The product complex number is z1z2 = r1r2[cos (θ1+θ2) + isin (θ1+θ2)]
[tex]Z_1\times Z_2= r_1(cos \theta_1 + isin \theta_1) \times r_2(cos \theta_2 + isin \theta_2)[/tex]
r-radius/radii
m-modulus/moduli
theta-argument represent angle theta
[tex]= r_1r_2(cos \theta_1 + i sin \theta_1) (cos \theta_2 + isin \theta_2)[/tex]
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 + i^2sin\theta_1sin\theta_2[/tex]
What is the value of i square in complex number?The value of i square is
[tex]i^2=-1[/tex]
Therefore,we get,
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 + (-1)sin \theta_1 sin \theta_2)[/tex]
[tex]= r_1r_2(cos \theta_1 cos \theta_2 + i cos \theta_1 sin \theta_2 + i sin \theta_1 cos \theta_2 - sin \theta_1 sin \theta_2)[/tex]
Since we know that,
[tex]cos(\theta_1+\theta_2)=cos\theta_1cos\theta_2-sin\theta_1sin\theta_2[/tex]
[tex]sin(\theta_1+\theta_2)=sin\theta_1cos\theta_2+cos\theta_1sin\theta_2[/tex]
So using above value we get,
[tex]= r_1r_2(cos \theta_1 cos \theta_2 - sin \theta_1 sin \theta_2) + i (cos \theta_1 sin \theta_2 + sin \theta_1 cos \theta_2)[/tex]
[tex]=r_1r_2cos(\theta_1+\theta_2)+isin(\theta_1+\theta_2)[/tex]
Therfore the product of the complex number is z1z2 = r1r2[cos (θ1+θ2) + isin (θ1+θ2)].
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Find volume and round to the nearest whole cubic yard.
Enter the value of p so that the expression 4 (n+8) is equivalent to (n+p)4
Which of the following is most likely the next step in the series?
Answer:
(D) a hexagon......................
ASAP help me plz!!! It’s 2 questions btw
Answer:
60
Step-by-step explanation:
I hope you understand what I wrote
Can someone please help me? And it says “Solve each equation. Then, prove that your answer solves the original equation?
Step-by-step explanation:
We need to solve each equation.
a. 6c = 30
c = 30/6 = 5
b.
2d-6=12
Adding 6 both sides
2d-6+6=12+6
2d = 18
d = 9
c.
[tex]\dfrac{x}{3}+9=2\\\\\dfrac{x}{3}=-7\\\\x=-21[/tex]
d.
50=14+3m
50-14=3m
36=3m
m = 12
Hence, this is the required solution.
Helpppp please prettty pleaseee THIS IS TIMED. I WILL MARK Brainliest. NO LINKS Please Or I WILL REPORT YOU. PLEASE GIVE EXPLANATION
Answer:
Please show the picture or question.
determine the value of x in the equation below. (3a3)x=27a9
Answer:
[tex]x = 9 {a}^{6} [/tex]
Step-by-step explanation:
[tex] = > {3a}^{3} x = 27 {a}^{9} [/tex]
[tex] = > {a}^{3} x = \frac{27a^{9} }{3} [/tex]
[tex] = > {a}^{3} x = 9a ^{9} [/tex]
[tex] = > x = \frac{9 {a}^{9} }{ {a}^{3} } [/tex]
[tex] = > x = 9a^{9 - 3} [/tex]
[tex] = > x = 9 {a}^{6} [/tex]
hence, the answer is x = 9a⁶.
Please answer 15 and 16 hurry pls!!
Answer:
15) letter A
16) letter C
Step-by-step explanation:
Used a graphing calculator,
hope this helps.
45. Find the median of the numbers 34, 47,
46, 68, 76, 81
Answer:
the median is 57.5
Step-by-step explanation:
If four is subtracted from twice a number, the result is fourteen what is the equation
Answer:
2x - 4 = x - 10
Step-by-step explanation:
A segment has an endpoint at (2, 4) and a midpoint at (4, -2). What are
the coordinates of the other endpoint?
Answer: (6, -8)
Step-by-step explanation: endpoint 1 is 6.3 away from the midpoint. Double that makes 12.6, so find the point that is 12.6 away from the original endpoint. Using a graph helps! I personally use geogebra.
Hope this helped! Please give brainliest if it did ;)
For the Past year, national percentages of people's preference in car color are as follows: White: 35%, Silver: 28%, Blue: 24%, Red: 10%, Other: 3% Of the 9,000 people who bought cars in San Jose recently, the following is the record of colors: White 3,145; Silver 2510; Blue 2,165; Red 905; Other 275 Use "Goodness of Fit Test" and the Chi Square distribution What is the value of the Chi Square Test Statistics for this problem to the nearest third decimal place? What is the p value for chi square?
Answer:
35%
Step-by-step explanation:
4
The portable basketball hoop shown is made so that BA= AS = AK. The measure of BSK is 76. What is m(angle)AKB?
Answer:
have you found the answer
a golden padlock weighs 4/5 of a pound, but only 3/4 of the padlock is real gold. How many pounds of real gold are in the padlock?
Answer:i dont know
Step-by-step explanation:
Help me
The real amount of gold in the padlock is 3 / 5 pounds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a golden padlock weighs 4/5 of a pound, but only 3/4 of the padlock is real gold.
The amount of the golden padlock is calculated as,
Amount = 4 / 5 x 3 / 4
Amount = 3 / 5 pounds
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there are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 14 meters?
Answer:
551
Step-by-step explanation:
Answer:
551.18 inches
Step-by-step explanation:
convert 14 m to cm, so multiply 14 by 100, to get 1400, then convert to inches, so divide by 2.54, which gives you 551.18 inches
Write the equation of the line that passes through the points (7, -3) and (7, 0).
Answer:
x = 7
Step-by-step explanation:
Since the x- coordinates of the 2 points are equal, both 7 , then the line is vertical with equation
x = c
where c is the value of the x- coordinates the line passes through, then
x = 7 ← equation of line
Answer:
I hope this is right, im not sure because they are coincides or the same lines when overlapped, but I tried.
3x+0
Step-by-step explanation:
Using the formula mx+b we can get our answer.
We know that the two points pass through (7, 0)
mx+b is (slope)x+(y-intercept)
The slope of the two lines is 3 so we can replace m for 3:
3x+b
the y-intercept does not exist for these two lines as they are coincides, so we can just put it at 0, so we now have our equation 3x+0.
A slide was installed at the local swimming pool, as shown here
What is the length of the slide?
Answer:
21.47 ft (rounded to the near hundreths)Step-by-step explanation:
Pythagorean Theorem : Right triangle with legs a and b and hypotenuse c
a=19 b = 10 c= x
19² + 10² = x²361 +100 = x²461 = x²x = square root of 461
x= 21.4709... (21.47 )
The required length of the slide installed at the local swimming pool is 21.47 ft.
A slide was installed at the local swimming pool, as shown here, what is the length of the slide is to be determined.
Perpendicular length = 10ft
base length = 19ft
In a right-angled triangle, its side of the right angle triangle, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
Let the length of the slide at the local swimming pool is x,
applying Pythagorean theorem
hypotenuse² = perpendicular² + base²
x² = 19² + 10²
x² = 361 +100
x² = 461
x = √461
x = 21.47 ft
So, x = 21.47 is the length of the slide.
Thus, The required length of the slide installed at the local swimming pool is 21.47 ft.
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The area of the figure is ______ sq units
What is the value of P for the following triangular prism? 19 yd 7 yd 35 yd 12 yd
Answer: 12 yards
Step-by-step explanation:
I just had this question and 12 was the answer! May I have brainliest please?
The value of P for the following triangular prism, 12 yd
What is Perimeter of prism?Perimeter is the distance around the edge of a shape.
Perimeter of the prism = side + side + side
= 5+4+3
= 12 yd
Hence, the value of P = 12 yd
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Yousef buys 40 tokens at the carnival. He gives his sister tokens for 5 kiddie rides. He wants to use the remaining token for thrill rides for himselt.
thrill rides use 5 tokens each and kiddie rides use 3 tokens each, what is the largest number of thrill rides Yousef can go on?
Answer:
5 rides
Step-by-step explanation: Multiply the number of kiddie rides his sister will go on (5) by the amount of tickets it costs each (3). subract that from 40 (the initial amount of tickets). then divide that by 5 (amount of tickets for 1 thrill ride)
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two-tailed, left-tailed, or right-tailed. The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months. A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.
Choose the correct null and alternative hypotheses below.
A. H0: μ = 22.1 months
Ha: μ > 22.1 months
B. H0: μ = 22.1 months
Ha: μ 22.1 months
C. H0: μ = 22.1 months
Ha: μ < 22.1 months
D. H0: μ > 22.1 months
Ha: μ = 22.1 months
E. H0: μ 22.1 months
Ha: μ = 22.1 months
F. H0: μ = 22.1 months
Ha: μ > 22.1 months
Which of the following is the correct classification of the hypothesis test?
A. Two-tailed
B. Left-tailed
C. Right-tailed
Answer:
Option B:
[tex]H_0: \mu = 22.1[/tex]
[tex]H_a: \mu \neq 22.1[/tex]
Classification:
The hypothesis test is Two-tailed.
Step-by-step explanation:
The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.
This means that the null hypothesis is that the mean is of 22.1 months, that is:
[tex]H_0: \mu = 22.1[/tex]
A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.
At the alternate hypothesis, we test if this mean is different of 22.1, that is:
[tex]H_a: \mu \neq 22.1[/tex]
Which means that the answer is given by option b).
Which of the following is the correct classification of the hypothesis test?
We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.
Please help and explain ( Brainliest for answer!)
Answer:
AD = 3
Step-by-step explanation:
Pythagoras theorem formula: a² + b² = c² (c being the hypotenuse, the longest side of the triangle).
Using this formula, you can easily say that c²-b²=a². c=5, b=4, making the equation 5² - 4² = a ².
Expanding the formula, you'll get 25 - 16 = a².
25 - 16 = 9.
This means that 9 = a².
To find a, you need to root 9. Using a calculator, you'll know that this number is 3, meaning that AD = 3.
Help please i really need help with this.
Answer:
Sorry too hard
Step-by-step explanation:
i will give Brainiest if your right
Use the diagram of the parallelogram to answer the question. 18 m 10 m 6 m *not drawn to scale What is the perimeter of the parallelogram? A. 34 m B. 54 in O C. 56 m D. 62 mm OE. E. 108 m
Help will give brainliest
Answer:
i think it might be E: 108 m ? im not sure
22,5,22,13,12,24,24,9,24,19 range mean median and mode
Answer:
19 is the range.
17.4 is the mean.
20.5 is the median.
24 is the mode.
Step-by-step explanation:
Range - The difference of the largest number and the smallest numberMean - To calculate the mean, add up all the numbers, then, divide the sum by the count.Median - The "middle" number after putting the numbers in numerical orderMode - The most frequently appearing numbers-------------------------------------------------------------------------------------------------------------
22, 5, 22, 13, 12, 24, 24, 9, 24, 19.
Now that we know what these words mean, we can solve this.
Range: 24 - 5 = 19
19 is the range.
-------------------------------------------------------------------------------------------------------------
Now, let's calculate the mean.
Mean: 22 + 5 + 22 + 13 + 12 + 24 + 24 + 9 + 24 + 19 = 174
There are 10 numbers in total.
174 ÷ 10 = 17.4
17.4 is the mean.
-------------------------------------------------------------------------------------------------------------
5, 9, 12, 13, 19, 22, 22, 24, 24, 24
In this case, there are two medians.
So to find the median, we have to add both the medians of this data set, then, divide the sum by 2.
19 + 22 = 41
41 ÷ 2 = 20.5
20.5 is the median.
-------------------------------------------------------------------------------------------------------------
5, 9, 12, 13, 19, 22, 22, 24, 24, 24
24 appears the most; 24 is the mode.
Daniel loves pizza, so he decided to enter a pizza eating contest. Each contestant was given a 25inch pizza and the winner was determined by who ate the most! Daniel ate the entire pizza and won! How much pizza did he eat? (Hint 25 is the diameter?
Answer:
490.87 inches²
Step-by-step explanation:
Hi there!
What we're trying to find: the area of the circular-shaped pizza
What we know: the diameter of the pizza (25 inches)
Area of a circle = [tex]\pi r^2[/tex] where r is the radius of a circle
To find the radius, divide the diameter by 2:
25 inches ÷ 2 = 12.5 inches
Plug 12.5 inches into the area equation
[tex]A=\pi r^2\\A=\pi (12.5)^2\\A=\pi (12.5)^2\\A=156.25\pi \\A=156.25\pi \\A=490.87[/tex]
The area of the circle (pizza) is approximately 490.87 inches².
Therefore, Daniel ate 490.87 inches² worth of pizza.
I hope this helps!
Solve for x. What does X =?
Answer:
x=50
Step-by-step explanation:
When Nathaniel left his house in the morning, his cell phone battery was partially
charged. The charge remaining in Nathaniel's battery, as a percentage, can be
modeled by the equation B = 52 - 6.5t, where t is the number of hours since
Nathaniel left his house. What is the slope of the equation and what is its
interpretation in the context of the problem?
Answer:
Slope -6,5
Step-by-step explanation:
Slope of the equation is -6.5 which is mean that every our his battery lose 6.5 percent of charge. 52 represent here the percentage of battery at the time he left the house.
3x^2+23x^343x^2+13x-10
Answer:
mathmaticicans :impossible
Step-by-step explanation:
some random kid :the answer is aproximatly 42