Answer:
the missing values is 5
I hope it's helps you
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
help help help help
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
help me pls??????? :)
Answer:4 in each bad 2 left over
Step-by-step explanation:
Answer:
4 in each bag and 2 left over
Step-by-step explanation:
divide 14 by 3
3 goes into 14, 4 times
14 - 12 = 2
4 in each bag and then 2 left over
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?
Answer:
9 years older
Step-by-step explanation:
The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )
In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so
[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides
40x + 150 = 30x + 180 ( subtract 30x from both sides )
10x + 150 = 180 ( subtract 150 from both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Then
Michell is 8x = 8 × 3 = 24 years old
Connor is 5x = 5 × 3 = 15 years old
Mitchell is 24 - 15 = 9 years older than Connor
Write and solve a word problem that can be modeled by addition of two negative integers.
Answer:
Step-by-step explanation:
Question:
Max needs to purchase a car and withdraws $100 from his bank. In a few days he withdraws another $50 to make same repairs. In total what is the change in his bank balance from theese two costs?
Solution:
(-100) + (-50) =
-150
Answered by G a u t h m a t h
solue for &
X(3 + X) = 3x + x²
3x+x^2=3x+x^2
3x-3x=x^2-x^2
which means x=0
Brody works part-time at a veterinarian's office in addition to going to college, and he is paid twice a month. Which type of budget would likely work best for Brody?
The type of budget that would likely work best for Brody is biweeky budget.
Budget is an economic term that refers to the planning and advance formulation of expenses and income. The budget is a tool to organize expenses depending on the amount of money available.
The type of budget that would be best for Brody is a biweekly budget because he receives his payment every fifteen days (twice a month). So, he can schedule his expenses each time he receives his payment, in this way he does not spend all his money before he receives the next payment.
Additionally, weekly, monthly, and dairy are not correct options because they do not fit the time periods in which Brody receives payment for his services.
Learn more in: https://brainly.com/question/141889
Note:
This question is incomplete because options are missing, here are the options.
Daily budget
Biweekly budget
Monthly budget
Weekly budget
PLZ HELP!! ASAP PLZ!! NO FILES.
Answer:
Slope is (1/4)
Step-by-step explanation:
The slope is calculated by (6-5)/(5-1)=1/4
Solve for p.
–
19p–2p+16p+12=
–
18
p=
Answer:
6
BRAINLIEST, PLEASE!
Step-by-step explanation:
-19p - 2p + 16p + 12 = -18
-5p + 12 = -18
-5p = -30
p = 6
Answer:
p = 6
Step-by-step explanation:
Given
- 19p - 2p + 16p + 12 = - 18 ( simplify left side )
- 5p + 12 = - 18 ( subtract 12 from both sides )
- 5p = - 30 ( divide both sides by - 5 )
p = 6
in 16 years, Marissa will be five times older than she is today. How old is she?
Answer:
4
Step-by-step explanation:
1 5
2 10
3 15
4 20
i wrote it out
x+16=5x
16=4x
4=x
Marissa is currently four years old.
What is algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.
Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
Let's represent Marissa's current age "x".
According to the given question, in 16 years she will be five times older than she is today, which we can express as:
x + 16 = 5x
Solving for x, we can subtract x from both sides:
16 = 4x
Dividing both sides by 4, we get:
x = 4
Therefore, Marissa is currently 4 years old.
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What is | −34 | ?
-------
l l
-------
l l
--------
Step-by-step explanation:
Here,
| −34 |
= 34
As,
| | are absolute symbols so it's denote only the neutral number such as, | - 1 | = 1
Answer:
34
Step-by-step explanation:
|-34|
The absolute value bars means taking the non-negative value
|-34| = 34
Explain why they substituted cos(60) with 1/2 ?
(Look at image)
9514 1404 393
Answer:
equals can be substituted anytime anywhere
Step-by-step explanation:
cos(60°) = 1/2, so wherever one appears, the other can be substituted. This is allowed by the substitution property of equality.
__
If you don't substitute at some point, you find the answer to be ...
x = 10/cos(60°)
Most of us are interested in a numerical value for x, so we prefer that cos(60°) be replaced by a numerical value.
if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me
Solve the equation |8y+4|=2|y−1|.
Explain.
[tex]\\ \sf\longmapsto |8y+4|=2|y-1|[/tex]
[tex]\\ \sf\longmapsto 8y+4=2y-1[/tex]
[tex]\\ \sf\longmapsto 8y-2y=-1-4[/tex]
[tex]\\ \sf\longmapsto 6y=-5[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{-5}{6}[/tex]
7t + 6 + 3v + 6v
Hey can someone help ne
Answer:
7t + 6 + 9v
Step-by-step explanation:
7t + 6 + 3v + 6v (since 3v and 6v are like terms you will add them both.)
7t + 6 + 9v
Hope this helps, thank you :) !!
Answer:
7t+6+9v
Step-by-step explanation:
7t+6+3v+6v
7t has no opponent it is =7t
6 is on it own =6
3v+6v=9v,reason is 3v has an opponent which is 6v so addition of 3v and 6v is =9v
so ur ans. is =7t+6+9v
3. Find the product, using suitable properties :
a) 26 x (-48) + (-48) x (-36)
b) 625 x (-35) + (-625) x 65
please answer fast 10 marks
a) 26 x (-48) + (-48) x (-36) = ( –1248) + ( + 1728) = – 1248+ 1728 = 480
b) 625 x (-35) + (-625) x 65 = ( –21875) + ( –40625) = – 21875 –40625 = –62500
I hope I helped you^_^
Answer ASAP please!
………
Answer:
47.746, answer choice C
Step-by-step explanation:
47.746
Which function represents g(x), a refection of f(x)=1/2(3)^x across the y-axis
Answer: g(x) = (1/2)3^-x reflection over y axis yields (-x,y)
pls help me ASAP !!!!!!!!!
Consider these four statements about a line that passes through two points on a plane.
Statement A: The lines on a different plane from the points.
Stament B: The line lies in only one plane.
Statement C: The line is on the same plane as the points.
Statement D: The line passes through only one plane.
Which statement is true?
Answer:
4
Step-by-step explanation:
find the area of circle having its radius 15cm
Answer:
A≈706.86
Step-by-step explanation:
welcome to brainly
Answer:
Let π =22/7
area of circle = πr²
= 706.86
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Please help me find x
Need help fast!!
Answer:
x = 100°
Step-by-step explanation:
p and q are parallel lines. Construct line 'l' parallel to p and q
a = 30° {p// l when parallel lines are intersected by transversal alternate interior angles are congruent}
c +110 = 180 {linear pair}
c = 180 - 110
c = 70°
b= c {q // l when parallel lines are intersected by transversal alternate interior angles are congruent}
b = 70°
x = a + b
x = 30° + 70°
x = 100°
Pls help answer, also explain. I will give brainliest
Answer:
8 lb box
Step-by-step explanation:
Find which laundry detergent has a lower unit price
The unit price is how much something costs for a single unit
In this case, it is how much the detergent costs for 1 pound
7.4/8 lbs = 0.925 dollars per lb
5.38/4 lbs = 1.345 dollars per lb
Since 1.345 > 0.925, the 8 lb box is a better buy
Case 1
Cost of 8 pound detergent = $7.40
So, cost of 1 pound detergent
= $7.40 ÷ 8
= $0.925
Case 2
Cost of 8 pound detergent = $5.38
So, cost of 1 pound detergent
= $5.38 ÷ 4
= $1.345
$0.925 < $1.345
$0.925 < $1.345So, cost per pound in 8 pound box < cost per pound in 4 pound box
So, buying the 8 pound box is better.
4.
Find the inverse of A if it has one, or state that the inverse does not exist.
Answer:
Hello,
[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]
Step-by-step explanation:
See jointed file
The inverse of the matrix A is
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]
The matrix A is a square matrix and its determinant is not zero.
So the inverse exist.
The inverse of matrix A.
We will change the rows into columns and columns into rows.
So,
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
Thus,
The inverse of the matrix A is given above.
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Independent Practice
Which model is most appropriate for the set of points?
(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)
A.
exponential
B.
linear
C.
quadratic
Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
≈ 5.51 hours
Equation: 4.25h + 10
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
The rent cost for the helmet is $10.
The rent cost for the bike per hour is $4.25.
We need to find the number of hours Amanda rented the bike as she paid $33.38 in total.
We also have to make an equation that would solve this problem.
Consider h = number of hours Amanda rented the bike.
The cost for renting the helmet = $10.
And rent cost for the bike per hour = $4.25.
Amanda's total cost = Helmet rent cost + bike rent cost
Since we do not know the number of hours the bike was rented we will denote bike rent cost = $4.25 x h
We have,
$33.38 = $10 + $4.25 x h
33.38 = 10 + 4.25 x h
33.38 - 10 = 4.25 x h
23.38 = 4.25 x h
h = 23.38 / 4.25
h = 5.5011
Rounding to the nearest tenths we get,
h = 5.5 hours
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
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Sheldon is baking 2-inch cookies. He has 3 trays that are the same size. On one tray, he makes 5 rows with 4 cookies in each row. He cannot fit any more cookies on the tray. He fills the second tray completely and only part of the third tray. How many cookies could Sheldon have made?
Answer: Sheldon has made 50 cookies
Step-by-step explanation: for the first test because there are 5 rows and 4 cookies on each row you would multiply 4 times 5. That equals 20. The first tray has twenty and all trays are the same size so if the second one is completely full then it also has twenty. The third one is only half way full meaning twenty divided by two equals ten. Ten is the amount of cookies on the third tray. If you add that all together that is 20+20+10=50
The number of cookies made by Sheldon will be equal to 50.
What is an arithmetic operation?
The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
For the first test, you would multiply 4 by 5 because there are 5 rows and 4 cookies on each row. 20 is the result.
Since all trays are the same size and the first tray has twenty, if the second tray is totally filled, it will also have twenty.
Twenty divided by two equals 10 because the third one is only half full.
There are ten cookies on the third tray.
The total is,
20+20+10 = 50.
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Which of the following steps were applied to ABC obtain AA'B'C?
12
8
B
6
A
-6
-2
4
6
10
A. Shifted 4 units left and 3 units down
B. Shifted 4 units left and 2 units down
C. Shifted 3 units left and 3 units down
D. Shifted 3 units left and 2 units down
Will give brainliest pls help!!!
Answer: B
Step-by-step explanation:
The transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, a triangle ABC has undergone a transformation to form A'B'C' we need to identify the steps of transformation
So, considering the point B and B', we see, that, x-coordinate of B is at 5 and that of B' is at 1, that mean there is a shift of 4 units left,
Now, consider the y-coordinate, we see, that B is at 9 and B' is at 7 that gives a downward shifting of 2 units.
Hence, the transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
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