx is k = ln(3).
What is differential rule of exponential function?By multiplying the original exponential function by the derivative of its power, one can differentiate an exponential.
The rule for differentiating an exponential function is f(x)=a^u = a^t ln(t).
The given function is:
x(t) = 3^t
Using the differential rule for the exponential function we have:
d/ dt (3^t) = 3^t ln(3)
Substituting the value of x(t) in the equation with 3^t ln(3) we have:
3^t ln(3) = k 3^t
Since 3^t is a non-zero expression the value of k corresponding to the given value is:
ln(3) = k
Hence, the value of k such the the solution of differential equation of dx/dt = kx is k = ln(3).
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Assume you have a future liability of $12000 per year for 4 years beginning 7 years from today. You will fund this liability over the next 5 years, with the first deposit to occur 1 year from today. If you earn an interest rate of 8% per year, compounded annually, on deposits, how much will you have to deposit at the end of each of the next 5 years to fund this liability?
$6273.04 have to deposit at the end of each of the next 5 years to fund this liability
PV of Annuity = P*[1-{[tex]{1+i}^{n}[/tex]}]/i
Where, P = Annuity = 12000, i = Interest Rate = 0.08, n = Number of Periods = 4
PV at 6 years from today = 12000*[1-{(1+0.08)^-4}]/0.08 = 12000*0.26497/0.08 = $39745.52
PV at 5 years from today = PV at 6 years from today/[1+Interest Rate] = 39745.52/[1+0.08] = $36801.41
FV of Annuity = P*[{[tex]1+i^{n}[/tex]}-1]/i
Where, FV = 36801.41, i = Interest Rate = 0.08, n = Number of Periods = 5
Therefore,
36801.41 = P*[{(1+0.08)^5}-1]/0.08
2944.1127 = P*0.469328
Therefore, Amount to be deposited =
P = 2944.1127/0.469328 = $6273.04
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for the fractured expression use the distributive property to write an equivalent expression
3(2x + 11y)
An equivalent expression of 3(2x + 11y) is 6x + 33y.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
3(2x + 11y).
The distributive property:
a(b + c) = ab + ac.
So,
3(2x + 11y) = 6x + 33y
Therefore, 6x + 33y is an equivalent expression.
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Question content area top
Part 1
Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x - 68 = 34 - 8x . Your friend arrives at the incorrect answer x = -2 . Find the correct value of x. Then find the error your friend possibly made.
What possible error could your friend have made to get x = -2 ?
A.
Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side.
B.
Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x.
C.
Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side.
The value of x is 6
The possible error could your friend have made to get x = -2 is Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x. Option C
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variable, terms, coefficients, factors and constants.
These expressions are also made up of mathematical or arithmetic operations. These operations include;
SubtractionDivisionMultiplicationFloor divisionAdditionBracketParenthesesFrom the information given, we have the equation;
5x + 4x - 68 = 34 - 8x
collect like terms
5x + 4x + 8x = 34 + 68
Add or subtract the like terms
17x = 102
Divide both sides by the coefficient of the variable, we get;
17x/17 = 102/17
x = 6
Hence, the value is 6
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer: the answer is 189
Step-by-step explanation:
Please help asap with correct answer I will give brainliest please!!!
Answer:
I cant really see it sorry, make it a big bigger please and I will try my best.
suppose limx→0f(x)=1 and limx→0g(x)=−7. name the rule or limit law that is used to accomplish each step of the following calculation.
Step 1: limx→0[f(x)+g(x)] .Rule or Limit Law used: Sum Rule for Limits.
Step 2: limx→0f(x)+limx→0g(x) .Rule or Limit Law used: Limit of a Sum Rule.
Step 1: limx→0[f(x)+g(x)]
This first step is using the sum Rule for Limits. This rule states that the limit of the sum of two functions is equal to the sum of the limits of the individual functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the limits of f(x) and g(x) individually.
Step 2: limx→0f(x)+limx→0g(x)
This second step uses the Limit of a Sum Rule. This rule states that the limit of the sum of two functions is equal to the sum of the individual limits of the functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the individual limits of f(x) and g(x). This is the same result as in the first step, but using a different rule.
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Original Price Percent of Discount Sale Price
$69.80 60% $
Answer:$45.60
Step-by-step explanation:
p=%w
69.8(.60)w
/.6 /.6
116. =w
-69.8
46.5
Answer:
349/5/5
Step-by-step explanation:
(69,8) % of 60x$
simplify the expression
A 16 inch pendulum swings through an angle of 40. How far does the tip of the pendulum travel in a singles swing
The tip of the pendulum travels 22.33 inches in a singles swing.
A pendulum is a weight suspended from a pivot so that it can swing back and forth under the influence of gravity. Pendulums are commonly used as timekeepers in clocks, but they also have other applications, such as in seismology, where they can be used to detect earthquakes.
Each swing does an angle of 40° in each direction, so we have a total angle of 80°.
Then, we want to get the length of an arc defined by an angle of 80° on a circle with a radius of 16 in, this is:
L = (80°/360°) * 3.14 * (2 * 16 in)
= 22.33 in.
The distance that the tip of the pendulum travels on each swing is 22.33 inches.
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The tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.
To calculate how far the tip of the pendulum travels in a single swing through an angle of 40 degrees, we will use the formula:
Distance = 2 * PI * Length * (angle / 360)
Where PI is approximately 3.14 and Length refers to the length of the pendulum.
In this case, the length of the pendulum is 16 inches. Therefore, we can substitute these values into the formula:
Distance = 2 * 3.14 * 16 * (40 / 360)
Distance = 2 * 3.14 * 16 * 0.111
Distance = 28.3 inches
Therefore, the tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.
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How much are 1.5 pounds in kilograms?
1 pound is approximately equal to 0.45359237 kilograms. Therefore, 1.5 pounds is approximately equal to 0.45359237 x 1.5 = 0.68 kg
How to convert pounds into kilograms?It's a common conversion to make, as the pound is a unit of weight commonly used in the United States, while the kilogram is the standard unit of mass in the International System of Units (SI).Knowing the conversion from pounds to kilograms can be useful in many situations, such as when traveling to countries that use the metric system, or when converting recipes from American to metric measurements.Additionally, converting pounds to kilograms can be useful in a variety of industries, such as health and fitness, where people may need to track their weight in either unit.Keep in mind that the conversion between pounds and kilograms is not exact, as the conversion factor is an approximation.For more precise conversions, it's best to use a conversion tool or calculator to ensure accurate results.To learn more about pound to kilogram refer:
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two sides of a triangle measure 18 and 13 meters which measure could represent the perimeter of the triangle
Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.
what is perimeter ?An isolated path that surrounding, delimits, or embraces a two-dimensional shape or a single-dimension length sometimes referred to as the boundary. The perimeter of either an ellipse or circle refers itself to outermost area. The perimeter measurement has many legitimate applications. This perimeter of a form is its edge's circumference. Discover how to determine the perimeter by adding the lengths of such sides of various forms. Your can always find the perimeter of a polygon by multiplying its multiplicative inverse. The perimeter of an object is the space it around. At your house, a contained garden is one illustration. The perimeter of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.
given
The distance surrounding a closed-plane figure is its perimeter, or P.
P is equal to a plus b plus c, where a, b, and c are the lengths of the three sides, and let c be the third side's undetermined length.
P = 38 m, a = 13 m, and b = 18 m are the values provided. Now, to determine the third side's length c,
P = a + b + c
38m = 13m, 18m, and c
38 m = 31 m + c
38 m minus 31 m Equals 31 m minus 31 m plus c
7 m = 0 + c
7 m = c
Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.
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Alex, Bob, Clay, Daisy and Elly are eating a big cake.
After eating, there was one slice left, and they decided to leave it for Fredy but someone ate it!
Fredy knows that these 5
people are each telling one truth and one lie:
Alex says, "It wasn't Elly. It was Bob."
Bob says, "It wasn't Clay. It wasn't Elly."
Clay says, "It was Elly. It wasn't Alex."
Daisy says, "It was Clay. It was Bob."
Elly says, "It was Daisy. It wasn't Alex."
Who ate the last slice of cake?
The person who ate the last slice of cake is Daisy.
Who ate the last slice of cake?We have to know that the question that we have been asked here borders on the ability of the individual to be able to apply his or her reasoning so as to analyze the statement that have been made.
The person that is to be suspected is the one that is blaming everyone else as in this case can see is what Daisy is saying. We would pick up from there and then suspect a foul play and that is how we can know who ate the cake.
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Ruby’s model for a Fourth of July party hat is shown. The model is composed of a rectangle and 2 right triangles. What is the area of Ruby’s model for a Fourth of July party hat?
Total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
What is Area of Rectangle?The area of Rectangle is length times of width.
Let us find the area of the red colour right triangle.
Area of red triangle=1/2×13.5×9
=60.75 square cm.
Area of blue triangle=1/2×8×9
=36 square cm.
Area of rectangle=Length×breadth
=(13.5+8)4
=21.5×4
=86 square cm.
The total area of Ruby’s model for a Fourth of July party hat is
60.75+36+86
182.75 square centimeter.
Hence, total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
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A pump fills a pool at a constant rate. At the end of 18 minutes it has filled 2 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
The table can be written as,
Minutes Gallons
9 1
18 2
27 3
36 4
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
At the end of 18 minutes, it has filled 2.
This can be written as
y = kx
Where x is minutes and y is the number of gallons.
So,
2 = 18k
k = 2/18 = 1/9
Now,
The equation is y = (1/9)x
The table can be written as,
Minutes Gallons
9 1
18 2
27 3
36 4
Thus,
The table that represents the relationship between the number of minutes and the number of gallons of water in the pool is given above.
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at 9:30 a.m., sean started filling swimming pool. At 11:30a.m.,, he had filled 1,800 gallons. at what time will the pool be full?
At 2:30 AM,
the pool will be full.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
At 9:30 AM,
Sean started filling a 4,500-gallonswimming pool.
At 11:30 AM,
he had filled 1,800 gallons.
The unit rate = 1800/2 = 900 gallons per hour.
The pool completely filled in 5 hours.
Therefore, the pool be full at 2:30 AM.
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The complete question:
At 9:30 AM,
Sean started filling a4,500-gallonswimming =~ pool. At 11:30 a.m., he had filled 1,800 : gallons. At what time will the pool be full? :
LN = LN because of ____
Answer:
Reflexive Property
Answer:
reflexive property
Step-by-step explanation:
We can use the reflexive property to state that LN = LN.
It states that a value is equal to itself.
find the area of the trapezoid
The area of the trapezoid is 24 square units.
What is the area of the trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. In British and other dialects of English, it is referred to as a trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. Its parallel sides serve as its bases.
The area of a trapezoid can be calculated by using the formula:
Area = (a + b)h / 2,
where a and b are the lengths of the parallel sides and h is the height.
By the given figure, we can find the area of the trapezoid
Area = (a+b)h/2
Area = (4.3 + 7.7)*4/2
Area = 12*4/2
Area = 24 Square units.
Hence, the area of the trapezoid is 24 square units.
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What exactly is the relationship between the concepts of conjugate complex vector space and conjugations/real structures?
Conjugations and real structures are important tools used to study complex vector spaces.
A vector is a mathematical object with magnitude and direction. A complex vector space is a vector space where the vectors have complex numbers as components.
Conjugation is a mathematical operation that involves changing the sign of the imaginary part of a complex number.
Real structures refer to certain mathematical objects or operations that preserve the real part of a complex number.
The relationship between the concepts of conjugate complex vector space and conjugations/real structures is that they are both used to study complex vector spaces.
A conjugate complex vector space is a complex vector space equipped with a conjugation, which is an antilinear and involatile map.
The conjugation on a complex vector space allows us to distinguish between real and imaginary parts of a vector.
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How does counting cubes compare to multiplying dimensions when finding the volume of a rectangular prism?
Select from the drop-down menus to correctly complete the statements.
Amelie correctly determined the volume of this prism by counting unit cubes. She counted
Choose...
unit cubes.
Eloise correctly determined the volume of this prism by multiplying the three dimensions. She got a product of
Choose...
cubic units.
Amelie and Eloise correctly concluded that counting unit cubes gives
Choose...
result as multiplying the dimensions.
Eloise correctly determined the volume of this prism by multiplying the three dimensions, She got a product of (3×8×4) unit³.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
The given figure is a cuboid made up of unit cubes.
We know the volume of a cuboid is (length×width×height).
By observing the figure we have 3 unit cubes of width, 8 unit cubes of length, and 4 unit cubes of height.
Therefore, The volume of the cuboid is,
= (3×8×4) unit³.
= 96 unit³.
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109.What is the inverse natural function of the cosecant?a) Secantb) Sinec) Cosined) Tangent
The inverse of the cosecant function is the secant function so option A is correct.
In mathematics, the inverse of a function "f" is another function "g" such that when "f" is applied to an input "x", the result is "x". And when "g" is applied to the result, the original input "x" is recovered. This relationship can be expressed as: f(g(x)) = x and g(f(x)) = x.
The cosecant function is defined as the reciprocal of the sine function, so csc(x) = 1/sin(x). The inverse of the cosecant function is the secant function, which is defined as the reciprocal of the cosine function, so sec(x) = 1/cos(x).
In other words, when the cosecant function is applied to an angle "x", the result is 1/sin(x), and when the secant function is applied to the result, the original angle "x" is recovered. This relationship can be expressed as: sec(csc(x)) = x and csc(sec(x)) = x.
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