Answers
Answer:
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
Step-by-step explanation:
Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:
[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]
[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]
[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
Related Questions
Darrell builds and sells bookcases to earn money. He earns $20 for each bookcase he sells. The more bookcases he sells, the more money he earns. What is the dependent variable in this situation?
Answers
Answer: The total amount of money Darrell earns selling bookcases
Answer
Step-by-step explanation:
The dependent variable refers to the variable which is tested or measured or tested when an experiment is done. The dependent variable normally depends on the independent variable.
In this question, the independent variable is the bookcase while dependent variable is the total amount of money Darrell earns selling bookcases.
Find the coordinates of the points that are 20 units away from the origin and have a y-coordinate equal to −12.
Answers
9514 1404 393
Answer:
(-16, -12), (16, -12)
Step-by-step explanation:
The given values (side length and hypotenuse) have the ratio ...
12 : 20 = 3 : 5
This suggests that the triangle formed by the axes and the point 20 units from the origin is a 3-4-5 triangle, and the remaining side is 16 units from the y-axis. That means the points of interest are ...
(-16, -12) and (16, -12)
40 POINTS! Match each set of vertices with the type of triangle they form.
Answers
Answer:
#1 ((2, 0), (3, 2), (5, 1)) = right isoceles triangle ✔️
#2 ((4, 2), (6, 2), (5, 3.73)) = acute isosceles triangle ❌
so it is not part of graph
#3 ((-5, 2), (-4, 4), (-2, 2)) = Acute scalene triangle ✔️
#4 ((-3, 1), (-3, 4), (-1, 1)) = Right scalene triangle (or right triangle)✔️
#5 ((-4, 2), (-2, 4), (-1, 4)) = Obtuse scalene triangle ✔️
Step-by-step explanation:
the triangles are correct
Answer:
(2,0), B(3,2),C(5,1) is isosceles right angel
(-5,2), B(-4,4), C(-2,2) acute scalene triangle
(-3,1), B(-3,4), C(-1,1) right angel
(-4,2), B9-2,4), C(-1,4) obtuse scalene triangle
Step-by-step explanation:
Can you help me with this question? 15 points and brainliest if right!!
Answers
How to take a screenshot on an HP laptop
Press the Windows key and Print Screen at the same time to capture the entire screen. ...
Open an image editing program (Microsoft Paint, GIMP, Photoshop, and PaintShop Pro will all work).
Open a new image and press CTRL + V to paste the screenshot.
Line segment CD is the altitude drawn to hypotenuse EF in right triangle ECF. If EC = 10 and EF = 24, then, to the nearest tenth, find ED.
Answers
Answer:
4.2 = ED
Step-by-step explanation:
C is the Right Angle.You will do yourself a great favor by drawing your own diagram. The easiest way to do this is to find CF first. Use the Pythagorean Theorem.The next step is to find the area of the triangles using EC * CF which you just found. Equate that to the hypotenuse * altitude(CD) to find CDThen use Pythagoras again to ED.Step One
Find FC. That is the only side of the right triangle that you don't know the value of.
EC^2 + FC^2 = EF^2EC = 20FC = ?EF= 24 This the Hypotenuse.10^2 + FC^2 = 24^2100 + FC^2 = 576 Subtract 100 from both sides.FC^2 = 576 - 100 Combine the right FC^2 = 476sqrt(FC^2) = sqrt(476)FC = 21.817Step Two
Find CD. Do this by finding the area two ways. (Key Step)Area = hypotenuse * altitude / 2Area = EC * CF / 2EC = 10CF = 21.817hypotenuse = 24altitude = y24*y / 2 = 10 * 21.817 /212 y = 218.17/212y = 109.085y = 109.085/12y = 9.0904Step Three
Find EDED^2 = 10^2 - y^2ED^2 = 100 - 9.0904^2ED^2 = 100 - 82.6357ED^2 = 17.36sqrt(ED^2) = sqrt(17.36)ED = 4.1671ED = 4.230% of a sum of money is $234.
Use this fact to work out:
a 60%
b 90%
C 15%
d 3%
of the same amount.
Answers
Answer:
just took it, 15%
Step-by-step explanation:
I just took it online on ed
Answer:
30/100 × Y= 234
Y= 234÷30=7.8
7.8×100= 780
So the money is $780
Step-by-step explanation:
a. 60/100× 780 = $468
b. 90/100× 780 = $702
c. 15/100× 780= $117
d. 3/100 × 780= $23.4
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval
Answers
Did you manage to solve it?
3+2×(8-5)+6
please answer if you answer I will follow if it is right
Answers
Answer: 3+2×(8-5)+6 =15
[tex]\sf\purple{15}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3 + 2 \times (8 - 5) + 6 \\ \\ = 3 + 2 \times 3 + 6 \\ \\ = 3 + 6 + 6 \\ \\ = 15[/tex]
Note:-[tex]\sf\purple{BODMAS\: rule.}[/tex]
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Question 9
Find the volume.
Answers
Answer:
D. 50 yd³
Step-by-step explanation:
Volume of triangular pyramid = ⅓ * Base Area * height of pyramid
Base area = ½*b*h = ½*6*5
Base area = 15 yd²
height of pyramid = 10 yd
Volume of the triangular pyramid = ⅓*15*10
Volume of the triangular pyramid = 5*10
= 50 yd³
Brainliest, 10 Points, & Thanks if answer to these questions!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
+1 and -1 change the x postion
Please help me figure this out. No links
Answers
Answer
x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]
Step-by-step explanation:
x.1,2=[tex]\frac{-(-2)+ \sqrt{(-2)^2-4.1(-1)} }{2.1}[/tex]
apply rule -(-a)=a
[tex]\sqrt{(-2)^2+4.1.1}[/tex]
[tex]x1,2=\frac{-(-2)+2\sqrt{2} }{2.1}[/tex]
x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $20 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Answers
Answer:
The dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Step-by-step explanation:
Note: Kindly refer to the attached diagram where:
x = Length of the rectangular area
y = Width of the rectangular area.
The fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. This implies that it is $10 per foot. Otherwise, it will be $20 per foot. Since no fencing is needed along the barn, it implies that there is no fence along the northern length.
Since the farmer is not willing to spend more than $7000, we have:
10y + 20x + 20y = 7000
20x + 30y = 7000
Divide through by 20, we have:
x + 1.5y = 350
x = 350 - 1.5y …………………………. (1)
The fenced area is
A = x * y ………………………………….. (2)
Substituting equation (1) into (2), we have:
A = (350 - 1.5y)y
A = 350y - 1.5y^2 ……………. (3)
To maximize A, equation (3) is differentiated with respect to y and equated it to 0 as follows:
That is,
A'(y) = 350 - 3y = 0
Solving for y, we have:
y = 350/3
y = 116.67 ft
Substituting y = 116.67 for y in equation (1), we have:
x = 350 - (1.5 * 116.67)
x = 175ft
Therefore, the dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Henrieta drove 250 miles in 4 hours. How much miles did she drive in 10 minutes?
Answers
Answer:
625 miles
Step-by-step explanation:
250/4=62.5
62.5*10 = 625
Answer:
Below.
Step-by-step explanation:
There are 6 * 10 minutes in 1 hour and 4*6 = 24 10minutes in 4 hours.
So in 10 minutes she travels 250 / 24
= 10.417 miles to nearest thousandth.
A piece-wage earner collected the following weights of coffee beans each day over a week:13.3kg,10.8kg,14.4kg and 12,9kg.if she is paid at K5.80 per kilogram, estimate his earning for the week .note do not round off the rate payment
Answers
Answer:
14.4 should be around 14kg
12,9kg should be rounded to 12
Distinguish rational numbers from the following.
a. √25 b. √23 c. 1.01 d. 2.323223222... e. 3.786
Answers
Answer:
spongebob at the bottom of the sea
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
Do these ordered pairs represent a function?
(0, 1), (0, 2), (2,3), (4,8)
Answers
Answer:
No
Step-by-step explanation:
To be a function, each input can only go to one output
0 goes to 1 and 2 so it cannot be a functions
what is the end behavior of function h(x)=-4x^2+11
Answers
Answer:
[tex]-4x^{2} +11[/tex] is a parabola. The coefficient in front of the highest term (-4 in front of the [tex]x^{2}[/tex]) is negative, meaning both of the ends go towards negative infinity (point downward). So, as x approaches positive or negative infinity, y approaches negative infinity.
The end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].
According to theory of limits and differential calculus, all polynomial functions are continuous and differentiable function with no limits for [tex]x \to \pm \infty[/tex]. Therefore, we can conclude that function [tex]h(x) = -4\cdot x^{2}+11[/tex] diverges to [tex]-\infty[/tex] for [tex]x > 0[/tex] or [tex]x < 0[/tex].
That is,
[tex]x \to +\infty[/tex]
[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to +\infty} x^{2} + \lim_{x \to +\infty} 11[/tex]
[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]
[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E.[/tex]
[tex]x \to -\infty[/tex]
[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to -\infty} x^{2} + \lim_{x \to -\infty} 11[/tex]
[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]
[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E.[/tex]
Hence, the end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].
We kindly invite you to check this question related to limits: https://brainly.com/question/12383180
1.05^x=2
Solve for x
Answers
1.05^x = 2
Apply export rule ( logarithm s)
Xln1.05 = ln2
Divide both sides by ln1.05
X = ln2/ln1.05
X = 14.206
Round the answer as needed.
The Hamilton’s are installing a new pool in their backyard .The scale drawing below represents the new pool,where 1 centimeter represents 5 feet.
Answers
6cm X 5 = 40ft
20ft : 40ft pool
20x40 = 800 square ft
900sq ft - 800sq ft
100 square feet
If f(x) = x/2 -3 and g(x) = 3x² + x - 6, find (f + g)(x). O A. 3x O B. 3x² + 3x-9 3x O C. 3.x2 + x - 3 O D. 4x2-9
Answers
Answer:
4x2-9
Step-by-step explanation:
it would be that because the number is in the c acis
The box plots below show the math scores of students of two different classes, which statement is correct
Answers
Answer:
B
Step-by-step explanation:
Given the data:
Class A 55 72 75 89 95
Class B 55 70 75 94 100
CLASS A :
Minimum - 55
Lower quartile - 72
Median - 75
Upper quartile - 89
Maximum - 95
CLASS B :
Minimum - 55
Lower quartile - 70
Median - 75
Upper quartile - 94
Maximum - 100
Evaluating the statements given :
The median score of Class A is greater than the median score of Class B.
Median A = 75 ; Median B = 75 (median are equal), hence, A is not true
The lower quartile of Class A is greater than the lower quartile of Class B.
Lower quartile A = 72 ; Lower quartile B = 70 (A is greater than B) , hence, B is true
The upper quartile of Class A is greater than the upper quartile of Class B.
Upper quartile A = 89 ; Upper quartile B = 94 (A is less than B) , hence, statement is not true
The maximum score of Class A is greater than the maximum score of Class B.
Maximum A = 94 ; maximum B = 100 ; A < B ; Hence, statement is not true
112 1/2 as a decimal
Answers
Answer:
[tex] \frac{1}{2} \: as \: a \: decimal = \\ 0.5[/tex]
Step-by-step explanation:
thats the answer
The decimal form, the mixed fraction can be written as 112.5.
To find out mixed fraction in the form of decimal.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that:
The mixed fraction is a fraction whose nominator is greater than its denominator or improper fraction is a fraction in which the denominator is always less than the numerator.
112 1/2
= (2 x 112 + 1)/2
= (224 + 1)/2
= 225/2
To divide the 225 by 2 ,we get
=112.5
So, the decimal form, the mixed fraction can be written as 112.5
Learn more about fraction here:
https://brainly.com/question/24092047
#SPJ2
Find the area of a regular
polygon with 6 sides that has a
perimeter of 42 inches and an
apothem of 5 inches,
Answers
Answer:
The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.
The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.
Then the area is
A = (1/2)(8)(42) = 336/2 = 168 in2
I hope this helped!
Step-by-step explanation:
Mark me as brainlist pleasee
I need help with this
Answers
Answer:
Step-by-step explanation:
It was confusing
Jeff says the figure below is a rhombus. Is he correct? *
Answers
Answer:
yes it is
Step-by-step explanation:
it is quadrilateral
Answer:
yes
Step-by-step explanation:
just look up rhombus and then look at the pictures
Free question answer for points. If its correct ill mark brainliest
Answers
Answer:
[tex]14. \\841\rightarrow 800\\\\15.\\750[/tex]
Step-by-step explanation:
14:
Round the highest place means keeping the farther non-zero digit to the left, then rounding. Therefore, there should only be one non-zero digit in our final answer. The only answer choice that follows this and correctly rounds is [tex]\boxed{841\rightarrow 800}[/tex]
15:
There are 30 days in November. Therefore, the number of pages typed is equal to [tex]30\cdot 25=\boxed{750}[/tex]
Answer:
.
Step-by-step explanation:
(7x-2)-(x-9) {Pls Simplify this}
Answers
Answer:
6x + 7
Step-by-step explanation:
(7x - 2) - (x - 9)
7x - 2 - x + 9
6x + 7
Find the value of x to the nearest degree.
16
7
Not drawn to scale
x°
Answers
Answer:
66°
Step-by-step explanation:
Given the right angled triangle :
Opposite side = 16
Adjacent side = 7
Using trigonometric relation :
Tan θ = opposite / Adjacent
Tan x = (16/7)
x = tan^-1(16/7)
x = 66.37°
x = 66°
How many prime numbers less than 20
Answers
Answer:
Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17 and 19
Step-by-step explanation:
The sum of three numbers is 28. The second number is three times the first and the third is 7 less than the second. What are the numbers
Answers
First term: 5
Second: 15
Last : 8
Equation:
x+3x+3x-7=28
Solving:
3x+3x+x=7x
7x-7=28
7x=28+7
7x=35
x=5
Plug 5 into the equations and you’ll get:
First term = 5
Second term = 15
Third term = 8