Answer:
What is the question please respond so I may give a complete response
express a cosine and sine function in terms of an imaginary exponential. conversely, express the imaginary exponential in terms of cosine and sine
A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).
This formula can be derived by using the Taylor series for e^x, and replacing x with iθ.
A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).
Conversely, an imaginary exponential can be expressed in terms of cosine and sine by solving for θ in the above equation. This can be done by taking the inverse cosine and inverse sine of both sides to get θ = cos^(-1)(e^(iθ)) = sin^(-1)(i*sin(θ)). Combining these equations gives θ = sin^(-1)(i*(e^(iθ) - cos(θ))).
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Which of the following is the equation that represents the graph?
[tex]a)y=-\frac{2}{3}* -6\\b)y=-\frac{3}{2}*-6\\c)y=-\frac{2}{3} *-4\\d) y=-\frac{3}{2}*-4[/tex]
The linear function that models the graph is given as follows:
a) y = -2x/3 - 4.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The graph crosses the y-axis at y = -4, hence the intercept b is obtained as follows:
b = -4.
When x increases by 6, y decays by 4, hence the slope m is obtained as follows:
m = -4/6
m = -2/3.
Hence the function is defined as follows:
y = -2x/3 - 4.
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(a) Describe a in words a sequence of transformations that maps AABC to AA'B'C'
(b) Write an ordered-pair rule for each transformation in the sequence.
Transformation includes changing the position of a shape.
The sequence of metamorphosis is 90 degrees counterclockwise gyration, followed by a vertical restatement to the right by 2 units.
What's meant by sequence?
A grouping of two or further particulars in a logical sequence. The following arrangement of two or further effects chronological arrangement. an arrangement of analogous particulars or generalities in chronological sequence. The length of the sequence is determined by the number of particulars. In discrepancy to a set, the same particulars might appear further than formerly in a sequence at colorful points, and unlike a set, the order is important. The formal description of a series is a function from natural figures to the rudiments in each position. An listed family, which is a function from any indicator set, can be allowed of as a conception of the idea of a sequence.
The ordered brace- rule for each are :
(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)
The sequence of metamorphosis.
From the figure, we observed that ABC was rotated and also restated
So, the sequence of metamorphosis on ABC are
90 degrees counter clockwise gyration.
Vertical restatement to the right by 2 units.
The ordered brace rule :
When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :
x, y)->(- y, x)
When a point is restated 2 units right, the rule of metamorphosis is :
x, y)->( x 2, y)
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Transformation includes changing the position of a shape.
The sequence of metamorphosis is 90 degrees counter clockwise gyration, followed by a vertical restatement to the right by 2 units.
What's meant by sequence?A grouping of two or further particulars in a logical sequence.The following arrangement of two or further effectschronological arrangement. an arrangement of analogous particulars or generalities in chronological sequence.The length of the sequence is determined by the number of particulars.In discrepancy to a set, the same particulars might appear further than formerly in a sequence at colorful points, and unlike a set, the order is important.The formal description of a series is a function from natural figures to the rudiments in each position.An listed family, which is a function from any indicator set, can be allowed of as a conception of the idea of a sequence.The ordered brace- rule for each are :
(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)
The sequence of metamorphosis.
From the figure, we observed that ABC was rotated and also restated
So, the sequence of metamorphosis on ABC are
90 degrees counter clockwise gyration.
Vertical restatement to the right by 2 units.
The ordered brace rule :
When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :
x, y)->(- y, x)
When a point is restated 2 units right, the rule of metamorphosis is :
x, y)->( x 2, y)
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Cual es el mínimo común múltiplo de 29 y 35?
Answer:
1015
Step-by-step explanation:
29 es un número primo.
Por tanto:
29*35 = 1015
El mínimo común múltiplo de 29 y 35 es:
1015
Please help thanks!
PLS HELPP
Which line is parallel to the liney=4x+5?
A)y=-4x+2
B) y=4x+3
C)4x+5
D)y=-1/4x+9
Answer:
c
Step-by-step explanation:
it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier
Please answer this question for me
The criterion that she should use to prove that triangles RST and XYZ are congruent are:
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
What are congruent triangles?When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.
From the given triangles RST and XYX, it can be observed that;
TR ≅ XZ
RS ≅ XY
<R ≅ <X (given)
<T ≅ <Z (given)
Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
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One-half the sum of two numbers is 12. One of the numbers is three more than two times the other number. What are the two numbers?
Answer:
The two numbers are 17 and 7
Step-by-step explanation:
Translate this word problem into a math equation
If we let x and y be the two unknown numbers
One-half the sum of two numbers is 12 ==>
sum of two numbers : x + yone-half the sum of two numbers : (1/2)(x + y)one-half the sum of two numbers is 12: (1/2)(x + y) =12
So one equation is 1/2(x + y) =12
Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12
x + y = 24 (1)
One of the numbers is three more than two times the other number:
x = 2y + 3
or
x - 2y = 3 (2)
Equation (2) - Equation (1) =>
x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21
3y = 21
y = 21/3
y = 7
With y = 7, substituting in equation 1 gives
x + y = 24
x + 7 = 24
x = 24-7
x = 17
The two numbers are 17 and 7
A bowl at a delicatessen contains a mix of 15 apples, 12
oranges, and 9 pears. What is the probability of a customer
who gets one piece of fruit from the bowl randomly choosing
an orange or a pear?
The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36
What is Probability ?
Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes
Given ,
A bowl at a delicatessen contains a mix of 15 apples, 12 oranges, and 9 pears
so , we have to find the probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear.
Choosing orange or a pear ,
= 12c1 + 9c1
= 12+9
= 21
Total = 36.
Probability = 12 + 9 / 36
= 21 / 36 .
Therefore , The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36
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true/false. in the greek geocentric model, the retrograde motion of a planet occurs when: in the greek geocentric model, the retrograde motion of a planet occurs when: earth is about to pass the planet in its orbit around the sun. the planet actually goes backward in its orbit around earth. the planet is aligned with the moon in our sky.
According to the Greek geocentric paradigm, a planet moves retrogradely when it actually goes backward in its orbit around Earth. So the option b is correct.
The geocentric paradigm, also known as geocentrism, which is frequently and particularly shown by the Ptolemaic system, is an outdated explanation of the cosmos that places Earth at its center. The Sun, Moon, stars, and planets all orbit Earth according to the majority of geocentric models.
Since humans have been gazing up at the stars for thousands of years, our perception of what the Universe looks like has undergone a significant transformation.
In time, humanity also realized that the Earth was a sphere and developed logical justifications for how other heavenly bodies behaved. By classical antiquity, scientists had developed theories about how the planets moved and how all the celestial bodies interacted. This led to the development of the now-defunct Geocentric model of the cosmos, which described how the Sun, Moon, and firmament revolved around our earth.
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The complete question is:
In the Greek geocentric model, the retrograde motion of a planet occurs when (a) Earth is about to pass the planet in its orbit around the Sun. (b) the planet actually goes backward in its orbit around Earth. (c) the planet is aligned with the Moon in our sky.
Carl is preparing to clean out the gutters on his
house. The gutters are 24 feet from the ground.
The bottom of the ladder and the ground make a
60 degree angle. How far away from the house
should the ladder be placed in order to reach the
gutters?
Answer:
The gutters are 24 ft above the ground. For safety, the distance a ladder reaches up a wall should be four times the distance from the bottom of the ladder to the base of the side of the house. Therefore, the ladder must be 6 ft from the base of the house.
I need help giving out how to find the IQR of a data set
The bakery sales 9 sugar cookies for every 5 chocolate cookies sold. If the bakery sold 144 sugar cookies, what was the total number of cookies sold?
Answer:
224 total cookies sold
Step-by-step explanation:
if 9 sugar with every 5 cholates then, 144/9 = 16
so there were 16 times 5 cookies were sold with means
80 cholate cookies were sold
80+ 144= 224
:)
This is very very confusing
Write the domain of the function using interval notation.
Photo added to help answer the question
The domain of a function refers to the set of all possible inputs for the function.
Write the domain of the function using interval notation?In interval notation, the domain of a function is written as a set of values that the function's input can take on. For example, the domain for the function f(x) = x2 + 3 can be written as the set of all real numbers, or (-∞,∞), or in interval notation, (-∞,∞). This means that any real number can be used as an input for this function, and the output will be a real number as well.Interval notation is a way of writing the domain of a function in a compact form. It describes the range of values that the input of a function can take on. To write the domain of a function in interval notation, one must first identify the set of all possible inputs for the function. Then, one must identify the range of values that the input can take on within this set. This range of values can then be written as an interval in the form (a,b), where a and b are the lower and upper bounds of the interval respectively.For example, the domain of the function y = x2 + 2x + 3 can be written as the set of all real numbers, or (-∞,∞), or in interval notation, (-∞,∞). This means that any real number can be used as an input for this function, and the output will be a real number as well.Interval notation is a useful tool for quickly and concisely writing the domain of a function. It allows for a compact representation of the set of all possible inputs for a function, and is a useful tool for quickly determining the domain of a function.To learn more about the domain of the function using interval notation refer to:
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susan is conducting a survey about the electric bills of households in her city. from the electric company, she found that the population mean is $98.75 with a standard deviation of $10.45. susan has a sample size of 60. complete the equation that susan can use to find the interval in which she can be 68% sure that the sample mean will lie. 98.75 88.3 109.2 60 10.45 7.75 reset next
As per the given standard deviation, the interval in which she can be 68% sure that the sample mean will lie is 98.75 ± 10.45/ √60
In math the term called standard deviation is defined as a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Here we have given that the population mean is $98.75 with a standard deviation of $10.45 and the a sample size of 60.
Now, here we need to find the equation that Susan can use to find the interval in which she can be 68% sure that the sample mean will lie.
Here the distribution of the sample mean is approximately normal distribution with mean $98.75 and standard deviation approximately written as 10.45/√60
Here we have Symbolically written as,
=> X~ N(98.75, 10.45/√60) 2
Here by using empirical rule, then we find the limits for sample mean for which we're 68% sure that the sample mean will lie in that interval as one standard deviation away from its mean, then it can be written as
=> P (98.75 -10.45/√60 < x <98.75 +10.45/√60) ≈ 68%
Hence the equation is written as
=>98.75 ± 10.45/ √60
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HELP ASAP
14. Chung wants to determine the favorite hobbies.
among the teachers at his school. How could he
generate a representative sample? Why would it
be helpful to generate multiple samples?
Chung is going to be able to get the representative sample by carrying out a random selection.
It would be helpful to get the multiple samples because it is a way w=of getting the true representation of sample.
Why would it be helpful to generate multiple samples?Chung could generate a representative sample by randomly selecting a group of teachers from the school population and surveying them about their hobbies.
It would be helpful to generate multiple samples because, with only one sample, there's always a chance that the sample is not truly representative of the population. By generating multiple samples, Chung can compare the results and see if there is a consistent pattern among the samples, which would increase the likelihood that the results are representative of the population.
Additionally, by comparing multiple samples, Chung can also estimate the degree of variability in the population and the sample, this allow him to have more robust conclusions.
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De una botella que contenía 1litro de agua, Juan bebió 1/4 de litro.Expresa con forma de número decimal la cantidad de agua que queda en la botella
The fraction of water left from the bottle which was 1 liter is 3/4 liter.
How to calculate the fraction?Fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, from the bottle which was 1 liter, Juan drank 1/4. The amount that is left will be:
= 1 - 1/4
= 3/4
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a statistical study inbolves a data set of the different types of shoe designs by the designer calbvivn klein collected consistentyly over the years from 1987 to 2014 quizzlet
Answer:
c
Step-by-step explanation: got it right on test
5. The store is having a sale
on fruit. You can buy 6 kiwi for
$1.50. You can also get 5
mango for $3.00. What is the
total cost of buying 2 kiwis
and 3 mangoes?
Answer:
Step-by-step explanation:
1.50/6 = 0.25
3/5 = 0.6
0.25*2 = 0.5
0.6*3 = 1.8
1.80+0.50 = 2.30
$2.30
Which inequality is represented by this graph?
Answer:
x > 0
Step-by-step explanation:
An open circle means less than or greater than the number it is on.
A closed circle means less than or equal to, or greater than or equal to the number it is on.
This graph has an open circle on zero with the arrow pointing to the right.
so x>0
3w-4z=8 2w+3z=-6 solve.
Answer:
w = 0, z = − 2
Step-by-step explanation:
The solution for the given system of equations is: w = 0 and z = -2.
What is a system of equations?
A system of equations is a collection of two or more equations with the same set of unknowns. For a system to have a unique solution, the number of equations must equal the number of unknowns.
The equations are as follows:
[tex]3w-4z=8[/tex]-------- (1)
[tex]2w+3z=-6[/tex]-------(2)
The solution for the above equation,
Multiply the equation 1 by 2,
⇒([tex]3w-4z=8[/tex] )*2 --------- (3)
Multiply the equation 2 by 3,
⇒([tex]2w+3z=-6[/tex] )*3 --------(4)
Now solve equations 3 and 4 to get,
⇒ [tex]-17z=34[/tex]
⇒ [tex]z= -2[/tex]
Now substitute the value of z in equation 1,
⇒ [tex]3w-4(-2)=8[/tex]
⇒ [tex]\\3w=0[/tex]
⇒ [tex]w=0\\[/tex]
Hence we can conclude that the solution for the given system of equations is w = 0 and z = -2.
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9.) Multiple Choice: In triangle ABC, side AB has a length of 6cm and side BC has a length of 10cm. What is the length of AC?
The length of AC of the given right angle triangle is; AC = 8
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse, Opposite and the adjacent side.
Now, the given triangle is a right angle triangle and using Pythagoras theorem, we can say that;
AC = √(BC² - AB²)
Thus;
AC = √(10² - 6²)
AC = √64
AC = 8
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which of the following sentences are conditional statements? [more than one of the statements may be conditional.] group of answer choices i will order a pizza tonight only if we eat dinner at home. rain delayed the game. are you the only one home? discrete mathematics is required for a computer science transfer degree from foothill college.
I will order a pizza tonight only if we eat dinner at home is a conditional statement.
Sentences are groups of words that convey complete and logical meaning. They have subjects and predicates. It can be in form of exclamation and questions consisting of main and subordinating clauses.
Conditional statements are sentences where the subordinating clause influences whether the action that will be performed or not in the main clause. In these statements, the subordinating clause is also called the antecedent, and the main clause is called the consequent.
There are two types of Conditional statements, they are Implicative and predictive statements. Implicative sentences are based on facts whereas predictive statements depend on a situation dependent on a hypothetical case.
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Solve system of equations for unknown variables. X-4=11
The value of x which makes the equation true is 15.
What is the system of equations?
A system of equations is a set of two or more equations that contain multiple variables. These equations are typically used to describe a real-world situation and are solved simultaneously to find the values of the variables.
To solve a system of equations for unknown variables, you can use one of several methods, such as substitution, elimination, or graphing.
To solve a system of equations such as x-4=11, you have to find the value of x which will make the equation true.
x-4=11
x=15
Hence, the value of x which makes the equation true is 15.
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Trapezoid ABCD and trapezoid EFGH are
congruent. What is the difference between
the area of triangle ABC and the area of
triangle EFJ?
The difference between the area of triangle ABC and the area of triangle EFJ is 0 square unis
How to determine the difference in the areasFrom the question, we have the following parameters that can be used in our computation:
Trapezoid ABCD and trapezoid EFGH are congruent.
From the complete question added as an attachment
We can see that the two triangles have the same base and the same height due to the congruence of the two trapezoids
This means that their areas are equal
The difference between equal values is 0
Hence, the area difference is 0
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2. An Olympic sized pool holds 6.6 x 105 gallons. How many liters is that? (1 gallon = 3.79 Liters)
a. 1.7 x 105 L
b. 2.5x 106 L
c. 1.7 x 104 L
d. 2.5 x 107 L
It will take 51 days to fill the Olympic sized pool.
What is relation between time and work?Time and work have a relationship that is
Work Completed is equal to Time x Rate of Work.
Alternately, Rate of Work = Time Taken / 1.
Alternatively, Time Taken = 1 / Rate of Work
Considering that,
Pool volume is 6.6043 x 105 gallons, or 6,600,430 gallons.
9 litres of water are delivered through a hose every minute.
Therefore, the amount of water delivered by hose every hour is equal to (9 * 60) gallons.
Water provided by hosen each day is equal to (9 * 60 * 24) gallons, or 12,960 gallons.
Thus, the amount of time needed to fill the pool is equal to 6,600,430/12960.
There are 50.9 days needed to fill the pool.
51 days were needed to fill the swimming pool.
The Olympic-sized pool will therefore fill in 51 days.
The Complete Question is Olympic sized pool.
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Select the figure with an angle of 300°
on a circle in standard position.
The figure of the coterminal angle of 300° on a circle in standard position is attached in the solution.
What are Coterminal angles?Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.
Coterminal angles are two angles in the standard position where one angle is a multiple of 360 degrees larger or smaller than the other. That is, if angle A has a measure of M degrees, then angle B is co-terminal if it measures M +/- 360n, where n=0,1,2,3, ...
Starting from that position, 300° is drawn by moving around the circle to the left "counter-clockwise" and ending at the 300° measure.
The negative coterminal angle is the angle that would end in the same place if we went to the right instead of right on the circle. It is equal to the original 300° minus 360°
Coterminal angles Ac to angle A may be obtained by adding or subtracting k⋅360° or k × (2π)
Hence, Ac = A + k⋅360°, if A is given in degrees.
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State if the three numbers can be the measures of
the sides of a triangle.
4,7,8
Select the correct response:
O True
O False
True. The three numbers can be the measures of the sides of a triangle.
What is the triangle inequality theorem?
The triangle inequality theorem is a fundamental principle in Euclidean geometry that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that in any triangle, no side can be longer than the sum of the other two sides.
The three numbers 4, 7, and 8 can be the measures of the sides of a triangle. This is because of the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle, the sum of two sides must always be greater than the third side.
For example, in this case,
4 + 7 = 11 > 8,
7 + 8 = 15 > 4,
4 + 8 = 12 > 7
Hence, 4, 7, and 8 can be the measures of the sides of a triangle, so the correct response would be "True".
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5 A college student is paying for tuition through private loans. Two lenders have approved the student for a $25,000 loan. Offer 1: 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer 2: 3.75% annual interest compounded monthly for a 66-month term Assuming no payments are made, what is the difference in the account balances at the end of the loan terms? Round your answer to the nearest penny. $1,245.00 $1,770.87 $2,964.36 $3,319.94
The difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Offer 1- 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer
Offer 2- 3.75% annual interest compounded monthly for a 66-month term
In offer 1,
Total amount A = $32487.50
In offer 2,
Total amount =
[tex]A = P[ 1 + r/n]^{nt}[/tex]
[tex]A = 25000[ 1 + 0.0375/12]^{12*5.5}[/tex]
A = $30,716.63
Difference = 32487.50 - 30716.63
= $1770.87
Hence, the difference in account balance is $1770.87
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