If you're looking for the cube roots of √(3 + i ), you first have to decide what you mean by the square root √(…), since 3 + i is complex and therefore √(3 + i ) is multi-valued. There are 2 choices, but I'll stick with 1 of them.
First write 3 + i in polar form:
3 + i = √(3² + 1²) exp(i arctan(1/3)) = √10 exp(i arctan(1/3))
Then the 2 possible square roots are
• √(3 + i ) = ∜10 exp(i arctan(1/3)/2)
• √(3 + i ) = ∜10 exp(i (arctan(1/3)/2 + π))
and I'll take the one with the smaller argument,
√(3 + i ) = ∜10 exp(i arctan(1/3)/2)
Then the 3 cube roots of √(3 + i ) are
• ∛(√(3 + i )) = ¹²√10 exp(i arctan(1/3)/6)
• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + π/3))
• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + 2π/3))
On the off-chance you meant to ask about the cube roots of 3 + i, and not √(3 + i ), then these would be
• ∛(3 + i ) = ⁶√10 exp(i arctan(1/3)/3)
• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/3 + 2π/3))
• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/6 + 4π/3))
PLEASE HELP !!! URGENT
Answer:
The answer is B--> 111 degrees
Answer:
Here
X=75+36(Exterior angle of a triangle is equal to sum of interior opposite angle)
X=111
A cylinder has a base radius of 6 feet and a height of 12 feet.What is it's volume in cubic feet, to the nearest tenths place
Answer:
[tex]volume = \pi {r}^{2} h \\ = 3.14 \times {6}^{2} \times 12 \\ = 1357.2 \: {ft}^{3} [/tex]
Ella stacks two boards under a table to make it level. One board is į inch thick. The
other board is inch thick. Which equation most closely estimates the thickness of
5
12
the two boards?
Step-by-step explanation:
the problem description is incomplete or wrongly copied.
we don't know the thickness of the boards, and we cannot understand what we need to calculate, and what the answer options are.
5 bricks weigh 26 1/4 how much do 1 brick weigh
Answer:
5 1/4
Step-by-step explanation:
5 1/4 + 5 1/4 + 5 1/4 + 5 1/4 + 5 1/4 = 6 1/4
what is the value of the 5 in the number 624.95
Answer:
5 Hundredths
Step-by-step explanation:
The place value of 5 in 624.95 in 5 Hundredths or 0.05
Can I get the answer for 3 4 5 6
3) x=190, <BOC=85
4) x=177, <TOU=31
5) x=61, <LOM=110
6) x=55, <DOE=117
Express the given set in roster form.
Answer:
E= { 13 , 14 , 15 , .........94 }Step-by-step explanation:
hope it may help u
please mark as brainlist
(๑˙❥˙๑)
The cost of 120 PSP is Dh 15000. Find the cost of one PSP
Answer:
125
Step-by-step explanation:
120 units cost 15000.
so, 1 unit is then the 120th part of the total costs.
price of 1 unit = 15000/120 = 1500/12 = 125
Which algebraic expression is a polynomial?
Answer:
the last one is a polynomial
Step-by-step explanation:
PLEASE HELP WILL MARK YOU!!!
Answers:
a = 69b = 47c = 116d = 93e = 86==========================================================
Explanation:
For now, focus on the triangle with angles 'a', 71 and 40 degrees.
Recall that for any triangle, the inside angles always add to 180
a+71+40 = 180
a+111 = 180
a = 180-111
a = 69
---------------
Notice how angles b and 133 are adjacent and form a straight angle. This makes them supplementary. Meaning they add to 180
b+133 = 180
b = 180-133
b = 47
---------------
Let angle f be adjacent to angle c, and part of the triangle with angles 'a' and b.
Use the rule mentioned in the first section
a+b+f = 180
69+47+f = 180
116+f = 180
f = 180-116
f = 64
Now we can find angle c, because angles f and c are supplementary
c+f = 180
c+64 = 180
c = 180-64
c = 116
We could also use the remote interior angle theorem to say that a+b = c, so c = a+b = 69+47 = 116
---------------
Next, focus your attention on the 140 degree angle. The missing adjacent angle to this is 180-140 = 40 degrees
Now focus on the triangle that has angles d, 40, and 47. The "40" being what we just calculated in the previous paragraph.
We'll do the same thing as before
d+40+47 = 180
d+87 = 180
d = 180-87
d = 93
---------------
The angle just above angle d is also the same (vertical angles). This upper triangle has angles 40, d and g, where g is unknown. Let's find it.
40+d+g = 180
40+93+g = 180
133+g = 180
g = 180-133
g = 47
The vertical angle across from this is also 47 degrees.
Similarly, we can move that angle b over to its vertical pairing counterpart.
The smallest triangle at the very top has angles e, b, and g
e+b+g = 180
e+47+47 = 180
e+94 = 180
e = 180-94
e = 86
In need help with the answer
Answer:
2
Step-by-step explanation:
there is 2: 3 1
4
Sum of two numbers is 84. If one of the numbers exceeds the other by 12, the numbers are
Answer:
54 and 30
Step-by-step explanation:
84÷2=42-12=30
42+12=54
Please help me I need help no links please
How to solve and answer for the question
5
Step-by-step explanation:
AB=CD (Opposite sides of a parallelogram are equal)
11x-13=42
11x=42+13
11x=55
x=55/11
x=5
For breakfast one morning, mum made 10 rotis. Rahul ate 1 1/2 rotis, Priya ate 2
rotis and Aman ate 3 1/4 rotis.
1. How many rotis did the children eat in total?
2. How many rotis were left?
If f={(-1,-3), (1,1),(2,3),(4,6)} and g={(-1,-1),(1,7),(4,3)} what is (f+g)(4)?
Answer:
(f + g)(4) = 9
Step-by-step explanation:
We have that:
f = {(-1,-3), (1,1),(2,3),(4,6)}
this means that:
f(-1) = -3
f(1) = 1
f(2) = 3
f(4) = 6
and we also know that:
g = {(-1,-1),(1,7),(4,3)}
hich means that:
g(-1) = -1
g(1) = 7
g(4) = 3
Now we want to find:
(f + g)(4)
For the general case of two functions f(x) and g(x)
(f + g)(x) = f(x) + g(x)
Then:
(f + g)(4) = f(4) + g(4)
and we know both of these values, so we can just replace them:
(f + g)(4) = f(4) + g(4) = 6 + 3 = 9
Then we get:
(f + g)(4) = 9
formula of simple intrest
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Yes No No Opinion Number of individuals 40 60 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. 12. Refer to Exhibit 12-1. The calculated value for the test statistic equals a. 2 b. -2 c. 20 d. 4 Answer: 13 Refer to Exhibit 12-1. The number of degrees of freedom associated with this problem is a. 150 b. 149 c. 2 d. 3 Answer: Refer to Exhibit 12-1. The p-value is a. larger than 0.1 b. less than 0.1 c. less than 0.05 d. larger than 0.9 Answer: Refer to Exhibit 12-1. The conclusion of the test (at 95% confidence) is that the
a. distribution is uniform
b. distribution is not uniform
c. test is inconclusive
d. None of these alternatives is correct.
Answer:
hvbiknbtUKvfnvghj
vhkbn
bhjn
bhmm
bhnm
hgg
bjj
bhj
A bookshelf holds 5 sports magazines and 5 architecture magazines.
When 3 magazines are taken from the shelf at random, without replacement, what is the probability that all 3 are architecture magazines?
3/25
1/125
1/12
1/8
Answer:
1/12
Step-by-step explanation:
The first time the person picks a magazine, they have a 5/10 chance of drawing an architecture magazine.
The second time, they have a 4/9 chance because they have already removed one magazine from the bookshelf
The third time, they have a 3/8 chance because they have already removed 2 magazines.
Multiply all of the probabilities together
5/10 * 4/9 * 3/8 = 60/720
Simplify:
60/60 / 720/60 = 1 / 12
Hope this helps!
Help me with this math
Answer:
5196
Step-by-step explanation:
So it's 5040+(-156)
We have to find the absolute value
|-156|=156
5040+156=5196
Use this table to find how much tax you need to pay on a taxable income of 40,000
Answer:
$14,386.25
Step-by-step explanation:
Please guys answer me fast
Answer:
24 possible combinations in total,
just 3 that apply
{B,2},{B,4},{B,6}
one easy way to write the possibility is just
3/24 = 1/8 = 12.5%
Select all expressions equivalent to “-6z+(-5.5)+3.5z+5y-2.5.
*answer choices*
A.-8+5y+2.5z
B.-2.5z+5y-8
C.-8+5y+(2.5z)
D.2.5y+(-2.5z)-5.5
E.5y-8-2.5z
Answer:
B.) -2.5 z + 5 y - 8
Step-by-step explanation:
- 6 z + ( - 5.5 ) + 3.5 z + 5 y - 2.5
combine like terms
- 6 z + 3.5 z + 5 y -5.5 - 2.5
- 2.5 z + 5 y - 8
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
1. The given series is
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =
For n=1
L.H.S=4.6=24
R.H.S=[4×5×15]÷6
=300÷6
=50
So, for n=1,
L.H.S≠ R.H.S
Since the given expression is true for n=1 ,
So , the given series is untrue.
we should replace R.H.S by=4(n+1)(n+2)(4n-3)²
2.
12+42+72+.......+(3 n -2)2=
For n=1,
L.H.S=12
R.H.S=1×(6-3-1)/2
=2/2
=1
As L.H.S≠ R.H.S
We should Replace R.H.S by [(3 n-1)(3 n-2)]2
3.The given sequence is
2+4+6+....+2n=n(n+1)
L.H.S
P(1)=2
R.H.S
1×(1+1)
=1×2
=2
( b) L.H.S
P(n)=2+4+6+.....2 k
This is an A.P having n terms.
tex]S_{n}=
= n(n+ 1)
R.H.S=n(n+1)
So, P(k)=k(k+1)
(c) P(k+1)=2+4+6+.......+2(k+1)
This is an A.P having (k+1) terms.
=(k+1)(k+2)
So, P(k+1)= (k+1)(k+2)
(Btw this is not my answer)
Question 3 (1 point)
3
A sample proportion is calculated from a sample size of 3. How large of a sample
would we need in order to decrease the standard error by a factor of 8?
1) 93
2) 51
3) 24
4) 192
5) 8
Solve the following equation using the quadratic formula. x^2 - 8x + 97 = 0
Answer:
undefined in the set of real numbers
Step-by-step explanation:
See image below:)
Two competing companies are having sales on laptops. Laptop #AX330M has a retail price of $2,100. The Buy Less is advertising #AX330M for 15% off, while Sell More has stated they will match any competitor’s advertised special and take an additional 10% off of the competitor’s advertised price. How much money is saved by purchasing the laptop from Sell More instead of Buy Less?
Answer: I only need the points :) <3
Step-by-step explanation: Two competing companies are having sales on laptops. Laptop #AX330M has a retail price of $2,100. The Buy Less is advertising #AX330M for 15% off, while Sell More has stated they will match any competitor’s advertised special and take an additional 10% off of the competitor’s advertised price. How much money is saved by purchasing the laptop from Sell More instead of Buy Less?
Monica has a triangular piece of fabric. The height of the triangle is 27 inches and the triangle's base is 18 inches. Monica says that the area of the fabric is 486 in2. What error did Monica make? Explain your answer by entering the correct area of the fabric.
Monica forgot to multiply by___
The area of the fabric is ____ in.2
let f(x)=x-1 and g(x)=x^2+1
f(g)=___
Answer:f(g)=2
Step-by-step explanation:
factorise m2+10m-24 please step by step
m^2+10m-24
=m^2+12m-2m-24
=m (m+12)-2 (m+12)
=(m-2)(m+12)
Answer:(m-2)(m+12)
if wrong correct me pls
I hope it helps mate
HAVE A GREAT DAY
#Liliflim
