Express the product of z1 and z2 in standard form given that [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + isin(\frac{2\pi }{5})][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2}) + isin(\frac{-\pi }{2})][/tex]
![Express The Product Of Z1 And Z2 In Standard Form Given That [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + Isin(\frac{2\pi](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/5G9KMOszKLIwQijpYLrNGVfajcDALBBk.png)
Answers
Answer:
Solution : 5.244 - 16.140i
Step-by-step explanation:
If we want to express the two as a product, we would have the following expression.
[tex]-6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right]\cdot 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Now we have two trivial identities that we can apply here,
( 1 ) cos(- π / 2) = 0,
( 2 ) sin(- π / 2) = - 1
Substituting them,
= [tex]-6\cdot \:2\sqrt{2}\left(0-i\right)\left(\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right)[/tex]
= [tex]-12\sqrt{2}\sin \left(\frac{2\pi }{5}\right)+12\sqrt{2}\cos \left(\frac{2\pi }{5}\right)i[/tex]
Again we have another two identities we can apply,
( 1 ) sin(x) = cos(π / 2 - x )
( 2 ) cos(x) = sin(π / 2 - x )
[tex]\sin \left(\frac{2\pi }{5}\right)=\cos \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]
[tex]\cos \left(\frac{2\pi }{5}\right)=\sin \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex]
Substitute,
[tex]-12\sqrt{2}(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}) + 12\sqrt{2}(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4})[/tex]
= [tex]-6\sqrt{5+\sqrt{5}}+6\sqrt{3-\sqrt{5}} i[/tex]
= [tex]-16.13996 + 5.24419i[/tex]
= [tex]5.24419i - 16.13996[/tex]
As you can see option d is the correct answer. 5.24419 is rounded to 5.244, and 16.13996 is rounded to 16.14.
Related Questions
Solve and graph the inequality. 45x + 5 < −3
Answers
Answer:
x < -8/45
Step-by-step explanation:
Step 1: Write out inequality
45x + 5 < -3
Step 2: Subtract both sides by 5
45x + 5 - 5 < -3 - 5
45x < -8
Step 3: Divide both sides by 45
45x/45 < -8/45
x < -8/45
Step 4: Graph
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answers
Answer:
.87
Step-by-step explanation:
She gets 13 off so 100-13 =87
She will pay 87%
Multiply by .87
Kylie must multiply the price by 0.87 to get the discounted price.
Given that,
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
let the price be x,
Now,
According to the question,
discounted price = x - 13% of x
Discounted price = x - 0.13x
Discounted price = 0.87 x
The coefficient of the x represents the multiplication factor for Kylie.
Thus, Kylie must multiply the price by 0.87 to get the discounted price.
Learn more about percentages here:
brainly.com/question/13450942
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Decide whether the pair of ratios form a proportion 15/12=4.5/3.6
Answers
Answer: Yes they form a proportion. The given equation is a true equation.
==========================================
Explanation:
The idea is that if we have
a/b = c/d
then that it is the same as
a*d = b*c
This is known as cross multiplication. We'll use this rule to get
15/12 = 4.5/3.6
15*3.6 = 12*4.5
54 = 54
We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).
--------
You could also use your calculator to see that
15/12 = 1.25
4.5/3.6 = 1.25
showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.
Answer:
15/12=4.5/3.6 = True
Step-by-step explanation:
Simplify the following: Left-hand
15/12
Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.
The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:
Answer: 5/4
______________________________
Approximate the following:
4.5/3.6
Hint: | Express 4.5/3.6 in decimal form.
4.5/3.6 = 1.25:
Answer: 1.25 = 5/4
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answers
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below.
Age (in years) Height (inches)
7 47.3
8 48.8
5 41.3
8 50.4
8 51
7 47.1
7 46.9
7 48
9 51.2
8 51.2
5 40.3
8 48.9
6 45.2
5 41.9
8 49.6
Requried:
a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
c. How much of the variation in the sample values of height does the model estimated in part (b) explain?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Age(x)
7
8
5
8
8
7
7
7
9
8
5
8
6
5
8
Height (Y)
47.3
48.8
41.3
50.4
51
47.1
46.9
48
51.2
51.2
40.3
48.9
45.2
41.9
49.6
The estimated regression equation:
ŷ = 2.73953X + 27.91395
Where ;
X = independent variable
ŷ = predicted or dependent variable
27.91395 = intercept
C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:
Using the online pearson correlation Coefficient calculator :
The correlation Coefficient is 0.9696.
which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.
Choose the expression that is equivalent to -4 - (-9).
A 4 + 9
B 4 - 9
C -4 + 9
D -4 + (-9)
Answers
Answer:
d
Step-by-step explanation:
[tex]\\ \sf\longmapsto -4-(-9)[/tex]
[tex]\\ \sf\longmapsto -4+9[/tex]
Option C is correct .
Note:-
(-)(-)=(+)(+)(-)=(-)(-)(-)=(+)(+)(+)=(+)if 405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
Answers
Step-by-step explanation:
Pls Mark me
Brainliest!!!!The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answers
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
Relating a Polynomial Identity to Pythagorean Triples
In this activity you'll relate polynomial identities with Pythagorean triples. Answer the following questions
based on this triangle with side lengths x^2 – 1, 2x, and x^2 + 1.
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
For x > 1, we can apply Pythagoras theorem as below.
[tex]\text{Let's estimate this sum of two squares.} \\\\(2x)^2+(x^2-1)^2=4x^2+x^4-2x^2+1=x^4+2x^2+1\\\\\text{Let's estimate this square, now.} \\\\(x^2+1)^2=x^4+2x^2+1\\\\\text{The two expressions are equal, meaning.} \\\\(2x)^2+(x^2-1)^2=(x^2+1)^2\\\\\text{Using Pythagoras' theorem, we can say that this is a right triangle.}[/tex]
Thank you
price.
A shopkeeper marks the price of his her goods 40 % above the cost price and
allows 20% discount. If his her purchase price of an item is Rs 6.000. how much
should a customer pay for it levying 13 % VAT!
e 990 the honorariter
Answers
Answer:
73%
Step-by-step explanation:
Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?
Answers
Answer:
Reserve rate = 9%
Step-by-step explanation:
Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.
first, let us calculate the reserve amount as follows:
Reserve = Deposit - (free amount to lend out)
Reserve = 28,000 - 25,480 = $2,520
[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]
Therefore the reserve rate = 9%
WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWER ITS PRETTY EASY If it is 3:00 p.m. and you move the minute hand of the clock 270 degrees clockwise, what time will it be?
Answers
Answer:
3:45 pm
Step-by-step explanation:
Every 90 degree = 15 minutes
270 degrees = 15 x 3 = 45 minutes
3:00 + 0:45 = 3:45 pm
Hope this helps!
Answer:
3:45 pm
Step-by-step explanation:
∆T = (270/360)° × 60 minutes
=45 mins
Time = 3hrs + 45 mins
3:45 pm
I NEED FULL EXPLANATION
(4 - 3i) ^2
Answers
Answer:
Rewrite
( 4 − 3 i ) 2 as ( 4 − 3 i )( 4 − 3 i ) . ( 4 − 3 i) ( 4 − 3 i ) Expand ( 4 − 3 i ) ( 4 − 3 i )
using the FOIL Method.
4 ⋅ 4 + 4 ( -3 i ) − 3 i ⋅ 4 − 3 i ( − 3 i )
Simplify and combine like terms.
7 − 24 i
Step-by-step explanation:
Answer:
7 -24i
Step-by-step explanation:
(4 - 3i) ^2
(4-3i) * (4-3i)
FOIL
first 4*4 = 16
outer 4 * -3i = -12i
inner -3i *4 = -12i
last -3i*-3i = 9i^2 = 9 (-1) = -9
Add together
16 -12i-12i -9
Combine like terms
7 -24i
Find the value of each expression.
30 ÷ 3 × 2
Answers
Answer:
Step-by-step explanation:
1) First division has to be done.
2) After that multiplication has to be done.
30 ÷ 3 * 2 = 10 * 2
= 20
Answer:
20
Step-by-step explanation:
30 ÷ 3 × 2
(Since it’s division and multi platoon, we just go left to right)
10 × 2
20
Factor: x^3-2x^2-8x
1. (x-4)(x+2)
2. x(x+4)(x-2)
3. x(x-4)(x+2)
4. (x-4)(x^2+2x)
Answers
Answer:
x( x-4)(x+2)
Step-by-step explanation:
x^3-2x^2-8x
First factor out the greatest common factor x
x( x^2 -2x -8)
What 2 numbers multiply to -8 and add to -2
-4*2 = -8
-4+2 = -2
x( x-4)(x+2)
What are the roots for x?
Answers
Answer:
B
Step-by-step explanation:
Use the quadractic equation, x=-b+or-sqrtb^2-4ac/2a, then simplify.
I'm really sorry that it looks messy, I don't know how to make my text look better :(
Help !!!!!!!!!!!!!!!
Answers
Answer:
9/4 = 2 1/4
Hope this Helps!?
A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each of four different types of soil and measures the growth in inches for each plant after one month resulting in the data below.
Soil 1 Soil 2 Soil 3 Soil 4
12.6 12.2 12.2 11.1
12.6 12 10.6 11.7
14.3 13 9.1 9.6
1. What null hypothesis is the researcher testing if she runs an ANOVA with this data?
a.The mean growth of the plant in each type of soil is the same.
b. One type of soil has a higher mean growth for the plant than the others.
c. The variability in growth of the plant in each type of soil is the same.
d. Oil 3 provides a lower mean growth for the plant than the other types of soil.
e. The mean growth of the plant is different in each type of soil.
2. What is the SStrt for the ANOVA? Give your answer to at least three decimal places.
3. What is DFerr for the ANOVA?
4. What is the value of the F statistic for the ANOVA? Give your answer to at least three decimal places.
5. Using a 0.05 level of significance, what conclusion should the researcher reach?
a. There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
b. Soil 1 has a higher mean growth for the plant than the other types of soil.
c. The mean growth of the plant is not the same for all soil types .
d. Soil 3 has a lower mean growth for the plant than the other types of soil.
Answers
Answer:
(1) Option a
(2) 13.737
(3) 8
(4) 3.803
(5) Option a
Step-by-step explanation:
In this case, we need to determine whether the soil type effects the growth of a certain type of plant.
Perform the ANOVA test for the provided data on Excel.
Go to Data - Data Analysis - Anova: Single factor
Select the data for the growth.
Press OK.
The output is attached below.
(1)
The hypothesis for the study can be defined as follows:
H₀: The mean growth of the plant in each type of soil is the same.
Hₐ: The mean growth of the plant is different in each type of soil.
Correct option a.
(2)
The sum of square for treatment is:
[tex]\text{SS}_{trt}=\text{SS}_{BG}=13.737[/tex]
(3)
The degrees of freedom of error is:
[tex]\text{DF}_{err}=\text{DF}_{WG}=8[/tex]
(4)
The F statistic for the ANOVA is:
[tex]F=3.803[/tex]
(5)
The p-value of the test is:
[tex]p-value=0.058[/tex]
Decision Rule:
Reject H₀ if the p-value of the test is less than the level of significance.
[tex]\text{p-value}=0.058>\alpha=0.05[/tex]
The null hypothesis was failed to be rejected.
Conclusion:
There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
Correct option a.
20 kg potatoes are sold at $12.80 each.If you have only $48, how many 20kg bags can you buy
Answers
Answer:
3 bags
Step-by-step explanation:
you can buy three, 20 kg bags
one (1) 20kg bag = $12.8 (1)
three (3) 20 kg bags = $12.8 (3)
= $38
your balance 10 dollars
3x^2+4x-5 find the coefficient
Answers
HELLO THERE
3 and 4 is the answer
I hope I helped
If m2 DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc in circle 0.
Find measure of arc DC.
Answers
Answer:
44°
Step-by-step explanation:
Given:
m<DOC = 44°
m<COB = 80°
Required:
Angle measure of arc DC
SOLUTION:
A central angle is said to be equal to the angle measure of the arc it intercepts or corresponds with. Therefore, angle measure of arc DC = m<DOC.
measure of arc DC = 44°
Rectangle with the dimensions of 2 2/5 wide and 4 1/8 long what is the area
Answers
Answer:
10 5/16
Step-by-step explanation:
2 2/5 x 4 1/8 = 10 5/16
Simplify: 9h-12h=54-23
A. 3h=-77
B.3h= 31
C.-3h= -31
D.-3h= 31
Answers
Answer:
c is the answer
Step-by-step explanation:
-3h = 31
-9h-12h = -3h
54-23= 31
Answer:
[tex]\boxed{C. -3h = 31}[/tex]
Step-by-step explanation:
Hey there!
9h - 12h = 54 - 23
Simplify
-3h = 31
C. -3h = 31
Hope this helps :)
Find the product. (7x+2)(x−1) A 8x+1 B 6x+3 C 7x2−5x−2 D 7x2−2
Answers
Answer:
7x^2 -5x-2
Step-by-step explanation:
(7x+2)(x−1)
FOIL
first 7x*x = 7x^2
outer 7x*-1 = -7x
inner 2x
last 2*-1 = -2
Add them together
7x^2 -7x+2x -2
7x^2 -5x-2
Answer:
[tex] \boxed{\red{7 {x}^{2} - 5x - 2}}[/tex]
Answer C is correct
Step-by-step explanation:
[tex](7x + 2)(x - 1) \\ 7x(x - 1) + 2(x -1 ) \\ 7 {x}^{2} - 7x + 2x - 2 \\ = 7 {x}^{2} - 5x - 2[/tex]
The sides of a rectangle are in ratio 2:5,the longer side is 20 cm. Find the length of the shorter side
Answers
Answer:
8 cm
Step-by-step explanation:
x:y= 2:5
x/y = 2/5
5x = 2y
y is the longer side
5x=2(20)
x=8 cm
The length of the shorter side is 8 cm.
What is rectangle?
A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.
Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).
Given, sides of a rectangle are in ratio 2:5.
Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.
We know length of a rectangle is longer than breadth.
So, length of the rectangle is 20 cm.
According to question,
[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]
So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.
Breath is shorter side of rectangle.
Therefore,The length of the shorter side is 8 cm.
Rectangle related one more question:
https://brainly.com/question/15019502
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Find the average rate of change of g(x) = 2x^3 - 5 from x= -4 to x= 2
Answers
Step-by-step explanation:
the average change rate is the change of the functional values from the beginning to the end of the interval, and then that divided by the length of the interval.
like with every average or mean value calculation.
g(-4) = 2×(-4)³ - 5 = -128 - 5 = -133
g(2) = 2×2³ - 5 = 16 - 5 = 11
so, on an interval of x values of 2- -4 = 6 units the function changes its values by 11 - -133 = 144 units.
the average charge rate for this x interval is therefore
144 / 6 = 24 = 24/1
for 1 unit change of x, g(x) changes in the average by 24 units.
Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c>=0 where a, b, and c are integers with no common factor greater than 1.) Help please!! I have to finish it by tonight!! Thank you!!
Answers
Answer:
Below
Step-by-step explanation:
First let's find the equation of the doted line.
Notice that the line is crossing these points:
● (0,1)
● (1,2)
The equation of the line has the following form:
● y = ax+c
C is the y-intercept wich is given by the output of 0.
Notice that the output of 0 is 1.
● y = ax+1
● a = rise / run = (2-1)/(1-0) = 1
So y = x + 1
■■■■■■■■■■■■■■■■■■■■■■■■■■
Notice that the line divide the plan into 2 areas.
● y > x+1 => x+1-y < 0
● y < x+1 => x+1 -y > 0
To khwo wich one that represent the shaded area take a point and replace x and y by its coordinates
● (-1,2)
● -1+1-2 = 0-2 = -2
It is a negative value so the inequality is
● y > x+1
6x+6+9x+9=? Please help
Answers
Answer:
15x + 15
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables. Set the equation so that the terms are grouped:
6x + 9x + 6 + 9
Combine like terms:
(6x + 9x) = 15x
(6 + 9) = 15
15x + 15 is your answer.
~
Answer:
15x+15
Step-by-step explanation:
6x+9x=15x
9+6=15
6x+6+9x+9=15x+15
find the unknown angles
Answers
Answer:
y=135
x=45
Step-by-step explanation:
x= 45
It is an isosceles so
180-90=90
90/2= 45
y=135
angles on a straight line add up to 180 so
180-45=135
Hope this helps!
What numbers are equivalent to 25%
Answers
Answer:
0.25 decimal
1/4 decimal
Step-by-step explanation: