Convert the complex number from rectangular form to polar form. z = -14 + 8i
Final answer:
To convert z = -14 + 8i to polar form, calculate the magnitude as √(260)≅17, and the argument by adding π to the arctan(8/-14), which accounts for the angle being in the second quadrant. Express the number in polar form using these values.
Explanation:
To convert the complex number z = -14 + 8i from rectangular form to polar form, we start by finding the magnitude (r) and the argument (θ) of the complex number. The magnitude is given by √(x² + y²), which in our case is √((-14)² + 8²) = √(196 + 64) = √(260)≅17. The argument θ is the angle with respect to the positive x-axis which can be found using the arctan function: θ = arctan(y/x). However, since our x is negative and y is positive, our complex number is in the second quadrant, so we need to add π radians (or 180 degrees) to the arctan(y/x) value to obtain the correct argument in the complex plane.
θ = arctan(8/-14) + π ≅ arctan(-4/7) + π. We then get the polar form: z = r(cos(θ) + i sin(θ)) or z = r eˣiθ. Substituting the magnitude and argument into this formula, we find the polar form of the complex number z.
Which of the f-values satisfy the following inequality? f+8≤12 Choose all answers that apply:
A
f = 4
B
f = 5
C
f = 6
What is the area of the region of the complex plane defined by $|z|<5$?
This will be the same area as that inside a circle with a radius of 5
So....the area will be ≈ pi * 5^2 ≈ 25 pi units^2
The area of the region of the complex plane defined by |z|<5 is 78.5 square units.
Explanation:The region of the complex plane defined by |z|<5 is the inside of the circle with radius 5 centered at the origin. To find the area of this region, we can use the formula for the area of a circle, which is A = πr². In this case, the radius is 5, so the area is A = 3.14 × 5² = 78.5 square units.
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what are the steps for using a compass and a straightedge to construct the bisector of
ANSWER:
How to construct a Line Segment Bisector AND a Right Angle
using just a compass and a straightedge.
STEP-BY-STEP EXPLANATION:
Steps:
1)Place the compass at one end of line segment.
2)Adjust the compass to slightly longer than half the line segment length
3)Draw arcs above and below the line.
4)Keeping the same compass width, draw arcs from other end of line.
5)Place ruler where the arcs cross, and draw the line segment.
Dale drove 845 miles in 13 hours. at the same rate, how long would it take him to drive 585 miles?
FREE POINTS!!!!!!!!!!!
2+3(8-2)= x
Answer:
30
Step-by-step explanation:
You need at least 5000 points to earn a gift card from your bank. You currently have 2700 points. What inequality represents the number of points you need to earn a gift card.
You need to bake some banana bread and some zucchini bread for a fund raiser at school. You plan to bake at least 4 and at most 12 loaves of bread. You need at least twice as many loaves of banana bread as zucchini bread.
The problem is an algebraic translation of a real-life situation using inequalities. The number of loaves, for both banana and zucchini bread, must be between 4 and 12, with banana bread needing to be twice as many as zucchini.
Explanation:This question deals with the concept of inequality and translating word problems into algebraic expressions. In this question, if x represents the number of zucchini bread loaves you bake and y represents the number of banana bread loaves, then the inequalities can be written as:
4 ≤ x + y ≤ 12y ≥ 2xThese inequalities mean that the total number of loaves of bread, including both banana and zucchini, should be no fewer than 4 and no more than 12, and the number of banana bread loaves should be at least twice the number of zucchini bread loaves.
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The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function h(t)=300-16t2. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall.
Answer:
-96 feet/sec.
Step-by-step explanation:
The height h of a falling object after t second when it is dropped from a platform 300 feet above the ground is modeled by the function h (t) = 300 - 16t²
Then speed or average rate by which the object falls from height h will be [tex]\frac{d[h(t)]}{dt}=\frac{d(300-16t)^{2} }{dt}[/tex]
Speed = [tex]\frac{d}{dt}(300)[/tex] - [tex]\frac{d}{dt}(16t^{2} )[/tex]
= -16 (2t)
Speed = -32t
After 3 second speed of object will be
Speed = -32(3)
= -96 feet/second
Therefore, the average rate will be -96 feet/sec. during the first 3 seconds of its fall.
When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 102) + (2 × 101) + (3 × 100)] + [(4 × 102) + (2 × 101) + (3 × 100)] make the operation more like a polynomial addition problem?
6 ( y + 8 ) = 3 ( 2y - 7 )
What are the vertices for the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ? i need x y and z
The operations on geometric shapes that involves moving, flipping, change of shape, reflection and new shape creation through operations on another shape is known as transformations
The coordinates of the vertices of the image ΔX'Y'Z' after the composite transformation T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)The reason the above values are correct is as follows:
The given transformation sequence is T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180°
Where;
T₍₋₂, ₄₎ = A translation two (2) units to the left and four (4) units upwards
R₀ 180° = A rotation of 180° about the origin
The image and preimage of a 180° rotation transformation about the origin is as follows;
Preimage (x, y) [tex]\underset \longrightarrow {R_o \ 180 ^{\circ} }[/tex]Image(-x, -y)
It is to be noted that the first transformation to be performed in a composite transformation is the transformation to the right
The composite transformation is therefore presented as follows;
Combined; (x, y) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-x - 2, -y + 4 )
The coordinates of the vertices points on triangle ΔXYZ are X(2, 5), Y(3, 2), Z(4, 3)
Therefore;
The coordinates of the vertices points on triangle ΔX'Y'Z' after the composite transformations are;
X(2, 5) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-2 - 2, -5 + 4 ) = X'(-4, -1)Y(3, 2) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-3 - 2, -2 + 4 ) = Y'(-5, 2)Z(4, 3) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] Z(-4 - 2, -3 + 4 ) = Z'(-6, 1)Which gives that the coordinates of the triangle ΔX'Y'Z' after the transformation, T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are;
X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)
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What is the parents function of f(x)=3x-5
Why does the sum of -4 and 3 complain more than the sum of -3 and 5
Final answer:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The sum of two numbers depends on their signs and the rules of adding negative and positive numbers.
Explanation:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The reason why the sum of -4 and 3 is a smaller number than the sum of -3 and 5 is because of the rules of adding positive and negative numbers:
When two negative numbers add, the answer has a negative sign.When two positive numbers add, the answer has a positive sign.When two numbers with opposite signs add, the sign of the larger number is retained.In this case, -3 is larger than -4, so when adding 5 to -3, we retain the negative sign and get -1. However, when adding 3 to -4, we retain the negative sign and get -1, which is smaller than 2.
Which number is a composite number?
17
27
37
47
Abeer sat a French test and a Geramn test.
In the French test she scored 34 out of 50.
In the German test she scored 14 out of 20.
In which test did she do better?
You must show your working.
Final answer:
After converting Abeer's scores to percentages, it is clear that she did better in the German test with a score of 70%, as opposed to the French test where she scored 68%.
Explanation:
To find out in which test Abeer did better, we need to compare her test scores in percentages. For the French test, Abeer scored 34 out of 50, which we can convert to a percentage by dividing 34 by 50 and then multiplying by 100:
34 ÷ 50 = 0.68 × 100 = 68%
For the German test, she scored 14 out of 20, which we also convert to a percentage:
14 ÷ 20 = 0.70 × 100 = 70%
By comparing these percentages, we can see that Abeer did better in the German test where she scored 70% compared to the French test where she scored 68%.
The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) = 5x − 4 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Rules for Plotting Points:
1) Start at the origin: _________
2) If your x-value is ___________, move right; if it is ___________, move left;
if it is _____, don’t move.
3) If your y-value is ___________, move up; if it is ___________, move down;
if it is _____, don’t move.
Solve. 5t<-15
A) t > 3
B) t < 3
C) t > -3
D) t < -3
What %of 200 miles is 150 miles
LINEAR PROGRAMMING help must answer both questions and explain ur answer for brainliest.
Solomon is taking out a 5,320 two year loan with an APR of 10.25%. What will the finance charge be for this loan to the nearest dollar?
Use the information about sports in the photo to explain how inequalities can be used to describe school sports. Include an inequality describing the number of schools needed to add girls’ track and field so that the number is greater than the number of schools currently participating in girls’ basketball.
12. Find the surface area of each figure to the nearest tenth.Show your work.
e. What is a real-world example or use of surface area?
which graph has a slope of 4/5?
The only graph with a slope of 4/5 is;
Graph 2
The slope of the graph is simply rise divided by run or defined as the change in y-coordinates divided by the corresponding change in x-coordinate.
Thus; m = (y₂ - y₁)/(x₂ - x₁)
Graph 1; Let us pick two coordinates;
(1, 2) and (2, 3)
m = (3 - 2)/(2 - 1)
m = 1
Graph 2; Let us pick two coordinates;
(-1, 1 ) and (4, 5)
m = (5 - 1)/(4 - (-1))
m = 4/5
Graph 3; Let us pick two coordinates;
(-2,0) and (3, 2)
m = (2 - 0)/(3 - (-2))
m = 2/5
Graph 4; Let us pick two coordinates;
(1, 1) and (4, 5)
m = (5 - 1)/(4 - 1)
m = 4/3
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Ray's gym charges an initial sign-up fee of $25.00 and a monthly fee of $15.00.
Write a function that describes the gym's total membership fee for x months.
find the x and y intercepts -3x-6y=12
Answer:
x-intercept: -4y-intercept -2Step-by-step explanation:
The x-intercept is found where the graph crosses the x-axis, at y=0. Substituting that into the equation and solving for x, we get ...
-3x = 12
x = 12/-3 = -4 . . . . . x-intercept = -4
The y-intercept is found where the graph crosses the y-axis, at x=0. Substituting that into the equation and solving for y, we get ...
-6y = 12
y = 12/-6 = -2 . . . . . y-intercept = -2
_____
A graphing calculator confirms these values.
If the area of a square is 196 square meters, what is its perimeter
Rachel deposited $6,449.82 into a savings account with an interest of 6.9% compounded annually. About how long will it take for the accout to be worth $8,000?
Answer:
3 years and 3 months.
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A= P(1+\frac{r}{100})^t[/tex]
Where,
P = principal amount,
r = rate per period,
t = number of periods,
Here, A = $ 8,000, r = 6.9%, P = $6,449.82,
By substituting the values,
[tex]8000 = 6449.82(1+\frac{6.9}{100})^t[/tex]
[tex]\frac{8000}{6449.82}=(1+\frac{6.9}{100})^t[/tex]
[tex]\ln (\frac{8000}{6449.82})=t\ln(1.069)[/tex]
[tex]\implies t = \frac{\ln (\frac{8000}{6449.82})}{\ln(1.069)}=3.228[/tex]
Hence, it would be take 3.228 years or 3 years and 3 months.
Convert 2 3/25 as a decimal/