Answer:
74.1
Step-by-step explanation:
74.05 rounds to 74.1
4. Explain what an imaginary number is and its relationship to complex numbers. Then give
an example of where complex numbers occur naturally in mathematics.
Answer:
564643
Step-by-step explanation:
Answer:
In the real number system, there is no solution to the equation x^2=-1x
2
=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.
The backbone of this new number system is the number iii, also known as the imaginary unit.
i^2=-1i
2
=−1i, squared, equals, minus, 1
\sqrt{-1}=i
−1
=isquare root of, minus, 1, end square root, equals, i
By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i
5
i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.
However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−
2
i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.
Defining complex numbers
A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.
\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}
a
↑
Real
part
+
bi
↑i
Imaginary
part
\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.
The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.
Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts
7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.
4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd
9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd
-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd
Step-by-step explanation:
plz brian list and allways happy to help.
please help fill in the blanks!!
Answer:
1. 69
2. 198
3. 50
use subtraction and addition
you roll a six sided dice 60 times the number for which the experimental probability of rolling the number is the same as the theoretical probability is
Answer:
The answer is "12 times, a die was rolled. Identify the complete possibilities to roll exactly 6".
Step-by-step explanation:
Using formula:
[tex]P(X=K)=\binom{N}{K} P^{K} a^{N-K}[/tex]
So the value is [tex]P(X=6)[/tex]
solve the right triangle.
Answer:
b=4√10
Step-by-step explanation:
AB²=AC²+BC²
14²=b²+6²
b²=14²-6²=160
b=√160=4√10
delete my answer
Step-by-step explanation:
PLEASE HELP!!
What is x? Show your work.
Answer:
Girl i dont know im so sorry
Step-by-step explanation:
good luck on ur assignment tho xoxo
64 fluid ounces is the same as
Answer: 0.5 liquid gallon
Step-by-step explanation: Have a great day
42 is greater than 24, 24 is less than 42
Answer:
Step-by-step explanation:
42 > 24
24 < 42
The equation of a line is y= 4x - 1 and the point (3, p) lies on this line. Determine the value of P
Answer: 11
Step-by-step explanation:
Given
The equation of the line [tex]y=4x-1[/tex] passes through the point [tex](3,p)[/tex]
So, point must satisfies the line i.e.
[tex]\Rightarrow p=4(3)-1\\\Rightarrow p=12-1\\\Rightarrow p=11[/tex]
Therefore, the value of p is 11.
PLZ NEED HELP IS DUE TONIGHT !!!!!!!!!!!!!!!!
Answer: 9/20
How to: Simplify the expression.
Have a great day and stay safe ! sorry if im wrong .
Please do this for me I’m having a very hard time and failing math because of this!
Answer:
Which answer do you need
Step-by-step explanation:
Sue is two years older then Lily who is twice as old as Heather. if the total ages of all the girls is 27, how old is each girl?
Answer:
sue = 12
lily = 10
heather = 5
Step-by-step explanation:
'l' = lily's age
'h' = heather's age
sue = 'l + 2' but, since 'l' is 2h we can say sue's age is '2h+2'
l = 2h
2h+2 + 2h + h = 27
5h = 25
h = 5
l = 2(5) = 10
sue is 10+ 2, or 12
Which line has a slope of -2 and y-intercept of 3
Answer:
A
Step-by-step explanation:
The line has to go down when x move to the right due to the negative slope. So B and C cannot be right.
The line has to pass through (0,3), that's the y-intercept, so A and D can still both be right.
For every step to the right, the line has to move 2 down (slope -2). Only A does that. D moves 0.5 down for every step to the right.
Imani is a scientist working with a cylindrical beaker. The base of the right cylinder has a diameter of 19 cm. She fills the
beaker with 2256.254 Cms of an acid. Approximately how high did the acid fill up the beaker?
Answer:
7.96 cm
Step-by-step explanation:
radius of bottom: 19/2 = 9.5
area of bottom = pi * r^2 = 283.53
height * base area = volume
Help plz
6(2x - 11) + 15 = 3x + 12
Answer:
x = 7
Step-by-step explanation:
Lets do the brackets first,
6 × 2x = 12
6 × -11 = -66
------
Calculate the x constant:
12x - 3x = 9x
-------
Then the ones with no x:
-66 + 15 = -51
51 + 12 = 63
-------
Lastly, divide
63 ÷ 9 = 7
-------
Have a good day :)
John brother Ricky also works part time in the summer. Ricky started working at the same time as John with a. Account balance of $227and deposit $24 each week. Writ an expression for the amount Ricky has in the bank after w week
Answer:
$227 + $24w
Step-by-step explanation:
Initial balance = $227
Amount deposited per week = $24
Amount in account after w weeks
Total amount = initial balance + total weekly deposit
Total Weekly deposit = $24 * number of weeks
Number of weeks = w
Hence,.
Total deposit = $227 + $24w
Problem Lines AAA, BBB, and CCC show proportional relationships. Which line has a constant of proportionality between yyy and xxx of 333? Choose 1 answer:
Answer:
The answer is below
Step-by-step explanation:
The correct question is attached.
Two quantities are said to be proportional if as one quantity increases, the other quantity increases. Also, as one quantity decreases, the other quantity decreases.
Given the lines A, B and C. The constant of proportionality can be gotten by getting the equation of the line.
Line A passes through (0,0) and (1, 5). The equation of line A is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{5-0}{1-0}(x-0)\\\\y=5x[/tex]
The constant of proportionality between y and x is 5.
Line B passes through (0,0) and (3, 5). The equation of line A is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{5-0}{3-0}(x-0)\\\\y=\frac{5}{3} x[/tex]
The constant of proportionality between y and x is 5/3.
Line C passes through (0,0) and (3, 2). The equation of line A is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{2-0}{3-0}(x-0)\\\\y=\frac{2}{3} x[/tex]
The constant of proportionality between y and x is 2/3.
Answer:
line c
Step-by-step explanation:
AJ needs $800. So far, he has saved $290. If his job pays him $12 per hour, write and solve an inequality that can be used to determine the minimum number of hours that he needs to work in order to have enough money for the computer.
Answer:
The minimum number of hours is 43.
Step-by-step explanation:
Total money required = $ 800
Saved money = $ 290
Per hour income = $ 12
Let the number of hours be n.
According to the question
[tex]290 + 12n \geqslant 800\\\\12 n \geqslant 510\\\\n\geqslant 42.5[/tex]
So, the minimum number of hours is 43.
Answer:
800 - 290 = 510. 510 = 12h
Step-by-step explanation:
$800 is the amount he is trying to save.
$290 is the amount he has so far.
$800 - $290 = $510.
$510 is the amount more he needs to earn.
12h.
12 represents the amount he is paid every 1 hour
H represents the hours he works.
Hoy vamos de excursión con la escuela y nos ha tocado hacer los bocadillos para toda la clase. Si para hacer los bocadillos para mis 4 hermanos gastamos 2 barras de pan, ¿cuántas barras de pan necesitaremos para hacer los bocadillos de los 24 alumnos que hay en clase?Regla de tres
Answer:
12barras
Step-by-step explanation:
Hoy vamos a hacer una excursión con la escuela y tuvimos que hacer sándwiches para toda la clase. Si gastamos 2 hogazas de pan para hacer sándwiches para mis 4 hermanos, ¿cuántas hogazas de pan necesitaremos para hacer sándwiches para los 24 estudiantes de la clase?
De la pregunta anterior:
4 personas = 2 barras de pan
24 personas = x
Multiplicar cruzada
4 × x = 24 × 2 barras de pan
x = 24 × 2 barras de pan / 4
x = 12 barras de pan
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1/4 in. and width 1/6 in. The actual tiles have length 1/6 ft and width 1/9 ft.
What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile
Answer:
The answer is below
Step-by-step explanation:
The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.
Firstly we have to convert the model length and width from inches to feet.
1 feet = 12 inches
model length = 1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.
model width = 1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.
Therefore:
Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8
Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8
Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²
Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²
Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64
What’s the area of the shape?
Answer:
Hello! answer: 113.04
Step-by-step explanation:
It looks like you already selected the correct answer! What you do to find it is radius squared × 3.14 so
6 × 6 = 36 36 × 3.14 = 113.04 therefore that is the answer Hope that helps!
hey! i’ll give brainliest help thanks
Answer: The last one
Step-by-step explanation:
Answer:
D. 4th Option.
Explanation:
The cause is that a team is from your town and the effect is that you'll try to be a fan. The italicized words if and then indicate a cause and effect.
you dont need to show work
Answer:
Q1. A. 209.8
Q2. B. 313.6
Q3. 448.22 (not in ur options)
Step-by-step explanation:
Witch product is less then 5/8
7/10x5/8
4/3x5/8
9/7x5/8
3/2x5/8
Thank you
Answer:
Answer is 7/10 × 5/8
Step-by-step explanation:
only answer which is under 5/8ths being 7/16 :)
Answer:
7/10x5/8
Step-by-step explanation:
7/10x5/2=7/16
4/3x5/8=5/6
9/7x5/8=45/56
3/2x5/8=15/16
Pls solve I will mark brainliest
Answer:
292.5
Step-by-step explanation:
1/2*13(20cm+25cm)
Find m
p (8x+2)
q (10x-19)
r (16x-7)
Answer:
you have to add all the angles of a triangle so the value of m is 6
HELP! THIS IS DUE TODAY, and i will mark brainlest!
Answer:
c
Step-by-step explanation:
An input can only have one output.
I NEED THIS ASAP
Solve for X
Answer:
x^2 = 10
x = square root symbol with 10 underneath
Or x = 3.16227 (round to appropriate place)
—————
x^3 = 316
x = cubed root symbol with 316 underneath
or x = 6.81128 (round to appropriate place)
I answered them two different ways, because sometimes your teacher wants you to leave it under the square root or cube root symbol, when it can’t be solved to an exact integer.
A mechanic began pouring a full can of motor oil into a funnel. The can of motor oil has a radius of 2.5 inches and a
height of 6 inches. The funnel has a radius of 3 inches and a height of 5.5 inches. If the hole on the bottom of the
funnel is plugged so that the funnel is not able to drain, what percentage of the oil would remain in the can after the
funnel is completely filled?
I really need some help please
Answer:
y - 1 = 3/2(x - 4)
Step-by-step explanation:
plug in the given(known) x and y coordinates into the point-slope form:
=> y - 1 = 3/2(x - 4)
How can I calculate the maximum height of the ball? h=-16t^2+vt+h v is the initial velocity and I got 4.3cm h is the initial height and I got 14cm Range of the ball is 1.954m and the time in air is 2.1 When I solve the maximum height of the ball, it need to be ft/s.
Step-by-step explanation:
The path followed by the ball as a function of time is given by :
[tex]h=-16t^2+vt+h[/tex]
Where
v is initial velocity and h is initial height,
v = 4.3 cm/s = 0.043 m/s and h = 14 cm = 0.14 m
The equation becomes,
[tex]h=-16t^2+0.043t+0.14[/tex] ....(1)
It is a quadratic equation,
t = 0.095 s
Put the value of t in equation (1).
[tex]h=-16(0.095)^2+0.043(0.095)+0.14\\\\h=-0.000315\ m[/tex]
or
h = -0.00103 ft (negative sign shows height is in negative direction)