Step-by-step explanation:
cos θ - sin θ = √2 sin θ
cos θ + sin θ = √2 sin θ + 2sin θ
cos θ + sin θ = √2(sin θ + √2sin θ)
cos θ + sin θ = √2 cos θ. (Proven)
Given w= √ 2(cos(pi/4)+isin(pi/4)) and z=2(cos (pi/2)+i sin (pi/2)) what is w-z expressed in polar form?
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:
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The first 3 numbers in a sequence are 30000, 12000, and 4800. Use percent to describe the pattern in the sequence. List the next 2 terms.
Answer:
1920 and 768
Step-by-step explanation:
its 40% of the numbers
40% of 30000 = 12000
40% of 12000 = 4800
next numbers
40% of 4800 = 1920
40% of 1920 = 768
Give the equation in slope intercept form for each representation. Tell me if you can’t see the pic at the top.
what is the answer?
Answer:
A S A
Step-by-step explanation:
In ΔACE & ΔBCD,
∠A ≅ ∠B {Given} Angle
AC = BC {Given} Side
∠ACE = ∠BCD { Reflexive property} Angle
ΔACE ≅ ΔBCD ------>A S A Property
yo im timed please help!! at the top it says "car A is traveling east at a steady speed of 45 mph. after 2 hours it is 100 miles east of Johnstown . car B is traveling east on the same road. its distance east of Johnstown is represented by the graph" il give 20 more points if you're correct
Answer:
it could be C or a
Step-by-step explanation:
more likey c be sorry if it's wrong
uhmmmm... yea............
Answer:
You add 12.5+12.5+3.02+3.02 which equals 31.04
Step-by-step explanation:
Find the measurements of angles a, b and c. PLZ HELP
if the scientific notation is 9.63x10^-3 what would it look like in standard form? MARKING BRAINLIEST!!!!
Answer:
.00963
Step-by-step explanation:
Since its 10^-3, the decimal point moves to the left 3 times. hope this helped :)
pls answer both parts of this problem for a brainliest !!
Bianca can walk 5/6 of a mile in of an hour. What is her walking speed, in miles per hour?
Step-by-step explanation:
please see it, i work on paper worksheet
Answer:
2 1/2 miles
24 minutes per mile
if there are 25 members in a club and 40% are girls how many girls are in the club
Answer:
there are 10 girls in the club
Step-by-step explanation:
25*40% is equal to 10
Eliot needs to replace a window that is in the shape of a
semicircle.
K 1.5 ft
>
What is the area of the window? Use 3.14 for 1. Round your
answer to the nearest hundredth of a square foot.
353.25
a=(3.14*15^2)/2
a=706.5/2
a=353 sq in
What is it will mark Brainliest
Answer:
1
Step-by-step explanation:
what is 20r^2+11r-3=0 for all real solutions?
please answer fast
Answer:
r=0.2
r= -0.75
Step-by-step explanation:
if im wrong im sorry
Tiana’s car traveled 111 miles on 3/8 of a tank of gas. How far will she be able to go on a full tank of gas?
Answer:
Hiiiiiii
Step-by-step explanation:
So to get the answer you have to turn the 3/8 into a mixed number and divide it by 111
Please help me with this .
Answer:
x=4
Step-by-step explanation:
It's a parallel line so the equation is
100+19x+4=180
19x=180-100-4
19x=76
x=76/19
x=4
Answer: x = 4
Step-by-step explanation: The 2 angles are same-side interior angles, which are supplementary, and supplementary angles add up to 180, so we know that 19x + 4 = 80.
- 4. -4
19x = 76
/19. /19
X = 4
Mr Mason asks 240 year 11 students what they want to do next year. 15% of the students want to go to college. ¾ of the students want to stay at school. The rest of the students do not know. Work out the number of students who do not know.
Answer:
Number of students who do not know = 24
Step-by-step explanation:
Year II students = 240
15% of the students want to go to college.
Number of year II students who wants to go to college = 15% of 240
= 15/100 × 240
= 0.15 × 240
= 36
¾ of the students want to stay at school.
Number of students who wants to stay at the school = 3/4 × 240
= (3 × 240) / 4
= 720 / 4
= 180
Number of students who do not know = Total year II students - Number of year II students who wants to go to college - Number of students who wants to stay at the school
= 240 - 36 - 180
= 24
Number of students who do not know = 24
April took out a $600 loan from the bank.At the end of 5 years, she pays back the principle,plus $60 simple interest.What was the annual interest rate?
Answer:
April took out a loan of $600 and paid it back with simple interest of $60 after 5 years. The formula to calculate interest is given the principal and the time and the interest rate is . For this problem we have to find the interest rate given . To archive that , we can just solve the equation making the interest rate the subject of the formula as shown below,
I= Prt
=> r= I/Pt
=> r= 60/600x5 = 1/50
The interest rate is 1/50 or 0.02 as a decimal. The interest rate is 2% as a percentage.
PLEASE HELP FOR BRAINLEIST
Answer:
25.) Slope of AB = 5
Slope of CD = -1/5
Perpendicular
26.) Slope of EF = -3/5
Slope of GH = -3/5
Parallel
Step-by-step explanation:
Use this formula to find slope. [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Parallel lines have the same slope
Perpendicular lines have the opposite reciprocal and sign
25.)
Plug in AB slope is 5
2 - 7/ 3 - 4 = -5/-1 = 5
Plug in for CD slope is -1/5
3 - 4/ 2 - -3 = -1/5 = -1/5
The lines AB and CD are perpendicular because they have opposite reciprocals and opposite signs.
26.)
Plug in EF slope is -3/5
1 - 4/ 3 - -2 = -3/5 = -3/5
Plug in GH slope is -3/5
-5 - -2/ 4 - -1 = -3/5 = -3/5
The lines EF and GH are parallel lines because they have the same slopes.
Hope this helps ya!
Answer:
what the other person said
Step-by-step explanation:
you were already saved just give them brainliest now
Peter is a beekeeper who sells jars of honey and combs at the market. For each 10 jars of honey that he takes to the market carries 3 honeycombs. Which of the following could be what Peter brings to market?
On Sunday it was 89°F. On Monday it was 15° colder. What temperature was it on Monday?
°
I need help I dont understand
Answer:
74F
Step-by-step explanation:
If it is 89F on Monday and it went DOWN 15 degrees, you subtract. 89-15= 74. The temp on Monday is 74 degrees F
Find that x and y intercept 4x-5y=40
Answer:
x intercept: 10, y intercept: -8
Step-by-step explanation:
make into y = mx + b
4x = 5y + 40
4x - 40 = 5y
y = 4/5x - 8
plug in 0 for x, to find y intercept
y = -8
plug in 0 for y, to find x intercept
0 = 4/5x - 8, x = 10
this table shows a liner relationship. based on the information in this table. which equation can be used to model the relationship between x and y?
A) y =3x
B) y =85x
C) y = x + 3
D) y = 3x + 255
i think it is c if its wrong i apologize.
Is y=2x+3 proportional
Answer:
no
Step-by-step explanation:
I calculated
No because something proportional can't have a y-intercept, the 3 is the y intercept so your statement is not proportional.
Which expression shows 24 + 36 as a product of the greatest common factor (GCF) and a sum? *
A. 3(8+12)
B. 4(6+9)
C. 12(2+3)
D. 6(4+6
Answer:
D
Step-by-step explanation:
The product of the greatest common factor and a sum is 12 (2 + 3).
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
24 + 36
We have the following cases:
2 (12 + 18)
3 (8 + 12)
4 (6 + 9)
6 (4 + 6)
12 (2 + 3)
Now,
The greatest common factor.
12 x 2 = 24
12 x 3 = 36
Thus,
12(2 + 3) is the product of the greatest common factor and a sum of (2 + 3).
Learn more about expressions here:
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Charles charges 4 an our to baby sit he also adds an extra 10 dollars onto the total for families with more than 3 children. How much will charles charge to baby sit 4 children for 4 hourss
Answer:
i beleve 26 or 48
good luck
What is the value of x?
A. 88
B. 68
C. 38
D. 112
Answer:
B. 68
Step-by-step explanation:
Help Please! Solve For Y.
Answer:
i think 7
Step-by-step explanation:
[tex]y \times 3 = 27 \times 10[/tex]
AYYYYYYYYYYYYYYOOOOOOOOOOOOOOOOOOO
Get Ya free 25
Answer:
Ok
Step-by-step explanation:
A student bought some pens at 8 each and some pencils at 31.50 each. If the total
number of pens and pencils purchased is 16 and their total cost is 50, how many pens
did he buy?
be
as his
Step-by-step explanation:
Letthenumberofpensbexand
numberofpencilsbey
then
x+y=16ory=16−x
andtheirvalue
8x+1.5y=50
8x+(
2
3
)(16−x)=50
8x+24−(
2
3
)x=50
8x−(
2
3
)x=50−24
(
2
13x
)=26∴x=4
theny=16−x=16−4=12