Answer:
It is B.
Step-by-step explanation:
Edge2021
[tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "
What is polar form of complex number?"The polar form of complex number z = x + iy is [tex]z=r~(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^{2} +y^{2} }[/tex] and [tex]\theta=tan^{-1}(\frac{y}{x} )[/tex]"
For given question,
We have been given two complex numbers in polar form.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} ))[/tex] and [tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))[/tex]
We simplify above complex numbers.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} )) \\\\w=\sqrt{2}(\frac{1}{\sqrt{2} } +i~ \frac{1}{\sqrt{2} } ) \\\\w=1+i[/tex]
And the second complex number is,
[tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))\\\\z=2(0+i~1)\\\\z=0+2i[/tex]
Now if we find the value of w - z
⇒ w - z = (1 + i) - (0 + 2i)
⇒ w - z = 1 - i
Now we find the polar form of complex number.
[tex]r=\sqrt{1^{2} +(-1)^{2} } \\\\r=\sqrt{2}[/tex]
And the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{-1}{1} )\\\\\theta=tan^{-1}(-1)\\\\\theta=\frac{3\pi}{4}[/tex]
So, w - z in the polar form would be [tex]1+i=\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Therefore, [tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Learn more about the complex numbers here:
https://brainly.com/question/17162901
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Put the following numbers in order from least to greatest.
1/4 1/8 1/2
Answer:
1/8 1/4 1/2
Step-by-step explanation:
i hope it will help you
Step-by-step explanation:
1\8 1\4 1 \2
What is the solution set to this inequality??
x^2-12x+35<_ 3
-8,-6,-4
-10,-6,0
these are the possible test points for your three intervals
Answer:
4≤x≤8
Step-by-step explanation:
WHAT IS 24÷2 PLS PLS PLS PLS
Answer:
12
Step-by-step explanation:
24/2 = 12
Answer:
12
Step-by-step explanation:
HELP PLEASEEEE!!!!!!!!!!!!!!!!!
Answer:
-2
Step-by-step explanation:
Y-int is the point that touches the y-axis (the verticle line)
look at the point where it touches the y-axis
it is negative and it is 2. so it would be (0,-2) or -2
During hibernation, a garter snake’s body temperature never goes below 3 °C. Write an inequality that represents this situation.
Answer:
x ≥ 3*C
Step-by-step explanation:
What is the equation of a line with a slope of -2 which goes through the point (3, -1)?
Answer:
Step-by-step explanation:
y+1 = -2(x-3)
y = -2x + 6 - 1
y = -2x + 5
Which is the graph of f(x) = RootIndex 3 StartRoot x EndRoot – 4?
Answer:
please mark me brainliest and follow me my friend.
Q1. The speed limit on a road is 40km/h. A scooter drives 9
kilometers in 15 minutes. Is the scooter breaking the speed limit?
step by step explanation plz
Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package. She planted 15 saplings and has at most 20 left. How many packages of saplings did she start with? What would the solution look like on a number line graph?
When Rita started, she had
packages of saplings. The solution can be represented as
with an arrow to the
.
Answer:
If we represent x (number of packages of saplings) on a number line graph, it will start on number 4 (number of packages Rita still has) then moves to the right to number 7, that is the number of packages when Rita started to plant.
Step-by-step explanation:
Cindy used 6feet of ribbon to wrap 10 gifts . How much ribbon will she use to wrap 25/gifts ? ( all the gifts are the same size)
Answer:
15ft
Step-by-step explanation:
if she used 6ft for 10 gifts, you would multiply 6 by 2 equalling 12.
then multiply 6 by .5, 3. add 3 and 12
the answers 15 sorry i couldnt explain better but ya
pleaSe mark brainliest
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
The value of x of the solution to the system of equations
x = -8Hence, option (C) is true.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x=2y-4\\ 7x+5y=-66\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}x-2y=-4\\ 7x+5y=-66\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}x-2y=-4\mathrm{\:by\:}7\:\mathrm{:}\:\quad \:7x-14y=-28[/tex]
[tex]\begin{bmatrix}7x-14y=-28\\ 7x+5y=-66\end{bmatrix}[/tex]
subtracting 7x-14y=-28 from 7x+5y=-66
[tex]7x+5y=-66[/tex]
[tex]-[/tex]
[tex]\underline{7x-14y=-28}[/tex]
[tex]19y=-38[/tex]
so the equations become
[tex]\begin{bmatrix}7x-14y=-28\\ 19y=-38\end{bmatrix}[/tex]
solve 19y = -38
[tex]19y=-38[/tex]
Divide both sides by 19
[tex]\frac{19y}{19}=\frac{-38}{19}[/tex]
[tex]y=-2[/tex]
[tex]\mathrm{For\:}7x-14y=-28\mathrm{\:plug\:in\:}y=-2[/tex]
[tex]7x-14\left(-2\right)=-28[/tex]
[tex]7x+28=-28[/tex]
[tex]7x=-56[/tex]
Divide both sides by 7
[tex]\frac{7x}{7}=\frac{-56}{7}[/tex]
[tex]x=-8[/tex]
Therefore, the value of x of the solution to the system of equations
x = -8Hence, option (C) is true.
Dear Garden Designer,
Shed
I've ordered this shed. It is 2 meters wide, 3.25 meters
long and 2.8 meterstal
I have moved into a house with a smal garden that needs a total redesign
Please design my garden for me. I have attached an accurate scale drawing of my
garden to this emai. I ve listed below some features I want in the garden. I will email
you later about some other things I also want.
To start, please could you draw these features accurately on the plan, showing where
you think they should go in the garden. Send me your plan with an explanation of your
thinking
Best wishes,
Decking for barbeques
I want some decking near the patio doors
It should be big enough to seat at least six people
Mandy
Circular pond
I would like a circular pond.
I'd like its area to be about 7 m.
Path and Borders
I would like some flower borders. These should not be
more than one motor wide as I find wider ones difficult
to look after.
I'd like a gravel path 1 meter wide to go from the shed
to the house and from the garden gate to the house
I will cover the rest with grass
Answer:
Step-by-step explanation:MATHEMATICAL GOALS
This lesson unit is intended to help assess how well students are able to interpret and use scale
drawings to plan a garden layout. This involves using proportional reasoning and metric units.
COMMON CORE STATE STANDARDS
This lesson relates to the following Standards for Mathematical Practices in the Common Core State
Standards for Mathematics, with a particular emphasis on Practices 1, 3, 4, 5, and 6:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
8. Look for and express regularity in repeated reasoning.
This lesson gives students the opportunity to apply their knowledge of the following Standards for
Mathematical Content in the Common Core State Standards for Mathematics:
7.G: Draw, construct, and describe geometrical figures and describe the relationships between
them.
Solve real-life and mathematical problems involving angle measure, area, surface area,
and volume.
7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
7.RP: Analyze proportional relationships and use them to solve real-world and mathematical
problems.
INTRODUCTION
This lesson unit is structured in the following way:
• Before the lesson, students work individually on a task designed to reveal their current levels of
understanding. You review their responses and create questions to help them improve their work.
• At the start of the lesson, students reflect on their individual responses, before producing a
collaborative improved solution to the task. Then, in the same small groups students analyze
sample responses. They then discuss as a whole-class the methods they have seen and used.
• In a follow-up lesson, students reflect on their work. If time allows, an extension task is available.
MATERIALS REQUIRED
• Each student will need a copy of Design a Garden and Garden Plan, some blank paper, a miniwhiteboard, pen, and eraser, and the How Did You Work? questionnaire. The Garden Plan should
be copied at exactly 100% scale so the measurements are accurate. If this is not possible,
photocopy the rules on S-3, one rule per student, which should then match the Garden Plan
measurements. It will be useful to have spare copies of the Garden Plan.
• Each small group of students will need a new copy of the Garden Plan, the Assistants’ Methods, a
glue stick, felt-tipped pen, and a sheet of poster paper. For the optional extension Mandy’s Second
Email will be needed. Provide short rules, meter rules, string, protractors, scissors, glue, card,
plain paper, graph paper, and colored pencils for students who choose to use them.
TIME NEEDED
20 minutes before the lesson, a 110-minute lesson (or two 60-minute lessons), and 10 minutes in a
follow-up lesson. Actual timings will depend on the needs of your students.
A grocery store sells a bag 7 oranges for $2.66. if alexandra spent $3.42 on oranges how many did she buy
Answer:
9 oranges
Step-by-step explanation:
7 for 2.66 is 38c for 1
Step-by-step explanation:
if 7 gives 2.66
so 3.42×7÷2.66 gives 9 orange
Use the diagram below to answer the question. There is a small building that is 24 feet tallThe fire fighter is standing 7 feet away from the building.
Answer:
24- 7 = 17
Step-by-step explanation:
Bradley answered 80% of the questions on his science test correctly. There were 30 questions on the test, and all the questions had equal value. How many questions did Bradley answer correctly on his test?
Answer:
24 correct questions
Step-by-step explanation:
Solve for u.
1- u = 235
Answer:
-234
Step-by-step explanation:
1-235=-234
Answer:
Step-by-step explanation:
1-u=235 subtract the 1 from both sides
-u=234 divide by -1
u= -234
Find what x equals please
Answer:
180-(35+28)->180-63=117 and 180-117=63 then 63+36=99 and 180-99=81 so x=99°
What is the slope of the linear function
y=5/2x-4
is it
5/2
-5/2
-4
4
Answer:
5/2
Step-by-step explanation:
To find slope, just look directly at what is connected to the X. Don’t worry about anything else
what is 90% of 130?
Answer:
117
Step-by-step explanation:
(0.9)(130)
=117
Answer:
117
Step-by-step explanation:
Step 1:
[tex]\frac{x}{130} = \frac{90}{100}[/tex] Equation
Step 2:
100x = 11700 Multiply
Step 3:
x = 11700 ÷ 100 Divide
Answer:
117
Hope This Helps :)
please help me find my answer for this I will name brainist.
Answer:
IT's -3.6 & 14.4 so D is the correct answer
Step-by-step explanation:
x= -3.6 y= 14.4
HOW I SOLVED IT
-3.6 x 3 = -10.8 2 x 14.4 = 28.8 - 10.8 = 18 so correct since it must equal to 18
-2/3 x -3.6 =2.4 + 12 = 14.4 so correct since y = 14.4
Brainilest would be appreciated :)
PLEASE HELP ME QUICKLY
I NEED HELP WITH THIS QUESTION
Answer:
69
Step-by-step explanation:
All of the angles in the triangle will add together to be 180 degrees. So to find angle M, you add the two angles that you have together (79 + 32) to get 111. You then subtract 111 from 180 to get angle M (69).
Mark brainiest pls :)
What is the average rate of change for [-1,2]?
Answer:
Step-by-step explanation:
The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
Paul was making some brownies and cupcakes for his school fundraiser. If the brownies needed 4.8 cups of sugar and the cupcakes needed 5.2 cups, how much sugar would he need altogether?
Answer:
10 cups in total.
Step-by-step explanation:
4.8+5.2= 10.00
add the .2 to the 4.8 you get get 5 then add 5.0+5.0
how to solve
[tex] \sqrt{4} x {}^{2} = x + 2[/tex]
Answer:
➩ [tex]x=2,-\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{4x^2}=x+2[/tex]
➨ We can also solve by completing both squares, however. Since we can pull out the square root.
[tex]\sqrt{4x^2}=|2x|[/tex] ➩ Define of Absolute Value/Square Root
➩ [tex]\sqrt{x^2}=|x|[/tex]
Thus, our new equation is ➩ [tex]|2x|=x+2[/tex]
To solve an absolute-value equation, let there be two conditions.
➨ Where x ≥ 0
[tex]2x=x+2\\[/tex]
Move x to another side
[tex]2x-x=2\\x=2[/tex]
➨ Where x < 0
[tex]-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}[/tex]
Maria made two batches of fruit punch. The table at the right shows how many quarts of juice she used for each batch. Write an equation that relates the proportional quantities. Convince Me! How does the equation change if the amount of grape juice is the independent variable, x, and the amount of apple juice is the dependent variable, y? A table with Apple Juice (x), Grape Juice (y) and Grape Juice/Apple Juice (y/x). The first row has x as 5 and y as 8. The second row has x as 10 and y as 16. In each row, the ratio of Grape Juice to Apple Juice is a blank to be filled. The constant of proportionality is . An equation that represents this proportional relationship is =
Answer/Step-by-step explanation:
The equation that relates the proportional quantities would take the following form ---› [tex] y = kx [/tex], where,
y = amount of Grape juice (dependent variable)
x = amount of Apple juice (independent variable)
k = constant of proportionality (y/x)
✔️Using any of the given pair, say, (5, 8),
Constant of proportionality = [tex] k = \frac{y}{x} = \frac{8}{5} = 1.6 [/tex]
Substitute k = 1.6 in [tex] y = kx [/tex].
An equation that represents the proportional relationship would be:
[tex] y = 1.6x [/tex]
Or
[tex] y = \frac{8}{5}x [/tex]
How the equation would change if:
y = amount of Apple juice (dependent variable)
x = amount of Grape juice (independent variable)
The constant of proportionality would change, that is using a pair, say, (8, 5),
[tex] k = \frac{y}{x} = \frac{5}{8} = 0.625 [/tex]
Substitute k = 0.625 in [tex] y = kx [/tex].
The equation would now be:
[tex] y = 0.625x [/tex].
Or
[tex] y = \frac{5}{8}x [/tex]
The length of a rectangle deck is 3 times its width. If the deck's perimeter is 16 ft, what is the deck's area?
Answer:12
Step-by-step explanation:
3x+3x+x+x=16
8x=16 so x =2
2*3=6 6*2=12
Answer:
12 sq ft
Step-by-step explanation:
let w = width
let 3w = length
w + w + 3w + 3w = 16
8w = 16
x = 2
Area = 3(2) x 2
A = 6 x 2
Helppp I’ll make u a brainlister
Answer:
108 deg
Step-by-step explanation:
Since sides DB and CD are congruent, then opposite angles are congruent.
m<C = m<B = 36
m<B + m<C + m<D = 180
36 + 36 + m<D = 180
m<D = 108
2a2 - ab - 3b2 + 9 when a = 3 and b = 2
2(3^2)−(3)(2)−3(2^2)+9
2(3^2)−(3)(2)−3(2^2)+9
= 9
Every day after dinner, a child is to put his plate in the sink. Which formula calculates percent of occurrences?
Answer:
Percent of occurrences= (Numbers of behavior/Numbers of opportunities)*100
Step-by-step explanation:
Based on the information given if a child is to put his/her plate in the sink everyday after having dinner the formula that will be use to calculates percent of occurrences is :
Percent of occurrences=( Numbers of behavior/Numbers of opportunities)*100
Where:
Numbers of behavior represent the Numbers of times the plate was put in the sink by child everday
Numbers of opportunities represent the Numbers of dinners the child had everyday
This oneeeee ty pleaseeee
Answer:
multiple choice?
Step-by-step explanation: