[100 points]
Using mathematically precise language, explain in detail how you would multiply the complex number z1=r1 (cos theta1+isin theta 1) with the complex number z2=r2 (cos theta 2+isin theta 2)
Answer:
Multiply the moduli and add the arguments.Step-by-step explanation:First write out the two terms being multiplied: z1z2= [r1(cos(theta 1) + isin(theta 1))][r2(cos(theta 2)+ isin(theta 2))] z1z2= r1r2 (cos(theta 1) + isin(theta 1))(cos(theta 2)+ isin(theta 2)) z1z2= r1r2(cos(theta 1)cos(theta 2))+(icos(theta 1)sin(theta 2))+(icos(theta 2)sin(theta 1))+(i^2 sin(theta 1)sin(theta 2)) Next group and rewrite the like term with the sums and differences. Your answer is the multiplication of the moduli and the addition of the arguments: z1z2= r1r2[cos(theta 1 + theta 2) + i sin (theta 1 and theta 2)].
The product complex number is [tex]z_1z_2[/tex]= [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].
What is Complex number?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.
We have,
z1=r1 (cos θ1 +i sin θ1)
z2=r2 (cos θ2 +i sin θ2)
where r-radius/radii
and, m-modulus/moduli
Now, the product is
[tex]z_1z_2[/tex] = r1 (cos θ1 +i sin θ1) x r2 (cos θ2 +i sin θ2)
[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 + i² sin θ1 sin θ2)
[tex]z_1z_2[/tex] = r1 r2(cos θ1 . cos θ2 +i cos θ1 sin θ2 + i sin θ1 cos θ2 - sin θ1 sin θ2)
We know,
cos (a + b)= cos a cos b - sin a sin b
sin (a+b) = sin a cos b + cos a sin b
Thus, [tex]z_1z_2[/tex] = [tex]r_1r_2[/tex][cos (θ1+θ2) + i sin (θ1+θ2)].
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Carson must create a new password for his Nintendo Switch. The password must contain five different letters and two different numbers, Both of the numbers must be at the end. He doesn’t want to use any letters in his name either. What is the total number of passwords Carson can create?
Using the common denominator, what is an equivalent fraction to 5/6
Hey there!
ORIGINAL QUESTION: “FINDING OUT WHATS EQUIVALENT TO 5/6”
We’re NOT sure what your equation should look like so we will make it like:
5/6 = z/6
CURRENT EQUATION:
5/6 = z/6
FIRST: CROSS MULTIPLY the NUMBERS
5(6) = z(6)
5(6) = 6(z)
NEW EQUATION (TEMPORARILY)
30 = 6z
6z = 30
DIVIDE 6 to BOTH SIDES
6z/6 = 30/6
CANCEL out: 6/6 because it give you 1
KEEP: 30/6 because it help solve for the z-value
NEW EQUATION: z = 30/6
SIMPLIFY IT!
z = 5
Thus, your answer is: 5/6 = 5/6
FUN FACT: THERE IS MULTIPLE FRACTIONS THAT ARE EQUIVALENT TO THE GIVEN FRACTION.
EXAMPLE(S):
• 10/12
• 20/24
• 30/36
• 40/48
• 50/60
• 60/72
ANYWAY!
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
PLEASE HELP!! ILL MARK AS BRAINLIEST AND GIVE 20 POINTS!!!!!
Select the correct answer.
What is the value of this expression when c= 25 and d= 14?
Answer: -10 or D
Step-by-step explanation: simplify radical then combine
Solve the equation.
7 t − 3 = − 59
t=_____
Hey there!
7t - 3 = -59
ADD 3 to BOTH SIDES
7t - 3 + 3 = -59 + 3
CANCEL out: -3 + 3 because it give you 0
KEEP: -59 + 3 because it help solve for the t-value
NEW EQUATION: 7t = -59 + 3
SIMPLIFY IT!
7t = -56
DIVIDE 7 to BOTH SIDES
7t/7 = -56/7
CANCEL out: 7/7 because it give you 1
KEEP: -56/7 because it help solve for the t-value
NEW EQUATION: t = -56/7
SIMPLIFY IT!
t = -8
Therefore, your answer is: t = -8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Prove that y=tan(mx) = sin(mx)/cos(mx)
The equation tan(mx) = sin(mx)/cos(mx) is a trigonometry equation
The trigonometry equation tan(mx) = sin(mx)/cos(mx) is true
How to prove the statement?The equation is given as:
tan(mx) = sin(mx)/cos(mx)
The tangent of an angle is the ratio of the sine and the cosine of the angle.
This means that:
tan(α) = sin(α)/cos(α)
By comparison, we have:
α = mx
Substitute α = mx in tan(α) = sin(α)/cos(α).
So, we have:
tan(mx) = sin(mx)/cos(mx)
Hence, the trigonometry equation tan(mx) = sin(mx)/cos(mx) is true
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Step-by-step explanation:
Below in the attached picture is the proof for tangent
How do I factor 4r^2 + 36r + 81
Answer:
How to solve your problem 42+36+814r2+36r+81
Use the sum-product pattern 42+36+814r2+36r+8142+18+18+81
Find the number of permutations of the letters of the word LOOPHOLE
Answer:
6!/3!=6x5x4x3x2/3x2=6x5x4=120
Step-by-step explanation:
There are L, O, O, P, H, O, L, E; 8 letters in LOOPHOLE. However, three letters repeat: OOO. That means we cannot count them as different and use ! for them.
L,P,H,L,E,O are the letters not double counted. There are SIX letters, so 6!, however, you still have to divide since there are the Os you have to consider.
You have to divide by 3! as they repeat 3 times.
Thus, 6!/3!
"There is a subset of permutations that takes into account that there are double objects or repetitions in a permutation problem. In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical" -www. ck12. org > probability > lesson > permutation
PLEASE HELPPPPPPPPPP!!!!!!
Find the surface area of the pyramid to the nearest whole number.
115 in2
186 in2
230 in2
179 in2
Answer:
I think the answer is 115 in2Step-by-step explanation:
If you multiply 7.2 x 7.2 then you say + 8 * 8 is 64 plus 64 equal to 115
could i have some super super quick help? :(( (part iv is not necessary)
might be getting the hang of it but i would still like some help
i)
Factor using completing square method
[tex]\dashrightarrow \sf y = -x^2+16x-64[/tex]
[tex]\dashrightarrow \sf y = -(x^2-16x+64)[/tex]
[tex]\dashrightarrow \sf y = -(x^2-8x-8x+64)[/tex]
[tex]\dashrightarrow \sf y = -(x(x-8)-8(x-8))[/tex]
[tex]\dashrightarrow \sf y = -((x-8)(x-8))[/tex]
ii)
Find zeros of a function, f(x) = 0
[tex]\dashrightarrow \sf -((x-8)(x-8))=0[/tex]
[tex]\dashrightarrow \sf (x-8)=0, \ (x-8)=0[/tex]
[tex]\dashrightarrow \sf x = 8[/tex]
iii)
In order to find vertex use the formulae : x = -b/2a
[tex]\dashrightarrow \sf x = \dfrac{-(16)}{2(-1)}[/tex]
[tex]\dashrightarrow \sf x = 8[/tex]
Then find y:
[tex]\dashrightarrow \sf y = -(8)^2+16(8)-64[/tex]
[tex]\dashrightarrow \sf y = 0[/tex]
coordinates: (8, 0)
iv) Sketched Below:
#1
y=-x²+8x+8x-64y=-x(x+8)+8(x+8)y=(x+8)(-x+8)y=-(x-8)(x-8)#2
Zeros are the x intercepts
Here they are
8,8#3
y=-x²+16x-64y=-[x²-16x+64]y=-(x-8)²+0Vertex form of parabola:-y=a(x-h)²+k
Vertex=(h,k)=(8,0)#4
Attached
1 yard (yd) = 3 feet (ft); 1 foot (ft) = 12 inches (in) how many inches are there in 5 yards?
Answer: 180 inches
Step-by-step explanation:
We can use dimensional analysis. Our desired units are inches per yard. Begin by writing down:
[tex]\frac{12in}{1ft}[/tex]
Then use the conversion factor of feet to yard. The units of feet will cancel giving:
[tex]\frac{12in}{1ft} *\frac{3ft}{1yd}=\frac{36in}{1yd}[/tex]
Multiply the top and bottom by 5 to get:
[tex]\frac{36in}{1yd} *\frac{5}{5} =\frac{180in}{5yd}[/tex]
given f(x)= 8x+1/2x-9 what is the end behaviors of the function
The behavior of the function f(x) describes the direction of the function
The behavior of the function is as x -> ∞, f(x) -> 4 and x -> -∞, f(x) -> 4
How to determine the end behavior?The function is given as:
f(x)= 8x+1/2x-9
Start by plotting the graph of the function f(x).
From the graph (see attachment), we have the following highlights:
The function has an asymptote at y = 4This means that: as x approaches infinity or negative infinity, f(x) approaches 4Hence, the behavior of the function is as x -> ∞, f(x) -> 4 and x -> -∞, f(x) -> 4
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Which expression is equivalent to
(3^2) ^-2. -81 , -12 , 1/81 , 1/12
Answer:
1/81
Step-by-step explanation:
First lets simplfy the equation :
(3^2)^-2
(remember that you can mutiply the exponent outside the paranthesis by the exponent inside so -2*2=-4)
3^-4
Now lets evaluate this further!
3^-4
(negative exponets mean that you have to raise the number but as the denominator of a fraction)
1/3^4
Now we can solve it fully
1/3^4
1/81
3 more than the product of a number and six is equal to 2
6x + 3 = 2
its the answer
easy peasy
Answer:
3 + 6(x) = 2
Step-by-step explanation:
Given statement:
3 more than the product of a number and six is equal to 2
Converting the statement into an equation:
{3} {more} than {the product of a number and six} is {equal to} {2}
↓ ↓ ↓ ↓ ↓
3 + 6 × x = 2
⇒ Equation formed: 3 + (6 × x) = 2
⇒ Equation formed: 3 + 6(x) = 2
The difference between the squares of two numbers is 15. Three times the square of the first number increased by the square of the second number is 49. Find the numbers
Answer: 256,1
Step-by-step explanation:
[tex]\sqrt{x} - \sqrt{y} =15\\\sqrt{y} = 49-3\sqrt{x} \\\\\sqrt{x} -(49-3\sqrt{x} ) =15 \\so, x=256\\substitute \{x}\ :\\\\\sqrt{y} = 49-3\sqrt{256} =y=1[/tex]
so, 256=x
and, y=1
Hope this Helped!
Answer:
1, 4 or -1, -4
Step-by-step explanation:
Let the two numbers be x and such that x > y.
According to the first condition:
[tex]x^2 -y^2= 15[/tex]
[tex]\implies x^2 =y^2+15[/tex]......(1)
According to the second condition:
[tex]3x^2 +y^2= 49[/tex]
[tex]\implies 3(y^2+15) +y^2= 49[/tex]
(From equation 1)
[tex]\implies 3y^2+45 +y^2= 49[/tex]
[tex]\implies 4y^2 =49-45[/tex]
[tex]\implies 4y^2 =4[/tex]
[tex]\implies y^2 =\frac{4}{4}[/tex]
[tex]\implies y^2 =1[/tex]
[tex]\implies y =\pm 1[/tex]
When y = 1
[tex]\implies x^2 =(1)^2+15=1+15=16[/tex]
[tex]\implies x =\pm 4[/tex]
When y = -1
[tex]\implies x^2 =(-1)^2+15=1+15=16[/tex]
[tex]\implies x =\pm 4[/tex]
Thus, the required numbers are either 1, 4 or -1, -4
Which equation can be used to solve the problem below?
If four times a number is increased by 15, the result is three less than six times the number. Find the number.
Question 7 options:
4 (x + 15) = 6x -3
4x + 15 = 6(x-3)
4x + 15 = 6x -3
4x + 15 = 3-6x
Answer:
4x + 15 = 6x - 3
Step-by-step explanation:
Four times an unknown number is 4x, add 15 like it says, then it says three less so it would be - 3 and then it says than six times the [unknown] number, which remains being x
hope this helps!
Which name best describes this triangle?
Answer:
Hi mate
The right angled triangle is the best name for it
Because it has an right angle or 90 degree angke
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEPlease help me answer this
Answer:
d is the answerbecause a= 1,1 then 1+1 = 2
there were 3 coins and they were tossed 200 times total. 23 times, 3 of them showed heads, 72 times, 2 of them showed heads, 77 times, 1 of them showed heads, 28 times, 0 showed heads. whats probability for each of the events?
Answer:
Step-by-step explanation:
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.Solution:Probability of an event, P(E) = Number of occurrences where the event takes place / Total number of occurrencesThe probability of 2 heads coming up when three coins are tossed simultaneously is given by the ratio of the number of times a particular outcome occurs to the total number of tosses.Total number of tosses = 200Number of 2 heads outcomes = 72Probability of 2 heads outcomes = Number of 2 heads outcomes / Total number of tosses= 72/200= 9/25
does it look correct
Answer:
2, 3, 4, 7, 8
Step-by-step explanation:
All correct!
Answer:
Yes it is totally corect you are very smart
Step-by-step explanation:
20 points if you answer please.. The container is partially filled with unit cubes. How many unit cubes fit in the container?
A drawing of a rectangular prism-shaped container partially filled with unit cubes. There are 9 cubes along the length, 7 cubes along the width, and 5 along with the height.
The container can hold
unit cubes.
Answer:
length times width times height. 9x7x5= 315 unit cubes
Step-by-step explanation:
Which angles are adjacent to each other? Select all that apply. 3 2 23 and 24 22 and 23 22 and 24 Z2 and 1
Answer:
angle 2 and angle 4
help if ur smart plssssssss
The answer would be ⁻[tex]\frac{19}{x-5\\}[/tex]
Answer:
[tex]\underline{\boxed{\sf \cfrac{-19}{x-5}}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x^2+10+25}{x+5}-\cfrac{x^2-6}{x-5}[/tex]
First, Let's factor the expressions that are not already factored in x^2+10+25/x+5
[tex]\sf \cfrac{(x+5)^2}{x+5}-\cfrac{x^2-6}{x-5}[/tex]
Now, cancel out x+5 in both numerator and denominator:-
[tex]\sf x+5-\cfrac{x^2-6}{x-5}[/tex]
Expand equations to make their denominators the same before adding or subtracting them. Multiply x+5 * x-5/x-5:-
[tex]\sf \cfrac{(x+5)(x-5)}{x-5}-\cfrac{x^2-6}{x-5}[/tex]
Now, Since [tex]\sf \frac{(x+5)(x-5)}{x-5}[/tex] and [tex]\sf \frac{x^2-6}{x-5}[/tex] and similar denominator, we'll subtrac their numerators.
[tex]\sf \cfrac{(x+5)(x-5)-(x^2-6)}{x-5}[/tex]
[tex]\sf \cfrac{x^2-5x+5x-25-x^2+6}{x-5}[/tex]
Combine like tems in [tex]\sf x^2-5x+5x-25-x^2+6[/tex] :-
[tex]\sf \cfrac{-19}{x-5}[/tex]
Therefore, your answer is D.
4 mg string streched and spring constant 20cm what force constant
Find the value of x. Circle geometry.
Answer:
x = 18
By Pythagoras Theorem:
[tex] {(x + 7)}^{2} = {(7)}^{2} + {(24)}^{2} \\ \\ \implies \: (x + 7)^{2} = 49 + 576 \\ \\ \implies \: (x + 7)^{2} = 625\\ \\ \implies \: x + 7 = \pm \sqrt{625}\\ \\ \implies \: x + 7 = \pm \: 25\\ \\ \implies \: x + 7 = 25 \: \: or \: \: x + 7 = - 25 \\ \\ \implies \: x = 25 - 7 \: \: or \: \: x = - 25 - 7 \\ \\ \implies \: x = 18 \: \: or \: \: x = - 32 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \neq \: - 32 \\ \implies \: x = 18[/tex]
While playing a real-time strategy game, Juan created military units for battle: long swordsmen, spearmen, and crossbowmen.
Long swordsmen require 75 units of food and 25 units of gold. Spearmen require 40 units of food and 30 units of wood.
Crossbowmen require 30 units of wood and 40 units of gold. If Juan used 1475 units of gold, 1500 units of wood, and 4025 units
of food to create the units, how many of each type of military unit did he create?
Juan created
long swordsmen.
Parti
Juan created 35 long swordsmen, 35 spearmen and 15 crossbowmen.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represnt the number of long swordsmen, y represent the spearmen and z represent the crossbowmen. Hence:
75x + 40y = 4025 (1)
25x + 40z = 1475 (2)
And:
30y + 30z = 1500 (3)
Hence;
x = 35, y = 35 and z = 15
Juan created 35 long swordsmen, 35 spearmen and 15 crossbowmen.
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please help me with this math question ( stop taking it down i did nothing wrong)
The area of the trapezoid is [tex]\frac{1}{2}(b1+b2)*h[/tex]
b1 ⇒ length of one of the bases ⇒ 3 kmb2 ⇒ length of the other base ⇒ 5 kmh ⇒ height of trapezoid ⇒ 9kmTherefore the area is:
[tex]\frac{1}{2}*(3+5)*9 =\frac{1}{2}*(8)*9=4*9=36km^2[/tex]
Area: 36 square kilometers
Hope that helps!
A. 30.95
B. 30.9
C. 31
D. 30.96
Answer:
C
Step-by-step explanation:
Express 16 minutes as a percentage of 20
Answer: 80.00
Step-by-step explanation: To convert minutes into percentages, divide the measured number of ... To write your answer in percentage form, multiply the decimal by 100
hope this helps ig
barbara purchased stock last year for 8500 and paid a 1.25% broker fee. she sold it for 7324 and had to pay a .5% broker fee.
Barbara's net loss on the sale of the stocks she purchased last year is 1245.63.
What is the net loss?A net loss is earned when the cost price of purchasing the stock is greater than the selling price.
Net loss = cost price - selling price
Cost price = 8500 + (8500 x 1.25%) = 8606.25
Selling price = 7324 + (7324 x 0.5%) = 7360.62
Net loss = 8606.25 - 7360.62 = 1245.63
Here is the complete question: barbara purchased stock last year for 8500 and paid a 1.25% broker fee. she sold it for 7324 and had to pay a .5% broker fee. Compute her net loss.
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