Answer:
Step-by-step explanation:
A complex number is a number that has both real and imaginary part. An example of a complex number is z = x+iy where x is the real part and y is the imaginary part.
If z = x+iy, the conjugate of z₁ will be x-iy
adding the complex number to its conjugate will give;
P = z+z₁
P = x+iy +(x-iy)
open the parenthesis
P = x+iy+x-iy
collect like terms
P = x+x+iy-iy
P = 2x
We can see that the resulting value does not contain the imaginary number i, hence the result is a real number.
Hence the result of adding a complex number to its conjugate is a REAL NUMBER
Taking the difference;
P = = z-z₁
P = x+iy -(x-iy)
open the parenthesis
P = x+iy-x+iy
collect like terms
P = x-x+iy+iy
P = 0+2iy
P = 2iy
We can see that the resulting value contains the imaginary number i, hence the of taking their difference is a complex number.
Hence the result of subtracting a complex number from its conjugate is an IMAGINARY NUMBER
3.99 4.29 and 2.89 range
Answer:
1.4
Step-by-step explanation:
Sample size: 3
Lowest value: 2.89
Highest value: 4.29
Range: 1.4
formula for calculating the range:
Range = maximum(x_i) - minimum(x_i)
where x_i represents the set of values.
missing angle for triangle
Answer:
86
Step-by-step explanation:
33+61=94
180-94=86
Solve each system of equations.
1.
2x – 3y = 3
- 4x + 6y = -6
Answer:
First one: x= -1/2
Second one: x= 1/4
(1 point) Find the antiderivative F of f(x)=4−3(1+x2)−1 that satisfies F(1)=−3.
The value of antiderivative F will be;
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Now,
Since, The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Hence, The antiderivative F of f (x) is,
⇒ F = ∫ (4 - 3 (1 + x²)⁻¹ ) dx
⇒ F = ∫ 4 dx - 3 ∫ (1 + x²)⁻¹ dx
⇒ F = 4x - 3 arc tan x + c
Where, c is constant of integration.
Here, The antiderivative of f (x) is satisfy F(1) = - 3,
So, Substitute x = 1, F = - 3
⇒ F = 4x - 3 arc tan x + c
⇒ - 3 = 4×1 - 3 arctan (1) + c
⇒ - 3 = 4 - 3π/4 + c
⇒ - 3 - 4 + 3π/4 = c
⇒ c = - 7 + 3π/4
Thus, The antiderivative F of f (x) is,
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
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a. Evaluate the polynomial
y = x3− 5x2 + 6x + 0.55 at x = 1.37.
Use 3-digit arithmetic with chopping. Evaluate the percent relative round-off error.
b. Express y as y = ((x − 5)x + 6)x + 0.55 (this is the same equation). Use again 3-digit arithmetic with chopping. Evaluate the percent relative round-off error and compare with part (a). Make the conclusion about which form of the polynomial is superior.
The form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).
To evaluate the polynomial [tex]y = x^3 - 5x^2 + 6x + 0.55[/tex]at x = 1.37 using 3-digit arithmetic with chopping, we substitute x = 1.37 into the expression:
[tex]y = (1.37)^3 - 5(1.37)^2 + 6(1.37) + 0.55[/tex]
Calculating each term;
[tex](1.37)^3[/tex]= 2.559
5[tex](1.37)^2[/tex]= 9.415
6(1.37) = 8.22
Substituting these values into the expression for y,
y = 2.559 - 9.415 + 8.22 + 0.55
y = 1.914
Now, let's move on to part (b).
We will express y as y = ((x - 5)x + 6)x + 0.55,
Now using 3-digit arithmetic with chopping.
Then, we substitute x = 1.37 into the expression:
y = ((1.37 - 5) 1.37 + 6) 1.37 + 0.55
Calculating each term separately:
(1.37 - 5) = -3.63
-3.63 x 1.37 = -4.98
-4.98 + 6 = 1.02
1.02 x 1.37 = 1.3974
Finally, adding 0.55:
y = 1.3974 + 0.55
y = 1.9474
Now, let's compare the percent relative round-off errors in both cases.
In part (a), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was also 1.914. Therefore, the percent relative round-off error is:
(1.914 - 1.914) / 1.914 x 100 = 0%
In part (b), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was 1.9474.
Therefore, the percent relative round-off error is:
(1.9474 - 1.914) / 1.914 x 100 ≈ 1.741%
Therefore, in this comparison, we can conclude that the form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).
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-13.3°C=_________K °C is Celsius and K is Kelvin
Answer:
259.85 K
Formula:
-13.3°C + 273.15 = 259.85K
Step by step solution:
To convert, just add 273.15 to the Celcius value to get the Kelvin value.
Hope this helps!
35. Explain the difference between the reciprocal of x^2
and the inverse of x^2. (number 35 in the pic)
Answer:
As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of [tex]x^2[/tex] is that [tex]\frac{1}{x^2} =x^{-2}[/tex] and [tex]\sqrt{x} =x^{\frac{1}{2}[/tex].
Step-by-step explanation:
First lets find both the reciprocal of [tex]x^2[/tex] and the inverse of
Recall that the reciprocal of a value is where you take a fraction and swap the places of the terms. In the case of [tex]x^2[/tex], 1 is the denominator, so
[tex]\frac{x^2}{1} =\frac{1}{x^2}[/tex]
To find the inverse of a function, you first need swap the locations of x and y in the equation
[tex]y=x^2\\\\x=y^2[/tex]
Now, you need to solve for y
[tex]y^2=x\\\\y=\sqrt{x}[/tex]
Now, lets rewrite each of these to better compare them
[tex]\frac{1}{x^2} =x^{-2}\\\\\sqrt{x} =x^{\frac{1}{2}[/tex]
As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of
The sum of a number and 5
Help
Hey there! I'm happy to help!
Let's call our number n.
The word sum means to add.
Therefore....
n+5
Have a wonderful day! :D
Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (–2,–2) and the directrix is at y = –4. B. The focus is at (–2,–3) and the directrix is at y = –5. C.The focus is at (–2,–2 1/2) and the directrix is at y = –3 1/2. D. The focus is at (–2,–1 1/2) and the directrix is at y = –2 1/2.
Answer:
C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]
Step-by-step explanation:
First of all, let us learn about the formula to find Focus and Directrix from the standard equation of a parabola.
Standard form of a parabola is given as:
[tex](x - h)^2 = 4p (y - k)[/tex]
where the focus is [tex](h, k + p)[/tex] and
the directrix is [tex]y = k - p[/tex]
Now, we are given the equation of parabola as:
[tex]y= \dfrac{1}2 (x+2)^2 - 3[/tex]
Let us try to convert it to standard form:
[tex]\Rightarrow y+3= \dfrac{1}2 (x+2)^2 \\\Rightarrow 2(y+3)= (x+2)^2 \\\Rightarrow (x+2)^2 = 2(y+3)\\\Rightarrow (x+2)^2 = 4\times \frac{1}{2}(y+3)[/tex]
Comparing the above with standard equation of parabola [tex](x - h)^2 = 4p (y - k)[/tex]:
[tex]h = -2, p = \frac{1}{2}, k = -3[/tex]
So, Focus is at [tex](h, k + p)[/tex]
[tex]k + p = -3+\frac{1}{2} = -2\frac{1}{2}[/tex]
Focus is at [tex](-2, -1\frac{1}2)[/tex].
Equation of directrix:
[tex]y = k - p=-3-\frac{1}{2}\\\Rightarrow y = -3\frac{1}{2}[/tex]
Also, please refer to the attached image for the diagram of given parabola, focus and directrix.
So, the answer is:
C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]
replace the values of m and n to show the soulutions of thie equation,
x2+6x-5=0
Find square of -9.2
Answer:
84.64.
Step-by-step explanation:
(-9.2)^2
= (9.2)^2
= 84.64.
Find the midpoint of the line segment with the given endpoints. (-10, 5), (-9, -9)
Answer:
[tex]=\left(-\frac{19}{2},\:-2\right)[/tex]
Step-by-step explanation:
[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-10,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(-9,\:-9\right)\\\\=\left(\frac{-9-10}{2},\:\frac{-9+5}{2}\right)\\\\Simplify \\=\left(-\frac{19}{2},\:-2\right)[/tex]
There are 7 books on the floor. The number of books on the shelf is 2 more than 3 times the number of books on the floor.
A number minus 6 is few then 8
Answer: true or yes
A number minus 6 is few then 8
Step-by-step explanation:
if you do 6-5=1 or 6-3=3 so true or yes ????
hoped this helped?????????
Can you please help me with this please and i will give you a branlist please help me thank you
Answer:
zx
Step-by-step explanation:
7x-6y=11 solve for y
Answer:
7x+11 = 6y
(7x+11)/6 = y
7x/6= y-11
There are multiple answers for this
Step-by-step explanation:
What is the square root of -16?
е в
-87
0 ООО
8
[tex]4i[/tex]
[tex]i=\sqrt{-1}[/tex]
[tex]\sqrt{-16}=\sqrt{-1}*4[/tex]
[tex]\sqrt{-16}=i*4[/tex]
[tex]4i[/tex]
Hope this helps.
頑張って!
145,973 write in sentence form
Answer:
one hundred forty-five thousand nine hundred seventy-three
hope this helps!
Eddie Lange earns $11.50 per hour. He worked 40 hours, plus time and a half for 7 hours?
Answer:
Total amount earned = $500.25
Step-by-step explanation:
Given:
Wage per hour = $11.50
Time worked = 40 hours
Extra time worked = 7 hour
Wage paid per extra hour = $11.50 / 2 = $5.75
Find:
Total amount earned
Computation:
Total amount earned = [Wage per hour][Time worked] + [Extra time worked][Wage paid per extra hour]
Total amount earned = [11.50][40] + [7][5.75]
Total amount earned = [460] + [40.25]
Total amount earned = $500.25
150 students in 3 classes
Answer:
50 if you're asking for dividing
Step-by-step explanation:
if you're dividing then it's 50 hopefully this is the answer your asking
Passports. In 2006, approximately 71 million valid
passports were in circulation in the United States.
This number increased to approximately 102 million
in 2011. What is the percent increase?
Answer:
0.437%
Step-by-step explanation:
given:
initial number = 71 M
final number = 102M
increase = final number - initial number
= 102 - 71
= 31 M
Percent increase
= increase / initial number x 100%
= (31 / 71) x 100%
= 0.437%
No. of valid passports in 2006 = 71M
No. of valid passports in 2011 = 102M
We have to find percentage increase in the number of passports[tex].[/tex]
[tex]\leadsto\sf\:\% Increase = \dfrac{N_2-N_1}{N_1}\times 100[/tex]
[tex]\leadsto\sf\:\% Increase = \dfrac{102M-71M}{71}\times 100[/tex]
[tex]\leadsto\sf\:\% Increase=\dfrac{31}{71}\times 100[/tex]
[tex]\leadsto\sf\:\% Increase=\dfrac{3100}{71}[/tex]
[tex]\leadsto\:\boxed{\bf{\blue{\% Increase=43.66\%}}}[/tex]
Hope it helps !
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A rectangle length is 5 more than its width. If the premiditer of the rectangle is 66 inches, what is the length of the rectangle
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{19 \: inches}}}}}[/tex]
Step-by-step explanation:
Let the width be 'w'.
Length of a rectangle ( l ) = 5 + w
Perimeter of a rectangle = 66 inches
First, finding the width of a rectangle
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}[/tex]
[tex] \dashrightarrow{ \sf{66 = 2(5 + w + w)}}[/tex]
[tex] \dashrightarrow{ \sf{66 = 2(5 + 2w)}}[/tex]
[tex] \dashrightarrow{ \sf{66 = 10 + 4w}}[/tex]
[tex] \dashrightarrow{ \sf{10 + 4w = 66}}[/tex]
[tex] \dashrightarrow{ \sf{4w = 66 - 10}}[/tex]
[tex] \dashrightarrow{ \sf{4w = 56}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{4w}{4} = \frac{56}{4} }}[/tex]
[tex] \dashrightarrow{ \sf{w = 14 \: inches}}[/tex]
Width of a rectangle ( w ) = 14 inches
Now, Substituting / Replacing the value of w in order to find the length of rectangle
[tex] \sf{length = 5 + w}[/tex]
[tex] \dashrightarrow{ \sf{length = 5 + 14}}[/tex]
[tex] \dashrightarrow{ \sf{19 \: inches}}[/tex]
Length of a rectangle = 19 inches
Hope I helped!!
Best regards! :D
the sum of 6 and the product of 8 and x" into mathematical expression
Answer:
6=8x
Step-by-step explanation:
Answer:
6+8x
Step-by-step explanation
We are going to make sure we can do this as best as possible. We need to make sure that the words that you are reading are making sense.
Sum can be taken out because its just 6. We do not know what adds to 6, it could be 1 +5, 2+4, 3+3, -3 and 9, WE DO NOT KNOW. So don't put extra information into the expression, when it is not given.
The and would be an addition to something, because when we are speaking and say the word AND, we want to add to that sentence. So, and is the plus sign.
6+
Then product is multiplication. So 8 times x.
Put it all together and you get the expression:
6+8x
I really hoped that helped you!
A cone has a volume of 180mm^3. If the height and radius of the cone are equal in length, find the radius r in mm. Round your answer to two decimal places
Answer:
r = 5.56 mm
Step-by-step explanation:
vol of cone = 1/3 π r² h
where
vol = 180 mm³
h = r
find r
plugin values into the formula:
180 = 1/3 * π r³
r³ = (180 * 3) / π
r = ∛171.9
r = 5.56 mm
Answer:
radius = 5.56 mm
Step-by-step explanation:
2. You need to buy grass seed for a new lawn. The lawn will cover a rectangular plot that is 60 feet by 90 feet. Each ounce of grass seed will cover 120 square feet. a. How many ounces of grass seed will you need to buy?
Answer:
45 oz
Step-by-step explanation:
first you need to find the are of the yard. To do that you multiply the length by the width: 60x90=5400 feet
next you divide by 120: 5400/120=45
therefore, you need to buy 45 ounces of grass seed.
7x(15+4) = (7x ) + (7+4)
What is the simplified form of the following expression
idk what this is
pls help
Answer:
Coplanar points
Step-by-step explanation:
Coplanar points are three or more points that lie in the same plane.
how can simplify 5x-4=6
A factory makes 300 sheets of construction paper per hour. How many sheets of construction paper will the factory make in 9 hours?
Answer:
2700
Step-by-step explanation:
One hour is 300 sheets. We need to find 9 hours,
so 300*9= 2700