The product $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{pi}{3})}\$.[/tex]
How to find the product $c_1 c_2$ in rectangular formLet $c_1$ and $c_2$ be the two complex numbers that frame an even triangle with $3+2i$ and $6+i$.
The dispose of between two complex numbers $a$ and $b$ is given by $|b-a|$. Since the triangle is even, the wipe out someplace in the scope of $3+2i$ and $6+i$ ought to be equivalent to the underlying venture with to the kill among $3+2i$ and $c$, conjointly make back the underlying speculation with to the take out among $6+i$ and $c$.
So, we have the following conditions:
$|6 + i - (3 + 2i)| = |c - (3 + 2i)|$
$|6 + i - (3 + 2i)| = |c - (6 + i)|$
Tackling these conditions, we get:
$|3 - i| = |c - (3 + 2i)|$
$|3 - i| = |c - 6 - i|$
Presently, let's discover the esteem of $c$:
$|c - (3 + 2i)| = |3 - i|$
[tex]\$|c - (3 + 2i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]
So, [tex]\$c - (3 + 2i) = \pm \sqrt{10} e^{i\theta}\$[/tex], where [tex]\$\theta\$[/tex] is the point between the positive genuine hub and the line interfacing $3+2i$ and $c$?
Presently, let's discover the esteem of $c$ utilizing the moment condition:
$|c - (6 + i)| = |3 - i|$
[tex]\$|c - (6 + i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]
So, [tex]\$c - (6 + i) = \pm \sqrt{10} e^{i\theta'}\$[/tex], where [tex]\$\theta'\$[/tex] is the point between the positive genuine hub and the line interfacing $6+i$ and $c$?
Since the triangle is equilateral, $theta$ [tex]\$\theta'\$[/tex] must vary by [tex]\$\pm[/tex] [tex]\frac{\pi}{3}\$.[/tex]
Presently, let's discover the item $c_1 c_2$:
$c_1 c_2 = (c - (3 + 2i))(c - (6 + i))$
$c_1 c_2 =[tex](\pm \sqrt{10} e^{i\theta})(\pm \sqrt{10} e^{i(\theta \pm \frac{\pi}{3})})\$[/tex]
$c_1 c_2 = [tex]10 e^{i\theta} e^{i(\theta \pm \frac{\pi}{3})}\$[/tex]
$c_1 c_2 = [tex]10 e^{i(2\theta \pm \frac{\pi}{3})}\$[/tex]
So, the item $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{\pi}{3})}\$.[/tex]
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What is the tangent ratio of angle yº?
Which is true given the linear equation below?
3x+4y=4
Answer:
y= −3/4x + 1
x= -4/3y + 4/3
Step-by-step explanation:
Let's solve for y.
3x+4y=4
Step 1: Add -3x to both sides.
3x+4y+−3x=4+−3x
4y=−3x+4
Step 2: Divide both sides by 4.
4y4=−3x+44
y=−34x+1
___________
Let's solve for x.
3x+4y=4
Step 1: Add -4y to both sides.
3x+4y+−4y=4+−4y
3x=−4y+4
Step 2: Divide both sides by 3.
3x3=−4y+43
x= -4/3y + 4/3
math papa algebra caculator, thank me later
Expand the function.
f(x) = (3x - 1)3
Answer:
[tex](a-b)^3 = a^3 - b^3 - 3a^2b + 3ab^2\\\\a = 3x, \ b = 1\\\\(3x-1)^3 = (3x)^3 - (1)^3 - 3(3x)^2(1) + 3(3x)(1)^2\\\\[/tex]
[tex]= 27x^3 - 1-3(9x^2)+ 9x\\\\=27x^3 -27x^2 +9x -1[/tex]
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
We have,
To expand the function f(x) = (3x - 1)³, we can use the binomial expansion formula, which states:
(a + b)³ = a³ + 3a²b + 3ab² + b³
In this case,
a = 3x and b = -1.
Substituting these values into the formula, we get:
[tex](3x - 1)^3 = (3x)^3 + 3(3x)^2(-1) + 3(3x)(-1)^2 + (-1)^3[/tex]
Simplifying further:
(3x - 1)³ = 27x³ - 9x³ + 9x - 1
Therefore,
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
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I need help with this problem
Answer:
D
Step-by-step explanation:
Suppose the two measures of a center are 82.5 degrees and 83.6 degrees. Which value is the median?
A. 82.5
B. 83.6
Answer:
83.05
Step-by-step explanation:
The two measures of the center are 82.5 and 83.6
The value of the median can be calculated a follows
= 82.5 + 83.6/2
= 166.1/2
= 83.05
Hence the value of the media is 83.05
Ricardo and John start swimming from the same location. Ricardo starts 15 seconds before John and
swims at a rate of 3 feet per second. John swims at a rate of 4 feet per second in the same direction as
Ricardo. Which equation could you solve to find how long it will take John to catch up with Ricardo?
Does anyone know the answer?
Answer:
t = (t₁ · vr)/ (vj - vr) = 45 seconds
Step-by-step explanation:
Given:
Initial time from Ricardo t₁ = 15 seconds, Ricardo's velocity (speed) vr = 3 ft/s,
John's velocity (speed) vj = 4 ft/s
Requested time when John catch Ricardo t = ?
During 15 seconds, Ricardo moved away
S = vr · t₁ = 3 ft/s · 15 s = 45 feet.
From that moment, the same time runs for both of them
Ricardo's path is S₁ = vr · t and John's path is S₂ = vj · t
S + S₁ = S₂ => S = S₂ - S₁ => 45 = vj · t - vr · t
When we draw t we get:
t ( vj - vr) = 45 t = 45 / (vj - vr) = 45 / (4 - 3) = 45 / 1 = 45 seconds
t = 45 seconds
S₁ = vr · t = 3 · 45 = 135 ft
S₂ = vj · t = 4 · 45 = 180 ft
Help pls
Bshdndbrjdhbdbdhdjd
Answer:
just function A
A is, for every 2x (2 steps) the value of y increased linearly by 2.5
B isn't, for every 10x (10 steps), the increase of y varies
A car travels a distance of 360 km in a time of 3 hours.
What is the car's average speed?
Answer:
convert km into m
1 km=1000m
360 km=1000*360m
=360000m
again,convert 3 hours into seconds
3 hours=60*60*3
=10800 second
average spped=total distance /time taken
=360000/10800
=33.33 m/s
Step-by-step explanation:
Question 2
A rectangular table has an area of 27 square feet. If its length and width are changed to 2/3 of their original size, what will be the effect on the area?
Answer
F ) It will increase by 12 square feet.
G )It will decrease by 12 square feet.
H )
It will increase to 39 square feet.
J )
It will decrease to 12 square
feet.
Answer:decrease by 12 feet
Step-by-step explanation:I did the math
A rectangular table has an area of 27 square feet. If its length and width are changed to 2/3 of their original size, the new area will be decreased by 12.
How does the area of a rectangle, and its length and width related?The area of a rectangle is the product of its length and width.
If a rectangle has a length L units and a width of W units, then
Area = L × W squared units.
A rectangular table has an area of 27 square feet. If its length and width are changed to 2/3 of their original size, what will be the effect on the area.
Area = L × W
Let the length and width are x and y
27 = x × y
xy = 27
The new area if its length and width are changed to 2/3 of their original size
Area = L × W
[tex]27 \times 2/3 \times 2/3\\\\= 3 \times 4\\\\= 12[/tex]
Therefore, the new area will be decreased by 12.
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Simplify 12(A - B).
I don’t understand?
Answer:
12A-12B
Step-by-step explanation:
In the parentheses, it is A-B. Using the distributive property you break up the parentheses then you have 12xA - 12xB. This is known as the "Santa Hat". The lines mean that you do each function to each constant, variable, or term.
Simplify this expression.
(2+3)65-7
Answer:
Make me Brainliest
Step-by-step explanation:
=5*65-7
=325-7
=318
What is the domain of the absolute value function below?
-2-
1 2 3 4 5 6 7 8 x
O XS-4
0 x 22
0 (-09-4)
Remember
Domain is set of x valuesRange is set of y valuesHere
there is no starting or ending point
so domain is
(-oo,oo)
The domain of the absolute value function given is (-∞, +∞).
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Domain of a function is the set of all the input values and the range of the function is the set of all the output values.
Given is an absolute value function.
Absolute value functions are functions which has the absolute value symbols in the expression.
From the graph, we can see that the value of x moves from negative infinity to infinity.
Domain of the function is the set of input values which is the set of values of x.
So the domain is (-∞, +∞).
Hence the domain is (-∞, +∞).
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Courtney would like to buy a new phone for $680. So far, she has saved $240. If she earns $8 an hour
babysitting, how many hours will she need to work to be able to buy the phone?
Answer:
she will need to work for 55 hours to buy the phone
Step-by-step explanation:
680 - 240 = 440
that's how much more she needs
449 ÷ 8 = 55
and that's the answer
55
hope that helped
Answer:
55 hours
Step-by-step explanation:
Well first we need to set up the equation
We know she needs 680$ to buy the phone so the equation must be equal to 240
She has 240 and earns 8 dollars per hr so were finding out how many hours of work is needed to be able to buy the phone
Represent the number of hours worked by "x"
Set the equation up as
240 + 8x = 680
Add -240 to both sides of the equation to make 240 be 0 and 680 be 440
8x = 440
divide both sides of equation by 8 to get what x equals
x=55
She needs to work 55 hours
This season, the probability that the Yankees will win a game is 0.6 and the probability that the Yankees will score 5 or more runs in a game is 0.57. The probability that the Yankees lose and score fewer than 5 runs is 0.34. What is the probability that the Yankees would score fewer than 5 runs when they win the game? Round your answer to the nearest thousandth.
The probability that the Yankees would score fewer than 5 runs when they win the game is 0.204 if the probability that the Yankees will win a game is 0.6
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability that the Yankees will win a game P(win) = 0.6
The probability that the Yankees will score 5 or more runs in a game is:
P(s>5) = 0.57
The probability that the Yankees lose and score fewer than 5 runs is:
P(s<5) = 0.34
To find the probability that the Yankees would score fewer than 5 runs when they win the game:
This is the case of probabilities of one event and another event together we will multiply the respective probabilities of the event:
= P(win)×P(s<5)
= 0.6×0.34
= 0.204
Thus, the probability that the Yankees would score fewer than 5 runs when they win the game is 0.204 if the probability that the Yankees will win a game is 0.6
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It takes 0.750.75 cups of sugar to make a batch of lemon cookies. I have 5.55.5 cups of sugar. How many batches can I make?
Select the correct image.
Answer:
Triangle 2
Step-by-step explanation:
That is Pythagorean Theorem, which is only for right triangles. The second triangle has the little square, so you know it is 90 degrees.
The two windows shown are similar. What is the height of the larger window?
On the Unit Circle:
If cos x < 0 which Quadrant(s) is the angle?
1. I &IV
2. II & III
3. I &II
4. III & IV
Answer:
Quadrant I and quadrant IV
Step-by-step explanation:
Given that cos x< 0
x < arccos 0
x < 90degres
Since cos s positive in the first and 4th quadrant, hence the angle lies in the Quadrant I and quadrant IV
Triangle JKL has the coordinates listed: J (5, -8), K (10, -8), L (7, -4) Where is J’ after a reflection over the y-axis?
The Rule for reflection over the y-axis is given by (x,y) to (-x,y).
so, J' (-10,-8)
✐----------------------
hope it helps...
have a great day!
Answer:
J' Coordinates = (-5, -8)
Step-by-step explanation:
We know that in the coordinate point J (5, -8);
x-value = 5
y-value = -8
In order to reflect J over the y-axis, we will keep the y-value of the coordinate same and then reverse the x-value to it's opposite, Therefore the J' coordinates would be;
x-value = -5
y-value = -8
J' Coordinates = (-5, -8)
Hope this helps!
C
y
0
5
1
1
20
2
80
3 320
Answer:
yes
Step-by-step explanation:
SOMEONE HELP ME WITH 13 and 14 please!!!! Will make
U brainlist!!!
Answer:
here u go
Step-by-step explanation:
and here is 8 and 9
0.6×8 and tell me how you got the answer pls
[tex]0.6 \times 8[/tex]
Answer:
4.8 is the answer!
Step-by-step explanation:
0.6 x 8 = 4.8
6 x 8 = 48
multiply 6 by 8, and move the decimal to the left one time, and get 4.8
Answer: 4.8
Step-by-step explanation: multiply 6*8 (which is 48) then move the decimal point one forward from the back
48.0 (this is before you move the point)
4.8 (this is after)
basically depending on how much numbers you have after the decimal point, that's how much you move forward!
Let me know if you have more questions!
Good luck!
If A = 30 degree and B = 60 degree , what is the value of sin(A+B). *
a) 0
b) 1/2
c) √3/2
d) 1
Answer:
I THINK it's B 1/2
Step-by-step explanation:
Sorry if wrong
Answer:
In this case, D
Step-by-step explanation:
Sin(30+60)=0.8939966636 which can be rounded to 0.89.
Now that we got that out of the way, we supposedly can follow the process of elimination.
It's clearly not A since we know the answer isn't equivalent to zero.
1/2 equals 0.5, meaning B's also not it.
We also know the answer isn't D, since 0.89 does not equal 1.
That only leaves C. Yet when check, just in case, √3/2 equals 1.22474487, meaning that's not the answer.
We've eliminated every answer so far, meaning we should go back and check our work. As I stated earlier, 0.8939966636 can be rounded to 0.89, but it can also be rounded to 1. Meaning, the closest answer to what we're looking for is D.
Of course, there could always be an error in the question itself, but unfortunately, there's no way to confirm that without asking your instructor or tutor.
I hope that helps.
F(x)=3x^2+2 the quadratic function g(x) is the function f(x) stretched vertically by a factor of 4. Enter the equation of g(x) in the box
Answer:
g(x) = 12*x^2 + 8
Step-by-step explanation:
For a function f(x), a vertical stretch of scale factor k is defined as:
g(x) = k*f(x)
In this case, we know that f(x) = 3*x^2 + 2
And the function g(x) is the function f(x) vertically stretched by a factor of 4, then we have k = 4
and:
g(x) = 4*f(x)
Replacing by the actual function, we get
g(x) = 4*(3*x^2 + 2)
g(x) = 4*3*x^2 + 4*2
g(x) = 12*x^2 + 8
HELP ME PLEASE... WILL GIVE BRAINLIEST. WORTH A LOT OF POINTS
Professor M presented the pair of equations shown below:
y = 6x − 10
y = 2x − 2
Part A: Explain to Professor M how you will solve the pair of equations by using either substitution or elimination. Show all the steps you use and write the solution in (x, y) form.
Part B: If she asked you to graph the two equations, at what point will the lines representing the two equations intersect? Explain how you know this.
Answer:
A) The solution is x = 2 and y = 2
B) The graphs would intersect at the point (2, 2).
Step-by-step explanation:
A)
We start with the system of equations:
y = 6*x - 10
y = 2*x - 2
To solve this, the first step is to isolate one of the variables in one of the equations.
Here we can see that the variable "y" is already isolated in both equations, so we can skip that step.
Now we can "replace" the "y" in one of the equations for the correspondent expression in the other.
we can write:
(6*x - 10) = y
and for the second equation, we know that y = 2*x - 2
So replacing that, we get:
6*x - 10 = 2*x - 2
Now we can solve this for x.
6*x - 2*x = - 2 + 10
4*x = 8
x = 8/4 = 2
Now to find the value of y, we can just input this value of x in any one of the two equations:
y = 6*2 - 10 = 12 - 10 = 2
y = 2*2 - 2 = 4 - 2 = 2
So the solution of the system is:
x = 2, y = 2
B) Because the solution of the system is the ordered pair (2, 2), this means that the ordered pair belongs to the graph of both lines, then we can conclude that these lines will intersect at that point (the one that is common to both lines). Actually, when we have a system of equations, graphing both equations and finding the points where the graphs intersect is one method to estimate the solution of the system.
The water tank in your school holds 20 liters of water. One day it was 34 full. That day, 14 liters of tank capacity was used up. How many liters of water remained in the tank at the end of the day
Answer:
20
Step-by-step explanation:
The water tank in the school hold 20 liters of water
One day it was 34 liters full
14 liters of water was used up
Therefore the quantity of water left can be calculated as follows
= 34-14
= 20
Hence 20 liters of water remains in the tank
√2,√5,√9,√15 order from least to greatest
Can someone answer this
Answer:
Step-by-step explanation:
Umm I believe it would be 7189939
On Tuesday afternoon at camp, Connor did archery and sailing before dinner. Archery started at 12:00 P.M. Connor spent 1 hour and 15 minutes at archery and 2 hours sailing. What time did sailing end?
Answer:
Sailing end at 3:15 AM
Step-by-step explanation:
Connor did archery and sailing before dinner (in that order).
He started at 12:00 PM
We know that:
In archery, Connor spent 1 hour and 15 minutes
In sailing, Connor spent 2 hours.
The total time spent is:
1 hour + 15 minutes + 2 hours
3 hours + 15 minutes.
Then sailing end 3 hours and 15 minutes after 12:00 pm = 0:00 am, this is:
3:15 AM
Sailing end at 3:15 AM
40 POINTS
Pleaseee help, I need to turn this in soon.
Answer:
The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.
Therefore, we have the following equation:
[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]
The Pythagorean identity comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
, where is the hypotenuse of the triangle and and are two legs of the triangle.
Therefore, we have the following equation: