Answer:
0.7239 +0.9435i . . . and 3 others
Step-by-step explanation:
Roots of complex numbers are most easily found when the numbers are in polar form. Then Euler's formula can be used.
__
polar/exponential formThe given number, written in polar and/or exponential form is ...
z⁴ = -√3 -i = 2∠210° = 2·e^(i(7π/6+2kπ))
rootsThe value of z is the fourth root of this. The fourth root of 2 multiplies the exponential term with 1/4 of the original exponent. We note there are four roots.
\(\displaystyle z=\sqrt[4]{2\cdot e^{i(7\pi/6+2k\pi)}}=\sqrt[4]{2}\cdot e^{i(7\pi/24+k\pi/2)}\\\\=\begin{cases}(\sqrt[4]{2}\cos(52.5^\circ)+i\sqrt[4]{2}\sin(52.5^\circ))&\approx 0.7239+0.9435i\\(\sqrt[4]{2}\cos(142.5^\circ)+i\sqrt[4]{2}\sin(142.5^\circ))&\approx-0.9435+0.7239i\\(\sqrt[4]{2}\cos(232.5^\circ)+i\sqrt[4]{2}\sin(232.5^\circ))&\approx -0.7239-0.9435i\\(\sqrt[4]{2}\cos(322.5^\circ)+i\sqrt[4]{2}\sin(322.5^\circ))&\approx 0.9435-0.7239i\end{cases}\)
_____
Additional comment
The value of z⁴ can also be written as 2∠-150°. The root found by the calculator (second attachment) has 1/4 of this negative angle, rather than 1/4 of the angle +210°.
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives
a) Somethingisnotinthecorrectplace.
b) All tools are in the correct place and are in excellent condition.
c) Everything is in the correct place and in excellent condition.
d) Nothing is in the correct place and is in excellent con- dition.
e) One of your tools is not in the correct place, but it is in excellent condition.
Answer:
A) ∃y(¬P(y))
B) ∀y(P(y) ^ Q(y))
C) ∀y(P(y) ^ Q(y))
D) ¬∃y(P(y) ^ Q(y))
E) ∃y(¬P(y) ^ Q(y))
Step-by-step explanation:
We will use the following symbols to answer the question;
∀ means for all
∃ means there exists
¬ means "not"
^ means "and"
A) Something(y) is not in the correct place is represented by;
∃y(¬P(y))
B) For All tools are in the correct place and are in excellent condition, let all tools in the correct place be P(y) and let all tools in excellent condition be Q(y).
Thus, we have;
∀y(P(y) ^ Q(y))
C) Similar to B above;
∀y(P(y) ^ Q(y))
D) For Nothing is in the correct place and is in excellent condition:
It can be expressed as;
¬∃y(P(y) ^ Q(y))
E) For One of your tools is not in the correct place, but it is in excellent condition:
It can be expressed as;
∃y(¬P(y) ^ Q(y))
,y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being
C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school.
C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school. The domain for X consists of all students in the school and the domain for Y consists of all classes being offered. To explain this statement further, firstly it should be noted that the statement is saying that a student (X) is enrolled in a class (Y). Secondly, the term “domain” refers to the set of all possible values that can be used for a given variable. In this case, the domain for X consists of all students in the school, while the domain for Y consists of all classes being offered at the school. Therefore, the statement C(X,y) is saying that a student from the school is enrolled in one of the classes offered by the school.
The complete question: Let C(X,Y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being
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- Jennifer opened a new savings account on Thursday with a deposit of $60. - She made a withdrawal of $40 on Friday. - She then made a deposit of $80 on Saturday. Which expression represents her new account balance?
Answer:
(60-40)+80
Step-by-step explanation:
How many 11-card hands are possible with a 20-card deck?
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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brainles for firs answered
Answer:
Hello! answer: 3/4
Step-by-step explanation:
9 ÷ 3 = 3 12 ÷ 3 = 4 then that is 3/4 and we can't reduce any further therefore 3/4 is the answer HOPE THAT HELPS
Segments AC and BD are diameters of circle O. Circle O is shown. Line segments A C and B D are diameters. Angle A O D is 73 degrees. What is the measure of Arc A D B? 107° 146° 253° 287°
Answer:
253°
Step-by-step explanation:
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: 253°
The solution is, the measure of Arc A D B is 253°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
given that AC and BD are diameters of circle O.
AC and BD intersect at point C the centre of the circle.
The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: the measure of Arc A D B is 253°.
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Purdue has 1320 employees and plans to increase the number of employees by 20% each year. Is this linear or exponential? Which equation describes this situation?
Please Help!!!
Answer Quickly!!
The exponential function that describes the situation is:
\(A(t) = 1320(1.2)^t\)
What is an exponential function?An increasing exponential function is modeled by:
\(A(t) = A(0)(1 + r)^t\)
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The parameters for this problem are:
A(0) = 1320, r = 0.2.
Hence the equation is:
\(A(t) = A(0)(1 + r)^t\)
\(A(t) = 1320(1 + 0.2)^t\)
\(A(t) = 1320(1.2)^t\)
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To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can be modeled by the function A(x) = 130 + 15x, where x represents the number of hours the accountant works to prepare the taxes and 130 represents the flat fee. What is the value of A(190) and its interpretation?
A(190) = 4; If the accountant takes 190 hours to prepare the taxes, the cost will be $4.
A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.
A(190) = 4; If the account takes 4 hours to prepare the taxes, the cost will be $190.
A(190) = 2980; If the accountant takes 2980 hours to prepare the taxes, the cost will be $190.
The value of A(190) and its interpretation is: B. A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.
CostGiven function:
A(x) = 130 + 15x
Let x represent the number of hours
Let the flat fee be 130
Let plug in 190 into the function as this will enable to determine the value of A(1900 and it interpretation.
Hence,
A(x) = 130 + 15x
A(x) = 130 + 15(190)
A(x) = 130 + 2,850
A(x) = 2,980
Therefore the value of A(190) and its interpretation is: B. A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.
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Answer:
(B) A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.
Step-by-step explanation:
Got it right on my quiz
Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign
explain whether 8t - 3y - 4t is equivalent to 7t +(-3t) - 3y.
Answer:
4t - 3y
Step-by-step explanation:
8t - 3y - 4t
8t - 4t - 3y
4t - 3y
7t +(-3t) - 3y
7t - 3t - 3y
4t - 3y
Answer:
These expressions are equivalent, as both of them simplify down to (4t - 3y).
Step-by-step explanation:
In order to determine if (8t - 3y - 4t) is equivalent to (7t + (-3t) - 3y) one must simplify each equation. Combine like terms by performing the operations between the coefficients of the variables.
8t - 3y - 4t
= 4t - 3y
7t + (-3t) - 3y
= 7t - 3t - 3y
= 4t - 3y
Please help I will give brainliest (use the Picture to answer the question
Answer:
1. QTS
2. QTS
3. 61˚
4. 32˚
5. PTS
Answer:
1. RTS . 2. QTS . 3.61° . 4. 32° . 5. PTS
Step-by-step explanation:
7/8 divided by 3/4 is what?
Answer:
1/8
Step-by-step explanation:
3/4=6/8
7-6=1
therefore 1/8
Answer:
7/6
Step-by-step explanation:
7/8 divided by 3/4= 7/8 x 4/3 = 28/24= 7/6
100 POINTS PLEASE HELP THERE IS A PIC JUST PLEASE CLICK ON IT PLEASEEE
Answer:0.0248
Step-by-step explanation:
To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.
To divide powers of the same base, subtract the numerators exponent from the denominators exponent
Multiply 1.24 and 3.6 to get 4.464
Calculate 10 to the power of 2 and get 100
Multiply 1.8 and 100 to get 180
Expand 4.464/180 by multiplying both numerator and denominator by 1000
Reduce the fraction 4464/180000 to the lowest term by extracting and canceling out 144
What is the product (-2d2+s)(5d2-6s)
Answer:
its A
Step-by-step explanation:
correct on edge
Find the missing length indicated
Step-by-step explanation:
there is a nice formula for the height in a right-angled triangle :
h = sqrt(p×q)
h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.
so, in our case
x = sqrt(25×144) = 5×12 = 60
Find the area of a trapezoid with bases of 16 feet and 10 feet and a height of 3 feet. 39 ft2 78 ft2 240 ft2 480 ft2
Answer: 39 ft2
Step-by-step explanation:
The area of the trapezoid is 39 square feet.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) × (base1 + base2) × height
Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:
Area = (1/2) × (16 + 10) × 3
Area = (1/2) × 26 × 3
Area = (1/2) × 78
Area = 39 ft^2
Therefore, the area of the trapezoid is 39 square feet.
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what is 94.01% of 161,809,242
Answer:
152,116,8684
Step-by-step explanation:
multiple
Answer:
152,116,868.404
Step-by-step explanation:
0.9401 x 161,809,242 = 152,116,868.404
if a coin is flipped 35 times and lands on heads 21 times what is the relative frequency of Landing on heads
Work Shown:
21/35 = (7*3)/(7*5) = 3/5
4. Calculate the compound interest earned when $8 500 at 8% per year for:
a. 3 years
b. 8 months
For an ordered pair (x,y) in a relation, the y element represents the
a.) range
b.) domain
c.) function
d.) input
y represents the range for an ordered pair (x, y). Option A is correct.
For an ordered pair (x, y), What y represents is to determine.
Range of the function is the output value of the function.
Here, in ordered pair (x, y) x represents the values of independent variable terms as domain. And for every value of x their is exist or output values y this set of y values is called as range.
Thus, y represents the range for an ordered pair (x, y).
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I need help with my math
Step 1: Pick any two points
The points are represented as (x1,y1), (x2,y2).
where x1= -4, y1= -8, x2= 0, y2= 4
Step 2: Write out the formula of the equation to use
\(\frac{y-y_1}{x-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}\)Step 3: Substituting the values and to get the equation
\(\begin{gathered} \frac{y-(-8)_{}}{x-(-4)}=\text{ }\frac{4-(-8)}{0-(-4)} \\ \frac{y+8}{x+4}=\frac{4+8}{0+4} \\ \frac{y+8}{x+4}=\text{ }\frac{12}{4} \end{gathered}\)\(\begin{gathered} \frac{y+8}{x+4}=\text{ 3} \\ \text{Cross multiply} \\ y+8=\text{ 3(x+4)} \\ y+8=\text{ 3x+12} \\ \text{Collect like terms} \\ y=\text{ 3x+12-8} \\ y=\text{ 3x + 4} \end{gathered}\)The equation that represents the graph is y= 3x+4.
Option A is the correct answer.
Suppose y = 2x – 2.5. Find x if y = 10.
What is 9.98- 2.53 and 7.68 + 13.07 and 100.03 - 16.28 show your work
Answer:
9.98- 2.53 = 7.45
7.68 + 13.07 = 20.75
100.03 - 16.28 = 83.75
Step-by-step explanation:
9.98
- 2.53
_____
7.45
1 1 - Process of carrying 10's
7.68
+ 13.07
_______
20.75
0000 13 ⇔ What the number becomes after carrying
↑↑↑↑↑
100.03
- 16.28
______
83.75
Happy New Year!
The table shows a function.
ху
2 20
3 10
40
Part A: Is the function linear or nonlinear?
Part B: How did you determine if the function was linear or nonlinear?
Part A: The function is nonlinear.
Part B: We determined the function to be nonlinear because the corresponding y-values do not change by a constant rate as the x-values increase, indicating a lack of a linear relationship.
Part A: The given function is nonlinear.
Part B: To determine whether the function is linear or nonlinear, we need to examine the relationship between the x-values and the corresponding y-values in the table.
In a linear function, there is a constant rate of change between the x and y values.
This means that for every increase in x by a fixed amount, the corresponding y value will change by a constant amount.
If we look at the x-values in the given table (2, 3, 4), we can see that they are increasing by a fixed amount of 1 each time.
However, when we examine the corresponding y-values (20, 10, 40), we don't see a constant rate of change.
The y-values are not changing by the same amount for each increase in x.
For instance, when x increases from 2 to 3, the y-value decreases from 20 to 10.
This indicates a non-linear relationship as the change in y is not constant for each unit increase in x.
Additionally, when x increases from 3 to 4, the y-value jumps significantly from 10 to 40, which further confirms the nonlinear nature of the function.
Based on these observations, we can conclude that the given function is nonlinear.
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Find the difference. Write your answer in scientific notation. ( 8.4 × 1 0 3 ) − ( 6.4 × 1 0 2 ) (8.4×10 3 )−(6.4×10 2 )
The difference is 7.76 × 10³ in scientific notation.
What is scientific notation?
Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.
We can perform the subtraction in the usual way, using the fact that the numbers are already in scientific notation:
(8.4 × 10³) − (6.4 × 10²) = 8.4 × 1000 − 6.4 × 100
= 8400 − 640
= 7760
To write this in scientific notation, we can express the result as a number between 1 and 10 multiplied by an appropriate power of 10. In this case, we can write:
7760 = 7.76 × 10³
Therefore, the difference is 7.76 × 10³ in scientific notation.
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What is the equivalent expression of 3x^2-4x-3
Answer:
C. 3(x+1)(x-1)-4x
Step-by-step explanation:
3(x+1)(x-1)-4x
(x+1)(x-1)=x^2-1
3(x^2-1)-4x
3x^2-4x-3
What is the difference between change in quantity and change in quantity demanded?
A change in demand means that the entire demand curve shifts either left or right. A change in quantity demanded refers to a movement along the demand curve, which is caused only by a chance in price.
Function g is defined as g(x)=f (1/2x) what is the graph of g?
Answer:
D.
Explanation
We know that g(x) = f(1/2x)
Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).
It means that f(-2) = 0 and f(2) = 0
Then, g(-4) = 0 and g(4) = 0 because
\(\begin{gathered} g(x)=f(\frac{1}{2}x_{}) \\ g(-4)=f(\frac{1}{2}\cdot-4)=f(-2)=0 \\ g(4)=g(\frac{1}{2}\cdot4)=f(2)=0 \end{gathered}\)Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.
Dave Flip a coin 20 times and got heads on eight of the flips Based on Dave's results what is the experimental probability of the coin landing on heads?
Answer:
Experimental probability of head = 2 / 5 or 40%
Step-by-step explanation:
Given:
Total chances of getting head = 20 times
Number of heads come = 8
Find:
Experimental probability of head
Computation:
Experimental probability of head = Number of heads come / Total chances of getting head
Experimental probability of head = 8 / 20
Experimental probability of head = 2 / 5 or 40%