evaluate the expression 4-2i/3i
and write the result in the form a+bi
Answers
The given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
\({\displaystyle i^{2}=-1}\)
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following expression -
(4 - 2i)/3i
We have -
(4 - 2i)/3i
4/3i - 2i/3i
- 2/3 + i(4/3)
Therefore, the given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
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Related Questions
What I need to know is the math problem...lol
Answers
Answer:
100k each without tax + interest
Step-by-step explanation:
In ΔQRS, m∠R = 57°, q = 9, and s = 5. Find the area of ΔQRS.
Answers
The area of ΔQRS is 26.10 square units.
What is triangle?
A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.
To find the area of \($\triangle QRS$\), we can use the formula:
\($Area = \frac{1}{2} \times base \times height$\)
where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.
First, we need to find the length of side \($QR$\). We can use the Law of Cosines:
\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)
where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:
\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)
\($QR \approx 8.02$\)
Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:
\($\sin(R) = \frac{opposite}{hypotenuse}$\)
\($\sin(57^\circ) = \frac{height}{8.02}$\)
\($height \approx 6.51$\)
Now we can find the area of the triangle:
\($Area = \frac{1}{2} \times QR \times height$\)
\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)
\($Area \approx 26.10$\) square units
Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.
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If 2+x=8, what is the value of x?
Answers
Step-by-step explanation:
2+X = 8
X = 8-2
X = 6
hence, the value of X is 6
hope it helpful
2+x=8
move +2 to get x by itself
sign changes from +2 to -2
2-2+x=8-2
x=8-2
x=6
answer:
x=6
Calculate the area of a circle with a radius of 5 meters
Answers
Ans: pi (5)^2 = 78.5( cor. to 3 sig. fig)/ 25 pi
4. A circle is represented by the equation x^2 + (y-3)^2 = 13. What are the coordinates of the center of the circle and the length of theradius?
Answers
How many miles per hour? please help i will give brainliest<3
Answers
Answer: 9mph
Step-by-step explanation: To figure this out (I'll just finish the problem for you), you have to essentially find a unit rate. Since you know the miles traveled and the time, all you have to do is divide the miles by the minutes to figure out miles per minute. In other words, how much distance is covered in one minute.
3/4 divided by 5 is 0.15. That's how many miles per minute. Now, since they're asking for miles per hour, not per minute, you'd have to multiply the rate by one hour (60 minutes).
0.15*60 = 9
So, the speed is 9 miles per hour
What is the remainder of the quantity 2 x squared plus 7 x minus 39 end quantity divided by the quantity x minus 7 end quantity? Please show all work
Answers
The remainder of the division is (x-3)(x+13)/x-7
How to determine the reminderFrom the information given, we have that;
2 x squared plus 7 x minus 39 end quantity quantity x minus 7 end quantityThis is represented as;
2x² + 7x - 39/x - 7
Now, factorize the numerator
Find the pair factors of -78 that sum up to 7, then substitute the value, we have;
2x² + 13x - 6x - 39/x- 7
(2x² + 13x) - (6x-39)/x-7
Factor the common terms
x(x + 13) - 3(x + 13)/x-7
Then, we get;
(x-3)(x+13)/x-7
Hence, the value is (x-3)(x+13)/x-7
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A runner sprinted 103.76 yd to finish a race.
Use the table of facts to find the distance she sprinted in feet.
Round your answer to the nearest tenth.
Answers
Answer:
311.3 feet
Step-by-step explanation:
1 yard = 3 feet
Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)
Rounding to the nearest tenth gives us 311.3 feet.
33 markers cost \$5.79$5.79dollar sign, 5, point, 79. Which equation would help determine the cost of 131313 markers? Choose 1 answer: Choose 1 answer: (Choice A) \dfrac{13}{\$5.79} = \dfrac{x}{3} $5.79 13 = 3 x start fraction, 13, divided by, dollar sign, 5, point, 79, end fraction, equals, start fraction, x, divided by, 3, end fraction A \dfrac{13}{\$5.79} = \dfrac{x}{3} $5.79 13 = 3 x start fraction, 13, divided by, dollar sign, 5, point, 79, end fraction, equals, start fraction, x, divided by, 3, end fraction (Choice B) \dfrac{x}{13} = \dfrac{3}{\$5.79} 13 x = $5.79 3 start fraction, x, divided by, 13, end fraction, equals, start fraction, 3, divided by, dollar sign, 5, point, 79, end fraction B \dfrac{x}{13} = \dfrac{3}{\$5.79} 13 x = $5.79 3 start fraction, x, divided by, 13, end fraction, equals, start fraction, 3, divided by, dollar sign, 5, point, 79, end fraction (Choice C) \dfrac{3}{\$5.79} = \dfrac{13}{x} $5.79 3 = x 13 start fraction, 3, divided by, dollar sign, 5, point, 79, end fraction, equals, start fraction, 13, divided by, x, end fraction C \dfrac{3}{\$5.79} = \dfrac{13}{x} $5.79 3 = x 13 start fraction, 3, divided by, dollar sign, 5, point, 79, end fraction, equals, start fraction, 13, divided by, x, end fraction (Choice D) \dfrac{13}{x} = \dfrac{\$5.79}{3} x 13 = 3 $5.79 start fraction, 13, divided by, x, end fraction, equals, start fraction, dollar sign, 5, point, 79, divided by, 3, end fraction D \dfrac{13}{x} = \dfrac{\$5.79}{3} x 13 = 3 $5.79 start fraction, 13, divided by, x, end fraction, equals, start fraction, dollar sign, 5, point, 79, divided by, 3, end fraction (Choice E) None of the above E None of the above Stuck?Review related articles/videos or use a hint. Report a problem
Answers
The cost of 13 markers is $326.17.
We have,
Let x be the cost of one marker.
3 markers cost $5.79.
We can set up a proportion:
3 markers / $5.79 = 1 marker / x
To determine the cost of 13 markers, we can use this proportion and solve for y, which represents the cost of 13 markers:
3 markers / $5.79 = 13 markers / y
Cross-multiplying
3 markers x y = $5.79 x 13 markers
Simplifying:
3y = $75.27
Dividing both sides by 3, we get:
y = $25.09
The equation that helps determine the cost of 13 markers is:
= 13 markers x $25.09 per marker
= $326.17
Thus,
The cost of 13 markers is $326.17.
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45,678 in expanded form
Answers
Answer:
40,000 + 5000 + 600 + 70 + 8
Step-by-step explanation:
take the numbers all off and break them down by their value.
What is 41 + 3 HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
44
Step-by-step explanation:
Answer: 44
Step-by-step explanation:
This is quite simple, Are you sure you can't do it on your own?
A box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant. What is the rate of change, in cm per minute, of the height when the height is 6 cm?
Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Answers
Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.
Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.
Therefore, we can write the volume of the box as
:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.
Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:
527 = constant × dh/dt
We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:
V = l × w × hV = 17 × 10 × hV = 170h
We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:
527 = constant × 6 cm
constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get
-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min
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what is the percent increase from 3.5 to 3.5
Answers
Answer:
0
Step-by-step explanation:
There is no increase
Answer:
0
Step-by-step explanation:
there is no increase in percent
The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answers
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
A bus can carry a maximum of 60 passengers. Each row accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry maximum number of passengers. Determine number of rows in the bus and no. Of passengers per row
Answers
Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Hannah is driving 680 miles from Nashville to Orlando . If she has 306 miles left to drive, what percent of the trip has she driven ?
Answers
Answer:
Step-by-step explanation:
680 - 306 = 374
374/680 = 11/20 =
55%
what happens to the graph when a zero is repeated vs when a zero is not repeated? Use y=(x-3)^2 and y=x-3 to explain.
Answers
Answer:
look at the screen shot
Step-by-step explanation:
Is this the graph of a function?
Answers
Answer:
function
Step-by-step explanation:
this graph is a function.
why?
if we draw a vertical line on all points of the function we can see that it only intersects ONCE. Therefore, it's a function. if it intersects more than once then it will not be a function
what are the assymptotes of this equation
Answers
Mathmatics For Calculus
Answers
The value of function f ' (2) is, 7/4.
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
We have to given that;
The function is,
⇒ f (x) = 7/x
Now, We an solve as;
⇒ f ' (2) = lim h → 0 ( f (2 + h) - f (2) / h )
⇒ f ' (2) = lim h → 0 ( 7 / (2 + h) - 7/2 / h )
⇒ f ' (2) = lim h → 0 ( 7/h (2 - 2 - h) / (2 + h)×2)
⇒ f ' (2) = lim h → 0 ( 7/h ( - h ) / 2 (2 + h) )
⇒ f ' (2) = lim h → 0 ( - 7 / 2 (2+ h))
⇒ f ' (2) = - 7/4
Thus, The value of function f ' (2) is, 7/4.
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Answer: a = 2 f(x) = x^5
Step-by-step explanation:
The ages of workers in a certain industry are approximately normally distributed with a mean of 30 years and a
standard deviation of 3.5 years. A recruiter wondered if that held true for workers in a certain state. The
recruiter took a random sample of n = 3 of these workers from the state, and the mean age of the workers in
the sample was ĉ = 26 years.
To see how likely a sample like theirs was to occur by random chance alone, the recruiter performed a
simulation. They simulated 200 samples of n = 3 ages from a normal population with a mean of 30 years and
standard deviation of 3.5 years. They recorded the mean of the ages in each sample. Here are the sample means
from their 200 samples:
Answers
Answer:
C. p-value is 0.07
Step-by-step explanation:
The sample mean was 4 years below the hypothetized mean, and 14 of 200 simulated results were this far or farther above or below the hypothesized mean.
Brainliest, please :)
| negative 9 | + | 12 | = what
a. negative 3
b. 3
c.negative 21
d.21
pleaz help might make brainliest
Answers
Answer:
21 (but see note)
Step-by-step explanation:
I am thinking you are showing the symbols for absolute values ( the vertical lines) so the absolute value of negative 9 is 9 and absolute value of positive 12 is 12 so it's just 9+12
Enid jogs on a treadmill for exercise. Each time she finishes jogging, the treadmill will report the number of calories she burned. Enid claims that the distance she jogs and the number of calories she burns are in a proportional relationship. Data from her last four jogs are shown.
HELP QUICK
Answers
The correct statement is: She should calculate the ratio between the number of calories she burned versus the number of miles she ran.
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: The table containing data calories vs miles run.
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.
Thus calculating the ratio for each pair of entries we get
1) ratio=118/1.2
=295:3a or unit rate 98.33 calories per mile
2) 190/2= 95:1 or unit rate 95 calories per mile
3) 226/2.4=565:6 or unit rate94.1
clea,rly the ratios are different.
Hence, The table containing the data doesn't form a proportional relationship.
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A game room has a perimeter of 70 ft. The length is 5 more than twice the width. How many feet squared of new carpeting should be ordered?
Answers
Answer:
A = 250 square ft
Step-by-step explanation:
Equations
Let's call:
x = width of the game room
The length is 5 more than twice the width, thus:
2x+5 = length of the game room
The perimeter of a rectangle is twice the sum of the width and the length:
P = 2( x + 2x + 5 )
And the perimeter is 70 ft:
2( x + 2x + 5 ) = 70
Operating:
2( 3x + 5 ) = 70
Dividing by 2:
3x + 5 = 35
Subtracting 5:
3x = 30
Dividing by 3:
x = 30 / 3
x = 10
The width is 10 ft and the length is 2(10)+5=25 ft
The area of the game room is:
A = 10 ft * 25 ft
A = 250 square ft
Two firms A and B produce goods A and B, respectively. The linear demands for the two goods are, respectively, QA=100-4PA+1.5PB QB=120-2PB+0.5PA Production costs are constant but not equal: LACA=LMCA=$2 LACB=LMCB=$3 Using calculus, derive the equations for best response curves. Sketch a graph of the two best-response curves. Label both axes and response curves. If firm A expects firm B to set its prices at $20, what is firm A’s best response? If firm B predicts firm A will price good A at $36, what is firm B’s best response? What is the Nash equilibrium price and quantity for each firm? How much profit does each firm earn in Nash equilibrium? If firm A and firm B set prices of $22 and $35 respectively, how much profit does each firm earn? Why don’t they choose these prices then?
Answers
31.5 profit does each firm earn in Nash equilibrium.
What does "equilibrium pricing" mean?
The cost to the customer of a good or service at an equilibrium price, sometimes referred to as a market-clearing price, is determined by supply and demand being equal or nearly equal.
Customers have access to all the units they wish to purchase, and manufacturers and vendors are free to move as many units as they like.
QA = 100 - 4PA + 1.5PB
QB = 120 - 2PB + 0.5PA
LMCA = 2
LMCB = 3
(1)
For firm A, Profit ZA = TRA - TCA = (PA x QA) - (LMCA x QA) = QA x (PA - LMCA)
ZA = (100 - 4PA + 1.5PB) x (PA - 2) = 100PA - 200 - 4PA2 + 8PA + 1.5PAPB - 3PB
ZA = 108PA + 1.5PAPB - 3PB - 4PA2 - 200
Setting dZA / dPA = 0, we get
108 + 1.5PB - 8PA = 0
8PA - 1.5PB = 108 ......(1) [Best response, firm A]
For firm B, profit ZB = TRB - TCB = (PB x QB) - (LMCB x QB) = QB x (PB - LMCB)
ZB = (120 - 2PB + 0.5PA) x (PB - 3) = 120PB - 360 - 2PB2 + 6PB + 0.5PAPB - 1.5PA
ZB = 126PB + 0.5PAPB - 1.5PA - 2PB2 - 360
Setting dZB / dPB = 0, we get
126 + 0.5PA - 4PB = 0
4PB - 0.5PA = 126 ......(2) [Best response, firm B]
(2)
From best response function of firm A:
When PA = 0, PB = 108 / 1.5 = 72 [vertical intercept]
From best response function of firm B:
When PA = 0, PB = 126 / 4 = 31.5 [vertical intercept]
(3) PB = 20
Best response, firm A: 8PA - 1.5PB = 108
8PA - (1.5 x 20) = 108
8PA - 30 = 108
8PA = 138
PA = 17.25
(4) PA = 36
Best response, firm B: 4PB - 0.5PA = 126
4PB - (0.5 x 36) = 126
4PB - 18 = 126
4PB = 144
PB = 36
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A 12 oz box of sugar costs $3.10 and a 36 oz box of sugar costs $7.90. Which box of sugar is the better buy?
Answers
Answer: 36 oz box
Step-by-step explanation:
3.1/12=0.258333
7.9/360.291444
Thus, the 36 oz box is the better buy
Nine busses of students, teachers, and parents went on a field trip. If 5 of the buses held 63 people each and the other buses held 54 people each, how many people went in all?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total number of people want in all is 531.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of buses = 9
Number of buses that has 63 people = 5
Number of buses that has 54 people = 4
The total number of people in all the buses.
= 5 x 63 + 4 x 54
= 315 + 216
= 531
Thus,
The total number of people want in all is 531.
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Find what percent 768 is of 3,200.
Answers
Answer:
3200 of 768 is 416.67%
Step-by-step explanation:
There's your answer hope this helps.
X% ————— 768
X= 24%
Find the value of x.
(3x +20)
(5x - 16)
0.5
74
O
18
2
Answers
Answer:
74 and 18
Step-by-step explanation:
what is the arithmetic sequence for 128,96,64,32 fraction form
Answers
--------------------
4n-1Step-by-step explanation:
128 and r = 3 over 4 (127,) . (3 over 4) apply the product rule to 3 over 4 and I don't kno the rest but that's it