Let z = equals 38 (cosine (startfraction pi over 8 endfraction) i sine (startfraction pi over 8 endfraction) ) and w = 2 (cosine (startfraction pi over 16 endfraction) i sine (startfraction pi over 16 endfraction) ) . what is the product of zw?
It sounds like you're saying
[tex]z = \dfrac38 \left(\cos\left(\dfrac\pi8\right) + i \sin\left(\dfrac\pi8\right)\right)[/tex]
[tex]w = 2 \left(\cos\left(\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi{16}\right)\right)[/tex]
The product [tex]zw[/tex] is obtained by multiplying the moduli and adding the arguments. In other words
[tex]z = |z| e^{i\arg(z)} \text{ and } w = |w| e^{i\arg(w)} \implies zw = |z||w| e^{i(\arg(z)+\arg(w))}[/tex]
where [tex]e^{it}=\cos(t)+i\sin(t)[/tex], so that
[tex]zw = \dfrac38\times2 \left(\cos\left(\dfrac\pi8+\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi8 + \dfrac\pi{16}\right)\right) = \boxed{\dfrac34 \left(\cos\left(\dfrac{3\pi}{16}\right) + i \sin\left(\dfrac{3\pi}{16}\right)\right)}[/tex]
Compute the probability of tossing a six sided die and getting a 7.
Answer:
0/6
Step-by-step explanation:
There are 6 numbers on the die: 1, 2, 3, 4, 5, 6
As you can see there is no 7, so the possibility is 0/6.
The adjacent sides of the parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram.
Answer:
P = 4x+10
Step-by-step explanation:
So a parallelogram has 2 set of sides which are parallel and equal. So if you're given two adjacent sides, that means you're given a side from each set of sides, which are equal. This means the perimeter is simply: 2(x+3) + 2(x+2). This can be further simplified by distributing the 2 which gives you the equation: 2x+6+2x+4, which further simplifies to 4x+10.
Given the slope of -4 that you just found. What is the slope-intercept equation of a line passing through (4, 9) and (6, 1) in the standard (x, y) coordinate plane? Use the point (4, 9) to find your equation. The line equation in slope-intercept form is Given the slope of -4 that you just found . What is the slope - intercept equation of a line passing through ( 4 , 9 ) and ( 6 , 1 ) in the standard ( x , y ) coordinate plane ? Use the point ( 4 , 9 ) to find your equation . The line equation in slope - intercept form is
Answer:
y = -4x + 25
Step-by-step explanation:
You are given the slope, but you can find the slope using 2 points. Slope is the change in y over the change is x. Your two y's are 1 and 9. Your two x's are 6 and 4.
1-9/6-2
1 - 9 = -8
6-4 = 2
-8/2 is -4.
We want an equation in the form y = mx +b. We have the m (slope), we now just need the b. We take either of the ordinal points (4,9) or (6, 1) to find b. They will both work, but the question tells us to us (4,9). 4 is the x and 9 is the y.
y = mx + b
9 = (-4)(4) + b a negative times a positive is a negative.
9 = -16 + b Add 16 to both sides
25 = b
We know now m which is -4 and b which is 25. We plug them into the model y = mx + b
y = -4x + 25
Find the gas mileage.
534 mi; 22 gal
Answer:
fvbafdbai
Step-by-step explanation:
gyhghg
I would to know how to solve this question
The information given about the probability shows that the expected maintenance cost is $22950.
How to calculate the cost?From the information given, the repair hours and the probability are given.
In this case, the maintenance cost will be:
= (8 × 0.05) + (10 × 0.12) + (12 × 0.15) + (14 × 0.32) + (15 × 0.22) + (17 × 0.14) × $1700
= 13.50 × $1700
= $22950
In conclusion, the correct option is D.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
What’s the correct answer answer asap
Answer:
I believe the answer is B, it makes the most sense
Step-by-step explanation:
Find the value of f(g(-1).
Answer: -8
Step-by-step explanation:
[tex]g(-1)=2(-1)+5=3\\\\f(g(-1))=f(3)=1-3^{2}=\boxed{-8}[/tex]
Answer:
b.) f(g(-1)) = -8
Step-by-step explanation:
Given following:
f(x) = 1 - x²g(x) = 2x + 5Start solving from the right while doing these sums.
f(g(-1))f(2(-1) + 5)f(3)1 - (3)²1 - 9-8Statistics 4. Hol (a) The average age of 5 students is 9 years. Out of them, the ages of 4 students are 5, 7, 8, and 15 years. What is the age of the remaining student?
Answer:
10 years
Step-by-step explanation:
the average or mean value is the sum of all data points divided by the number of data points.
x = the unknown age of the 5th student.
average = 9 = (5 + 7 + 8 + 15 + x)/5
45 = 5 + 7 + 8 + 15 + x = 35 + x
x = 45 - 35 = 10
the 5th student is 10 years old.
Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope.
A(3, 5), B(7, 6), C(6, 2), D(2, 1)
======================================================
Reason:
Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\[/tex]
Segment AB is exactly [tex]\sqrt{17}[/tex] units long, which is approximately 4.1231 units.
If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.
-------------------------
Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.
Let's find the slope of AB.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\[/tex]
Segment AB has a slope of 1/4.
Do the same for BC
[tex]B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\[/tex]
Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.
We don't have perpendicular lines, so the interior angles are not 90 degrees each.
Therefore, this figure is not a rectangle and by extension it's not a square either.
The best description for this figure is a rhombus.
Answer:
Rhombus
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. That is, they have the same midpoint. If they are the same length, that parallelogram is a rectangle. If they cross at right angles, it is a rhombus. If it is a rectangle and rhombus, then it is a square.
Diagonal midpointsThe midpoints of AC and BD are ...
(A+C)/2 and (B+D)/2
To determine if the midpoints are the same, we can skip the division by 2 and simply look at the sums:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
The midpoints of the diagonals are the same, so the figure is at least a parallelogram.
Diagonal vectorsThe diagonal vectors will be the same length if the figure is a rectangle. They will be perpendicular if the figure is a rhombus. The vectors are ...
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
The length of each of these is the root of the sum of squares of its components. These are obviously different lengths (3√2 vs 5√2).
The dot-product of these will be zero if they are perpendicular:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
ConclusionThe diagonals are different length and mutual perpendicular bisectors, so the figure is a rhombus.
__
Additional comment
Looking at the dot-product is a simple way to check that the slopes are opposite reciprocals. The slope of a vector with components (x, y) is m = y/x.
The requirement that slopes be opposite reciprocals means ...
y1/x1 = -1/(y2/x2) . . . . . . . . slope relationship
(y1)(y2)/((x1)(x2)) = -1 . . . . . multiply by y2/x2
y1·y2 = -x1·x2 . . . . . . . . . . multiply by (x1·x2)
x1·x2 +y1·y2 = 0 . . . . . . . . add x1·x2
This shows the vector dot product being zero is equivalent to the slopes being opposite reciprocals. The vectors are perpendicular in this case.
The equation of a line is y equals 4 over 3 x minus 5 over 3.
What would be the slope of a line perpendicular to this line?
A. -3/4
B. 5/3
C. -4/3
D. 3/5
Answer:
-3/4
Step-by-step explanation:
So you have the equation: [tex]y=\frac{4}{3}x-\frac{5}{3}[/tex]. For a perpendicular line, the only thing that matters is the slope. The slope of the perpendicular line can be defined as: [tex]\frac{a}{b} = > -\frac{b}{a}[/tex]. It's the reciprocal with the sign being the opposite. So if the sign of the original line was negative it's now positive, and if it's positive, it's not negative. The fraction is also flipped, even if it's an integer, it can be defined as a fraction e.g ([tex]6 = > -\frac{1}{6}[/tex] (sign also changed too))
So in this case the slope is 4/3x, since it's given in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept. So we flip it to get 3/4 and change the sign to negative to get -3/4
A bakery sold 12 vanilla cupcakes in a day, which was 6% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
200 cupcakes
Step-by-step explanation:
12 cupcakes = 6%
12/x=6/100 6x=1200 x=200
so 200 cupcakes
hope this helps
The total number of cupcakes the bakery sells that day is 200.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Given that,
A bakery sold 12 vanilla cupcakes in a day, which is 6% of the total cupcakes.
Let's say the total cupcakes were x
Then,
6% of x = 12
6 × x/100 = 12
Divide both sides by 6
x/100 = 2
Multiply both sides by 100
x = 200
Hence "The total number of cupcakes the bakery sells that day is 200".
For more about the percentage,
brainly.com/question/13450942
#SPJ2
The population of Nowhere, USA was estimated to be 886,000 in 2004, with an expected increase of 4% per year. At the percent of increase given, what was the expected population in 2005? Round your answer to the nearest whole number.
Answer:
y=886000(1.04)^t
t=1 year so answer is 886000*1.04 = 921440
Write the following number in Standard Form: 4.32x 10^-5
Answer:
0.0000432
Step-by-step explanation:
In scientific notation, 10 raised to a negative number means that the number is less than 1. If the exponent is -5, the decimal place needs to be moved to the left 5 places. This makes the number in standard form: 0.0000432.
Write the ratios for sin M, cos M, and tan M.
Answer:
Sin M= opposite/hypotenuse, cos M= adjacent/Hypotenuse, tan M= opposite/adjacent
Step-by-step explanation:
Answer:
sinM= [tex]\frac{opposite}{hypotenuse}[/tex]
cosM= [tex]\frac{adjacent}{hypotenuse}[/tex]
tanM= [tex]\frac{opposite}{adjacent}[/tex]
There are ten rappers performing live, the other 14 ill. what is the percentage of the ill rappers, and what would happen if you add 5 rappers to the performance. Does this make it more complicated?
Answer:
14/24 are ill so
58 percent
if you add 5 it does not get more complicated you just add 5 so 14/29
Hope This Helps!!!
The volume of a cube is 27 cubic in. Which expression represents s, the lenght of a side of the cube
Answer:
Hello i am here to give the answer of the above question................................................................................................................................
Solution:Here
Given,
Volume of a cube is 27 so.
Length of a side of the cube =?
So I think the correct answer of this question is 3
Thank you......... ..................
Part D
Whose tiles cover more area per tile? Use complete sentences to explain your reasoning.
The person that would cover the most tile is Bruce because 1/4 is bigger than 1/6.
How to solve for the size of the tilesBruce has been said to have the need for 1/4 square foot of tiles
Felicia on the other hand would need
1/6 for 1 sq foot
12 for 2 square foot
18 for 3 square foot
Bruce is knwon to cover
[tex]\frac{1}{4} x[/tex]
For felicia one square foot is covered by 1/6th
Now we have to know the one that is larger.
1/4 is bigger than 1/6
Hence we can conclude that Bruce is going to cover a larger are than Felicia.
Read more on areas here:
https://brainly.com/question/13875666
#SPJ1
Answer: The person who covered the most tiles is Bruce, because 1/4 is bigger than 1/9.
Step-by-step explanation:
How would you write 8^5 as a multiplication expression? A. 8 × 5 B. 8 × 8 × 8 × 8 × 8 C. 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 Reset Next
Answer:
8*8*8*8*8
Step-by-step explanation:
Answer:
8 x 8 x 8 x 8 x 8
Step-by-step explanation:
8^5 is basically 8 times itself five times.
Look at angle UVY and angle YVW in the image below. Which of the following is the best description for this pair of angles?
x²+x-6
p= -2, q=3.
Factor the quadratic trinomial.
What are the binomial factors?
O(x + 2)(x-3)
O(x-2)(x+3)
O(p-2)(q + 3)
QUICK PLEASE. Calculate the final amount if $10 000 invested for 6 years at 4% compounded quarterly.
The final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697
Compound interestThe formula for calculating the compound interest is given as:
A = P(1+r/n)^nt
Given the following parameters
A = 10000(1+0.04/4)^4(6)
A = 10000(1+0.01)^24
A = 10000(1.01)^24
A = 1.2697(10,000)
A = $12,697
Hence the final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697
Learn more on compound interest here: https://brainly.com/question/24924853
#SPJ1
What is the weighted average cost of capital if a business has a cost of equity of 12%, a cost of debt of 10%, tax rate of 25%, 20 million market value of debt, and 60 million market value of equity?
If the cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity then the weighted average cost of capital is 10.875%
Given cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity.
We know that weighted average cost of capital= cost of equity* weight of equity+ cost of debt* weight of debt.
Cost of debt (consider after tax)=10%(1-25%)
=10%*0.75
=0.075
Weight of equity=60/80
=0.75
Weight of debt=20/80
=0.25
Weighted average cost of capital=12%*0.75+0.075*0.25
=0.09+0.01875
=0.10875
=10.875%
Hence the weighted average cost of capital is 10.875%
Learn more about weighted average at https://brainly.com/question/18554478
#SPJ4
A cube has side length a. The side lengths are decreased to 50% of their original size. Write an expression in simplest form for the volume of the new cube in terms of a. An expression is .
Answer: (a * 50%)^3
Step-by-step explanation:
length = a
(a * 50%)^3
If a would've been the length and would've been decreased to 50%, the volume would be equal to that expression.
John needs 150 feet of rope to section off part of his barn. At a local hardware store he can buy a 30 yard spool for $24 or he can buy 150 foot at $.25 per foot. Which is the better buy?
Answer:
30 yards for 24 vs 1 foot for 25 cents
so lets multiple the yards by 3 to see how many feet
90 feet = 30 yards
90 feet 24 dollars
now lets divide 90 by 24
3.75 so 3.75 per foot
so the second one is way better
Hope This Helps!!!
Answer:
150 feet at $.25 per foot ($.75 per yard) is the better buy.
Step-by-step explanation:
150 feet is equal to 50 yards. So 2 30-yard spools would be $48. $48 for 60 yards equals $.80 per yard. So 150 feet at $.25 per foot ($.75 per yard) is the better buy.
Graph the given functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of the functions to obtain ordered pairs. Describe how the graph of g is related to the graph of f
Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.
How the graphs are related?
Here we have:
[tex]f(x) = \sqrt{x}[/tex]
first we want to evaluate it in x = 0, 1, 4, 9.
Doing that we get:
[tex]f(0) = \sqrt{0} = 0\\f(1) = \sqrt{1} = 1\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]
The other function is:
[tex]g(x) = \sqrt{x} -3[/tex]
Evaluating in the same values of x.
[tex]g(0) = \sqrt{0} -3 = -3\\g(1) = \sqrt{1} -3 = -2\\g(4) = \sqrt{4} -3 = -1\\g(9) = \sqrt{9} -3 = 0[/tex]
Then we can see that for all the values of x, g(x) is 3 units less than f(x).
Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.
If you want to learn more about translations:
https://brainly.com/question/24850937
#SPJ1
Alice and Dakota are packing gift boxes. Alice has already packed 21 additional boxes and is packing 8 additional boxes per hour. Dakota has already packed 28 additional boxes and is packing 6 additional boxes per hour. Which function can Alice and Dakota use to determine the total number of boxes they have packed after x hours? How many boxes will they have packed after 4 hours
when a relation is drawn on an xy-plane what is another name for the set of all x values from its graph
When a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.
What is a function?It should be noted that a function simply means an expression or rule that defines a relationship between variables.
In this case, when a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.
Learn more about graph on:
brainly.com/question/2855819
#SPJ1
PLEASE ANSWER ,Part I
In terms of the trigonometric ratios for ΔBCE, what is the length of CE? Insert text on the triangle in GeoGebra to show the length of CE. Take a screenshot of the triangle with the text, save it, and insert the image in the space below.
By applying the law of cosine, the length of side CE is equal to 9.22 cm and the image of right-angled triangle BCE is shown in the image attached below.
How to calculate the length of CE?In order to determine the length of side CE, we would apply the law of cosine because both side CE and side BC respectively represent the adjacent side and hypotenuse of right-angled triangle BCE.
cos(θ) = Adj/Hyp
Where:
Adj is the adjacent side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.Substituting the parameters into the formula, we have;
cos(θ) = CE/BC
cos(11.46) = CE/9.41
Cross-multiplying, we have:
CE = 9.41 × cos(11.46)
CE = 9.41 × 0.9801
CE = 9.22 cm.
By applying the law of cosine, the length of side CE is equal to 9.22 cm and the image of right-angled triangle BCE is shown in the image attached below.
Read more on law of cosine here: brainly.com/question/27613782
#SPJ1
identify the asymptotes and state the end behavior of the function f(x)=5x/x-25
Using it's concepts, it is found that for the function [tex]f(x) = \frac{5x}{x - 25}[/tex]:
The vertical asymptote of the function is x = 25.The horizontal asymptote is y = 5. Hence the end behavior is that [tex]y \rightarrow 5[/tex] when [tex]x \rightarrow \infty[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. They also give the end behavior of a function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex]
For the vertical asymptote, it is given by:
x - 25 = 0 -> x = 25.
The horizontal asymptote is given by:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5[/tex]
More can be learned about asymptotes at https://brainly.com/question/16948935
#SPJ1