Answers
1. [tex]i^{23}[/tex] = - i
2. [tex]\sqrt{-128}[/tex] = 8i√2
Explanation:Steps to simplify complex numbers:
Write the division as a fraction when dividing complex numbers. Then multiply both the numerator and the denominator by the denominator's conjugate. Then, use FOIL or the Distributive Property to simplify.Understanding how complex numbers work in their various operations requires simplifying complex numbers.1. To simplify [tex]i^{23}[/tex]
We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]
write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]
[tex](i^{4)^{5} } (i^{2} . i )[/tex] = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]
we know [tex]i^{2}[/tex] = -1
((-1²))⁵ [tex](i^{2} .i)[/tex]
we know that -1² = 1
= 1⁵ [tex](i^{2} .i)[/tex]
= 1 [tex](i^{2} .i)[/tex]
= [tex](i^{2} .i)[/tex]
here [tex]i^{2}[/tex] =-1
-1 . [tex]i^{}[/tex]
= - i
so [tex]i^{23}[/tex] is -i
2. To simplify [tex]\sqrt{-128}[/tex]
= [tex]\sqrt{(- 1) . (128)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]
here [tex]}\sqrt{-1}[/tex] = i
substituting i we get
= i . 8 √2
= 8i√2
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Related Questions
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
a. Ø
b. {all reals}
c. {1/7}
Answers
Answer:
A
Step-by-step explanation:
(-8x + x) + 15 = -7x +12
-7x +15 = -7x + 12
15 = 12 There are no solutions
please answer these question
What age would a dog be in human years if he is 3 in dog years?
what is glow in the dark things made out of?
Answers
Answer:
Dog be 28
Phosphors apparently
Step-by-step explanation:
"-2+8" > "-2" heeeeelpp
Answers
Answer: Yes this equation means 6 is greater than -2, making this a true statement if that was what you're asking for.
A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
Answers
The speed of the boat in still water is 6miles/hour miles per hour.
The speed of the current is 3miles/hour miles per hour.
The distance travelled by the boat downstream(with the flow current of river) is 240 miles.
The distance travelled by the boat upstream(Against the flow current of river) is 240 miles.
Time taken to travel downstream = 20 hours.
Time taken to travel upstream = 60 hours.
Let us say the velocity of the boat is V and the velocity of the current flow of river is U.
The relative velocity of boat with respect to ground while going downstream is,
velocity of boat in downstream = V + U.
As we know,
Velocity = distance/time
Putting values of downstream motion,
V + U = 240/20
V + U = 10
Let us say this is our equation 1.
The relative velocity of boat with respect to ground while going upstream is,
velocity of boat in upstream = V - U
As we already know,
Velocity = distance/time
Putting the values of upstream motion,
V - U = 240/60
V - U = 3
Let us say this is our equation 2.
Now, on adding equation 1 and 2.
V+U+V-U = 10 + 3
2V = 13
V = 6.5 miles per hour.
Rounding off to the nearest integer,
V = 6 miles/hour.
Putting V = 6.5 miles/hour in equation 1,
6.5 + U = 10
U = 3.5 miles/hour.
Rounding off to the nearest integer,
U = 3 miles/hour
The velocity of river current is 3 miles/hour and velocity of boat is 6miles/hour.
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A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours. Use this information to fill in the following blanks.
The speed of the boat in still water is ______ miles per hour.
The speed of the current is ______ miles per hour.
please show work out
find the dimension of A34×b41 matrix]
Answers
A34 should represent either a square matrix with number of columns=number of rows =34 or the 4th element in the 3rd row in the matrix A [which is not possible in the given matrix since each row has only 3 elements]
The dimension of a matrix is given as (the number of rows it has, say a) x (the number of columns it has, say b) [read as a by b].. The given matrix has 4 rows and 3 columns, so its dimension is 4x3.
For a matrix A of dimension axb to be multiplied with a matrix B of dimension cxd, the number of columns of matrix A should be equal to the number of rows of matrix B, that is b = c should be satisfied. In this case both matrices are of the same dimension 2x3 but 3 (number of columns in first matrix) is not equal to 2 (number of rows in second matirx). So these matrices cannot be multiplied as their dimensions do not match.
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Given a normal distribution with mean M = 8 and σ = 3,
What is the x value corresponding to z = 0.4?
Answers
123
[tex]123 > x = 10 > 6[/tex]
What is the length of cd ?
Answers
Answer:
7
Step-by-step explanation:
since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that
what is 0.4111111… as a fraction
Answers
Take 0.41111... as x
Thus 10x = 4.11111... and 100x= 41.1111...
=> 100x - 10x = 41.1111... - 4.111111
=> 90x=37
=> x= 37/90
=> 0.4111... = 37/90
What is the answer to f(2)=
Answers
the answer is 2f
Re-order terms so constants are on the left
f×2=2f
Which numbers I have to put in the boxes
Answers
find the area. please explain how to get it
Answers
Answer:
Step-by-step explanation:
(the small double lines like = means that the length of those sides are all same)
So, if one length is considered as x
the other two will also be x
we see that the length of one side is given which is 27
to find x
x + x + x = 27
3x = 27
so, x = 27/3
x = 9m
(the small vertical single line means that those sides are equal)
so if one side is y, the other two are also y
so , y + y+ y = 30
3y = 30
y = 10m
If we imagine the stairs to be made of small rectangles of length 10m and base 9m , finding area will be easier.
we will see that there are 9 rectangles in total
area of rectangle = length x base
so, area of 1 rectangle = 9x10
= 90[tex]m^{2}[/tex]
so area of 9 identical rectangles = 9 x 90
= 810 [tex]m^{2}[/tex]
NAME
DATE
PERIC
Lesson 3: More about Constant of Proportionality
Cool Down: Fish Tank
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table
as you answer the questions.
1.
How many gallons of water will be in the fish tank after 3 minutes? Explain your
reasoning.
2.
How long will it take to fill the tank with 40 gallons of water? Explain your reasoning
3. What is the constant of proportionality?
Answers
The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality then the constant of proportionality exists r = 1.6.
What is meant by constant of proportionality?The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality.
Given
x y
0.5. 0.8
1. 1.6
3. 4.8
25. 40
To estimate the constant of proportionality uses the following formula:
y = r x
Where r is the constant of proportionality;
Simplify the value of r, we get
r = y/x
Substitute the values of x = 0.5 and y = 0.8, in the above equation then
r = 0.8/0.5
r = 1.6
When x = 1 ; y = 1.6
r = 1.6/1
r = 1.6
When x = 3; y = 4.8
r = 4.8/3
r = 1.6
When x = 25 ; y = 40
r = 40/25
r = 1.6
The value of r exists constant.
Therefore, the constant of proportionality exists r = 1.6.
The complete question is:
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table and answer the question below.
time (minutes) water (gallons)
0.5 0.8
1
3
40
What is the constant of proportionality?
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0.8-2x=-1.4
Solve for x
Answers
Answer:
x= -0.3
Step-by-step explanation:
0.8-2x=1.4 Set up equation
-2x=1.4-0.8 Put Like terms together
-2x=0.6 Subtract like terms
x=0.6/-2 Divide
x=-0.3 Answer
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $456. What was the simple interest rate of the bonds?
Answers
5.7%
Explanaton:let amount invested = Principal = $8000
time = 1 year
rate = ?
Interest = $456
To get the rate, we'll apply simple interest formula:
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \end{gathered}[/tex][tex]\begin{gathered} 456\text{ = 8000}\times R\times1 \\ 456\text{ = 8000R} \\ \text{divide both sides by 8000:} \\ \frac{456}{8000}\text{ =}\frac{8000R}{8000} \\ \\ R\text{ = 0.057} \\ In\text{ percent, rate = 0.057}\times100 \\ \text{Rate = 5.7\%} \end{gathered}[/tex]Hence, the simple rate of the bonds is 5.7%
please help me solve this
Answers
It is to be noted that:
The current total bid for Empire design is $3,060,000The current total bid for Build-EM-UP-CO is $ 3,120,000.What is a bid?Bidding is an individual or business's offer to establish a price for a product or service or a demand that something be done. Bidding is a method of determining the price or worth of something. Bidding may be done by a person who is influenced by a product or service in a given setting.
The calculations are given as follows:
Given:
Proposal of Empire design:
$30000 x b
$ 60000/ I beam
Proposal of Build-EM-UP-CO.
$32000 x b
$ 40000/ I beam
Empire Design
Since b = 9ft; and number of I beams = 6, Hence
Total bid = (300,000 * 9) + (60,000 * 6)
= $3,060,000
Build-EM-UP-CO.
Recall that b = 9ft; and number of I beams = 6, Hence
Total Bid = (320,000 * 9) + (40,000 * 6)
Therefore,
Total bid = $3,120,000.
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Full Question:
For full details of the question, see the attached image
please help need this asap!!!!! PLEASE SOMEONE ANSWER I WILL GIVE EXTRA POINTS!!!
Answers
The area of the circles are as follows:
254.34 km²1962.5 mm²379.94 m² 907.46 cm²How to find area of a circle?The area of a circle can be found as follows;
area of a circle = πr²
where
r = radiusTherefore,
a.
area of the circle = πr²
diameter = 18km
r = 18 / 2
r = 9 km
Hence,
area of the circle = πr²
area of the circle = 3.14 × 9²
area of the circle = 254.34 km²
b.
area of the circle = 3.14 × 25²
area of the circle = 3.14 × 625
area of the circle = 1962.5 mm²
c.
area of the circle = 3.14 × 11²
area of the circle = 3.14 × 121
area of the circle = 379.94 m²
d.
area of the circle = 3.14 × 17²
area of the circle = 3.14 × 289
area of the circle = 907.46 cm²
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A farmer has 25 goats with a mean mass of 74 kg.
The farmer acquires a new goat and the mean mass becomes 72 kg.
What is the mass of the new goat?
Answers
Answer: 72
Step by step explanation:
sum of the masses of the 25 goats take as x then x/25=74 so 74×25=x x=1850 after buying a new goat number of goats =26
hope i helped <3
You invested $101 and received $106.05 after one year. What was the interest rate?
Answers
The rate of interest was 5%.
The rate of interest and simple interest can be related through the formula -
S.I. = PRT/100, where S.I. stands for simple interest, P stands for principal, R stands for rate of interest and T stands for time.
Amount = Principal + Interest
Interest = 106.05 - 101
Performing subtraction on Right Hand Side of the equation
Interest = $5.05
Rate of interest = (5.05×100)/(101×1)
Performing multiplication in numerator and denominator
Rate of interest = 505/101
Performing division
Rate of interest = 5
Therefore, to earn $106.05 from $101 in one year, the rate of interest should be 5%.
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Which is larger, 52 or 33?
Answers
Answer:
52
Step-by-step explanation:
52 is a bigger number than 33?
Quadrilateral ABCD is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation and location of quadrilateral EFGH.
Answers
The translation of Quadrilateral ABCD with coordinates A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) using the given transformation rule is; E(3, -1), F(7, -2), G(9, 1), H(7, 1)
What is the translation?
We are given the vertices of Quadrilateral ABCD as;
A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)
Now, we are told that it is first translated right by 6 units. This means that we would add 6 units to each x-value to get;
A'(-3 + 6, 4) = A'(3, 4)
B'(1 + 6, 3) = (7, 3)
C'(3 + 6, 6) = C'(9, 6)
D'(1 + 6, 6) = D'(7, 6)
It is now translated by 5 units downwards and we subtract 5 from each y-value and this gives us;
E(3, -1), F(7, -2), G(9, 1), H(7, 1)
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Complete question is;
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation and location of quadrilateral EFGH.
!!!Need Help ASAP
R=42−0.7t
Quinn returned home one summer's day to find it extremely hot. He turned the air conditioner on, and the room's temperature began decreasing at a constant rate. The equation shown above gives the room's temperature, R, in degrees Celsius, t minutes after Quinn turned on the air conditioner. What was the room's temperature, in degrees Celsius, when Quinn returned home?
Answers
The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.
What is the Y-intercept or Initial Value of a Linear Equation?The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".
Alternatively, it can be rewritten as y = b + mx.
R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.
Interpreting the equation, we can deduce the following:
The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.
The unit rate or rate of change (m) = -0.7 degrees per minute.
Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.
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Express each phrase as a rate and unit rate.
(Round your answer to the nearest hundredth.)
1) 7 calculators cost $120.00
Answers
Answer:
$100.00
Step-by-step explanation:
5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's
A 100ml tub of ice cream costs £1.50. Work out how much 500ml tub of ice cream would cost.
Answers
Answer:
Answer: 7.5 or 7 1/2.
Find the equation of the line that contains the point (-1,-6) and is parallel to the line 4x + 7y=11. Write the equation in slope-intercept form, if possible.
answer box to complete your choice.
Answers
Answer:
y = -4/7x - 46/7
Step-by-step explanation:
4x+7y=11
7y=11-4x
y=-4/7x + 11/7
Slope or parallel line: -4/7
Point=(-1,-6)
y+6 = -4/7(x+1)
y = -4/7x - 46/7
:]
(Can anyone answer this please? I need it ASAP!!) A2B3C4 (in hexadecimal) - 3F2E1D (in hexadecimal) = ______________
Answers
The hexadecimal value from the operation is 6385A7
Hexadecimal NumbersTo solve this problem, we have to subtract the hexadecimal numbers from one another.
In doing so, we would subtract 3F2E1D from A2B3C4.
This would give us,
[tex]A2B3C4 - 3F2E1D = 6385A7[/tex]
The value of the expression is 6385A7.
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a box has 12 red cards and 12 black cards. another box has 24 red cards and 24 black cards. you want to draw two cards randomly from one of the two boxes, one card at a time. which box has a higher probability of getting cards of the same color and why?
Answers
Select red from A and B then the probability of getting cards of same color is 12/24 * 24/48 = 1
Box A: 12 Red
12 Black
Box B: 24 Red
24 Black
One card is selected from Box A and placing the selected card into Box B.
One card is selected from Box B.
What is the probability that a red card is selected from Box B?
Two things can occur:
1) Select red from A and B:
12/24 * 24/48 = 1
2) Select black from A and red from B:
12/24 * 24/48 = 1
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Please help me find out what 758x92 is
Answers
Answer:69736
Step-by-step explanation:
is the answer
What is the equation of the line that passes through the point (−3,1) and has a slope of −3?
Answers
step-by-step explanation:
see image (also use some of my explanation from my previous answer)
Carmen is about to complete a jigsaw puzzle the puzzle and one remaining piece are shown below what transformation can shark Carmen apply to the final piece to fit into the puzzle
Answers
We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.
Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.
Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.
A =
h(a + b)/2 solve for b
Answers
Answer: b = (−ah+2a)/h
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Add (-1)/2ah to both sides.
Step 3: Divide both sides by h/2.