Answer:
sqrt(i) =0.707106781 + 0.707106781 i
Most of the numbers we know, and work with, are Real Numbers. The Real Number System includes counting numbers, fractions, terminating decimals, positive numbers, negative numbers, zero, repeating decimals, never ending and non-repeating decimals, numbers that are expressed as radicals, and even pi (π).
The natural numbers are the set of counting numbers
• There are infinitely many numbers in a set of numbers.
• The natural numbers are "closed" under addition and multiplication.
The addition of two natural numbers creates another natural number.
The multiplication of two natural numbers creates another natural number.
closed under addition and multiplication.
BUT ...
The subtraction of two natural numbers does NOT necessarily create another natural number
The division of two natural numbers does NOT necessarily create another natural number
The whole numbers are the set of counting numbers (natural numbers) along with zero
• There are infinitely many numbers in this set of numbers.
• The set of whole numbers is "closed" under addition and multiplication.
Integers:
• The integers are the set of all of the natural numbers,
plus their additive inverses and zero
• The integers are "closed" under addition, multiplication and subtraction,
but NOT under division
Rational Numbers:
• The rational numbers are the set of numbers which can be expressed as a ratio
(a fraction) between two integers.
• Integers are rational numbers since 5 can be written as the fraction 5/1.
• Decimals which terminate are rational numbers.
• Decimals which have a repeating pattern are rational numbers. 1/3 = 0.3333333...
• The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false. Some texts state that "the rationals are closed under division as long as the division is not by zero" which is a true statement.
Irrational Numbers:
The irrational numbers are the set of number which can NOT be written as a ratio (fraction).
• Decimals which never end nor repeat are irrational numbers.
• Irrational numbers are "not closed" under addition, subtraction, multiplication or division.
• Examples of irrational numbers: rad2, π
This is figured out by first figuring out that:
√(√(i)) = [tex]i^{1/4\\}[/tex]
Let [tex]\sqrt{i}[/tex] be a + b[tex]i[/tex].
Square both sides to get [tex]i[/tex] = (a + b[tex]i[/tex])(a + b[tex]i[/tex])
So, [tex]i[/tex] = a² - b² + 2ab[tex]i[/tex]
a² - b² is the real part. The real part is 0.
0 + [tex]i[/tex] = a² - b² + 2ab[tex]i[/tex]
a² - b² = 0
[tex]i[/tex] = 2ab[tex]i[/tex]
2ab = 1
ab = 1/2
b = 1/2a
Now, since a² - b² = 0,
a² - (1/2a)² = 0
a² - 1/(4a²) = 0
[tex]\frac{(4a^{4}-1 )}{4a^{2} }[/tex] = 0
That means the numerator MUST be 0.
[tex](4a^{4}-1 )}[/tex] = 0
[tex]4a^{4}[/tex] = 1
[tex]a^{4}[/tex] = 1/4
a = ± [tex]\frac{1}{\sqrt{2} }[/tex]
if a = [tex]\frac{1}{\sqrt{2} }[/tex] , then b = [tex]\frac{1}{\sqrt{2} }[/tex]
If a = -[tex]\frac{1}{\sqrt{2} }[/tex] , then b = -[tex]\frac{1}{\sqrt{2} }[/tex]
So, it's either a = -[tex]\frac{1}{\sqrt{2} }[/tex] and b = -[tex]\frac{1}{\sqrt{2} }[/tex] , or a = [tex]\frac{1}{\sqrt{2} }[/tex] and b = [tex]\frac{1}{\sqrt{2} }[/tex]
That's why sqrt(i) =0.707106781 + 0.707106781i, or sqrt(i) = -0.707106781 - 0.707106781i
A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ft/sec. The function s(t)=−16t2+20t+3 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
[tex]t=\frac{5}{8}s[/tex] and [tex]s(\frac{5}{8})=\frac{37}{4}ft[/tex]
Step-by-step explanation:
There are different approaches you can take to solve this problem. You can look at it from the geometric approach or the calculus approach. I will us the geometric approach.
When we analyze the given function for the height of the ball:
[tex]s(t)=-16t^2+20t+3[/tex]
we can see that we are dealing with a quadratic function. This means that the graph will be an inverted parabola, just like the one in the attached picture.
so the idea is to find the vertex of the parabola to find the highest the ball gets to be and the time it gets to be at that height.
In order to do so, we can use the vertex formula, which looks like this:
[tex]t=-\frac{b}{2a}[/tex]
this is use when you have a function with the form:
[tex]f(x)=ax^2+bx+c[/tex]
in this case:
a=-16, b=20 and c=3, so the formula then turns to:
[tex]t=-\frac{20}{2(-16)}[/tex]
which yields:
[tex]t=\frac{5}{8} s[/tex]
which is our first answer. So we can then use this to find the maximum height of the ball, just by substituting t into the original function:
[tex]s(\frac{5}{8})=-16(\frac{5}{8})^2+20(\frac{5}{8})+3[/tex]
which yields:
[tex]s(\frac{5}{8})=\frac{37}{4} ft[/tex]
which is our second answer.
plz help me i need it
I can't see the choices real well, but I think it's b, 35%.
Answer:
B 35% is the answer
A rectangular box is 8 inches long, 10 inches wide and 6 inches tall. What is the approximate length of its longest diagonal? 10 inches 14.1 inches 4.9 inches 24 inches
Answer:
d = 10 inches
Step-by-step explanation:
It is given that,
The length, breadth and the height of a rectangular box is 8 inches×10 inches ×6 inches
We need to find the length of its longest diagonal.
In a rectangle, 6 inches will act as perpendicular and 8 inches will be base. The diagonal can be calculated using Pythagoras theorem as follows :
[tex]d=\sqrt{8^2+6^2} \\\\=\sqrt{64+36}\\\\=10\ \text{inches}[/tex]
So, the length of its diagonal is 10 inches.
15!!! POINTS!!! PLS ANSWER THIS IM HAVING WAY TOO MUCH TROUBLE WITH IT. I’m in 10th grade and this is compound interest. PLS HELP ME IXLS SO FRUSTRATING!!! If you don’t know PLS don’t comment I’ve been doing this for over 2 hours pls
Answer:
well im in 7th sorry i cant help
Step-by-step explanation:
Answer:
6 years
Step-by-step explanation:
if we want to know how much i will get with interest
simple interest amount = principal amount × (rate / m) × n
plus the initial quantity
where m is 12 months per year
and n is the number of months
[tex]4451=2887(\frac{0.09}{12months/year})(n)+2887\\\\4451=2887[\frac{0.09}{12}(n)+1]\\\\(\frac{0.09}{12}\cdot n)+1=\frac{4451}{2887}\\\\\frac{0.09}{12}\cdot n=1.54-1\\\\n(0.09)=12(0.54)\\\\n=\frac{12(0.54)}{0.09}\\\\n=72.23\longleftarrow months[/tex]
so we need to convert it to years
[tex]72.23=12(6)+0.019[/tex]
6 years and 0 months
I apologize if there is some mistake in my answer
Select the correct answer.
What is the sqare root of 75 in simplest form?
Answer:
75 = 25 x 3.
Step-by-step explanation:
this is the answer the picture above
HELPP!!
Mary earns $12 per hour, plus 10% commission on all her sales. Mary worked 10 hours and her sales were $1,500. How much money
did Mary earn?
First, you multiply 12 and 10 to get how much money she earned in 10 hours. She earned 120 dollars in 10 hours. Next, you multiply 10% and 1500. You turn 10% into 0.10, and multiply by 1500 to get 150. Finally you would add 150 and 120 to get $270. Mary earned $270.
HELP!
I need the letter of it ill give the the brainiest
Answer:
It's B.
Hope this helped :)
What’s the unit rate of 2 1/3 miles in 2 hours
Answer:
7/6 miles
Step-by-step explanation:
As, Distance for 1 hour = x
For 2 hours = 2 1/3
For 2 hours = 2(x)
So, 2(x)= 2 1/3
2(x)= 7/3
So, x = 7/3 ÷ 2
So x= 7/3 x 1/2
Therefore, x = 7/6
Final answer= 7/6 miles per hour
Please answer correctly !!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!
Answer:
Not too sure because I don't know how it works for your site but drag the B dot to the A dot and drag that A dot to the C dot so their all going through the lines while being connected.
(sorry if its incorrect had a hard time reading the picture)
The solution of the
equation 4p-2=10 is
(a)1
(b) 2
(c)3
(d)4
Answer:
option c
steps.4p-2=10
4p=2+10
4p=12
p=3
Answer:
(c) 3
Step-by-step explanation:
4p - 2 =10
4p =10 +2
4p =12
P =12 :4
p=3
|5x|>-4
Solve the following inequality
Answer:
all numbers
Step-by-step explanation:
|5x|>-4
Absolute values are greater than or equal to zero
This says that our absolute value is greater than a negative number
This is always true so x can be any number, so it has infinite solutions
x is all real numbers
Fatima invests a total of $29,000 in two accounts. The first account earned a rate of return of 11%. However, the second account suffered a 7% loss in the same period. At the end of one year, the total of money gained was $1,570.00. How much was invested into each account?
Step-by-step explanation:
given data:
gained = $1,570
amount invested = $29,000
0.11x – 0.07( $29,000 – x ) = 1540
0.11x – ( 2030 – 0.07x ) = 1540
0.11x + 0.07 = 1540 +2030
0.18x = 3570
divide both sides by 0.18
x = 19833.33 ( amount invested at 11%.
$29,000 – 19833.33
= $9166.7 ( amount invested at 7%)
PLEASE HELPPPPPJohn and Kathy are shopping for their first home. Between the two of them, they feel they can afford a $1400 monthly house payment. The bank has already preapproved them for a 30-year loan with 5.4% interest. What is the maximum house price John and Kathy can afford?
Answer: $249,300
Step-by-step explanation:
The exact formula would be if I think this is right
PV = PMT(1-(1+r)^-n)/r with r & n adjusted for periodicity
= 1400(1-(1+.054/12)^-360)/(.054/12)
= $249,318.47
which you can round off to, say, $249,300 <------
note:
counterchechecked with a financial calculator
Answer:
239,600
Step-by-step explanation:
6thh grade is harddd yall
Answer:
56
Step-by-step explanation:
i recommend using mathaway, type in "4,8,14"
I need help asap pleaseeeee
Answer:
y=x-3
Step-by-step explanation:
thats the answer
What is the slope of this equation?
What is the y intercept? Explain how you know.
y=−2x+7
Answer:
slope=-2
y intercept= 7
Step-by-step explanation:
Equation of a line:
y=mx+c
where
m=slope of the line, and
c=y intercept
Comparing y=-2x+7 with y=mx+c,
m=-2
y intercept=7
Hope it helps:)
Idk how to do this soooo helppp
Answer:
basically u do the formulas and plug them in.
Step-by-step explanation:
Express 0.02as a percent
Answer:
2%
Step-by-step explanation:
Answer:
2%
Step-by-step explanation:
Just research it to save points. Have a nice day!
Can I have bainliest?
what’s 10/13 as a decimal rounded to the nearest tenth
Answer:
brainleist plzz
Step-by-step explanation:
Fraction Decimal Percentage
10/13 0.7692 76.92%
A fraction is a way to describe a part of a whole. The value of 10/13 as a decimal rounded to the nearest tenth is 0.8.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The given fraction can be written in decimal form by dividing 10 by 13, therefore, we can write the fraction as,
10/13
= 10 ÷ 13
= 0.76923
Since the number is needed to be rounded off to the nearest tenth, therefore, we need to look at the hundredth term, if that term is more than equal to 5, we will leave the tenth term as it is, while if the hundredth term is more than 5 we will round off the tenth term to the next term.
In this case, the hundredth position is taken by 6, therefore, the tenth term will become 8 from 7.
10/13
= 10 ÷ 13
= 0.76923 ≈ 0.8
Hence, the value of 10/13 as a decimal rounded to the nearest tenth is 0.8.
Learn more about Fraction here:
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10. The ratio of the number of male employees to the number of female employees in Westlake high school is 6:5. There are 40 females in the school. How many total employees are in Westlake high school?
Answer:
45
Step-by-step explanation:
Male = 6 Male = ?
Female = 5 Female = 40
^
? = 6x5 because 5x5 = 40
HELP! Please include the steps you took as I don't fully understand how to do this!
[tex]22x-17=12x+8[/tex]
plz help I will mark you brainlist plz
Answer:
this is hard is this algabra
find an equation of the line through (4,6) and parallel to y=3x+7
Answer: y = 3x - 6
Step-by-step explanation: A line that is parallel to another line must have the same slope, so you already have y = 3x + b. To find b, use the point that they give. b is the y-intercept, so just subtract 3(x) from the y coordinate of the point, where x is the x-coordinate of the given point.
Yall pray for me I'm doing a huge math test
Answer:
An animal shelter has $2500 in its reserve fund. The shelter charges $40 per animal placement and would like to have at least $4000 in its reserve fund. Write an inequality to represent this situation.
Step-by-step explanation:
plz answer
Answer:
OK
Step-by-step explanation:
What type of math geometry? Algebra?
Candidate A and Candidate B are running for mayor. A poll was taken to determine which candidate would likely win the election. The poll is accurate within ±5%. Write an absolute value equation to find the maximum and minimum percentage of voters who will vote for Candidate A if 38% of the voters in the poll voted for Candidate A. Let A represent the percent of voters who will vote for Candidate A.
Answer:
[tex]|A-38|=5[/tex]
33% or 43%
Step-by-step explanation:
Given that poll is accurate within [tex]\pm5[/tex].
38% voters have voted for candidate A.
[tex]A[/tex] is the percent of voters who will vote for candidate A.
So, value of A can be 38+5=43%
OR
38-5 = 33%
We will write an absolute function for the above situation.
But, first of all, let us have a look at the definition of Absolute value function.
[tex]|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.[/tex]
The the value of function gives us a negative sign when the value inside the modulus function is negative.
[tex]A-38[/tex] will be negative when [tex]A < 38[/tex] and
[tex]A-38[/tex] will be positive when [tex]A>38[/tex].
This difference is given as [tex]\pm5[/tex].
Therefore, the absolute value function can be written as:
[tex]|A-38|=5[/tex]
Case 1: [tex]A < 38[/tex]
As per definition of modulus function, it will open with a negative sign.
[tex]-A+38=5\Rightarrow A = 33[/tex]
Case 2: [tex]A>38[/tex]
As per definition of modulus function, it will open with a positive sign.
[tex]A-38=5\Rightarrow A = 43[/tex]
Therefore the answer is 33% or 43%
Pls help ASAP I will give brainlyest
Nile had 20% less strikeouts this year than last year. He had 124 strikeouts last year. Which steps are needed to calculate the number of strikeouts Nile had this year? Check all that apply
(A) Convert 20% to a decimal.
(B) Multiply: 0.2 × 124 = 24.8
(C) Divide: 124 ÷ 20 = 6.2
(D) Subtract: 124 – 24.8 = 99.2
(E) Add: 124 + 24.8 = 148.8
(F) Subtract: 124 – 6.2 = 117.8
Answer:
(A) Convert 20% to a decimal.
(B) Multiply: 0.2 × 124 = 24.8
(D) Subtract: 124 – 24.8 = 99.2
Step-by-step explanation:
Given parameters:
Number of strikeouts last year = 124
Percent reduction = 20%
Unknown:
Number of strikeouts this year =?
Solution:
To find the number of strikeout this year,
Convert 20% to a decimal = [tex]\frac{20}{100}[/tex] = 0.2
Now; Multiply: 0.2 × 124 = 24.8
The number of strikeouts this year = 124 - 24.8 = 99.2
f(x)= 3x^2-7 over
4x^2-3
-find f(2)
Answer:
5/13
Step-by-step explanation:
f(x) = [tex]\frac{3x^{2}-7 }{4x^{2}-3 }[/tex]
Substitute x for 2.
[tex]\frac{3(2)^2-7}{4(2)^2-3}[/tex]
Solve
[tex]\frac{3(4)-7}{4(4)-3}[/tex]
[tex]\frac{12-7}{16-3}[/tex]
f(2)= [tex]\frac{5}{13}[/tex]
The value of f(2) is 5/29.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 3x² -7/ 4x² - 3
Now, find the value of the function at x= 2
So, f(2)= 3(2)² -7/ 4(2)² - 3
f(2) = 3 x 4 -7 / 4 x 8 - 3
f(2) = 5/29
Hence, the value of f(2) is 5/29.
Learn more about function here:
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please help, i need it done soon
Answer:
Point C i think is: (33/8, 0)
Step-by-step explanation:
I hope this helps -w-
would you rather drive a car at the rate of 40 kilometers per hour or drive a car at a rate of 15 meters per second, and why? which one is correct
Answer: 15 meters per second
Step-by-step explanation: Kilometers are 1,000 times larger than meters
There were 60 children at the birthday. If 1/4 of them were boys how many were
boys?
Answer:
15
Step-by-step explanation:
60 x 1/4 = 60/4 = 15