Answer:
Since we know the dot product of unit vectors, we can simplify the dot product formula to a⋅b=a1b1+a2b2+a3b3. we can use the same formula, but with a3=b3=0, a⋅b=a1b1+a2b2.
Step-by-step explanation:
hope it will help uplease mark me brillientDrag the tiles to the correct boxes to complete the pairs.
Match each subtraction of complex numbers to its simplified difference.
Here are the complex numbers with their simplified differences
(7 -3i) - (6 - 4i) = 1 + i
(4 + 3i) - (6 +2i) = -2 - i
(4 + 5i) - (3 - 4i) = 1 + 9i
(5 + 4i) - (9 + i) = -4 + 3i
A complex number is when a real number and an imaginary number are added together
Complex numbers are usually in the form : a + bi
where a and b are real numbers and i is an imaginary number
An example of a complex number:
in this complex number : (7 -3i)
7 and 3 are real numbers while i is the imaginary number
How to simplify complex numbers
In order to simplify these set of complex numbers, remember that when there is a bracket in mathematics it signifies multiplication.
Here are the set of rules that guide multiplication :
1. When a negative value is multiplied by a positive value, the value becomes a negative value
For example, -1 x 1 = -1
2. When a positive value is multiplied by a positive value, the value remains a positive value
For example, 1 x 1 = 1
3. When a negative value is multiplied by a negative value, the value becomes a negative value
For example,-1 x -1 = 1
Solution to the questions:
Using the above information, the complex numbers can now be simplified
1. (7 -3i) - (6 - 4i)
this above equation becomes :
7 - 3i - 6 + 4i
add like terms together
7 - 6 - 3i + 4i = 1 + i
2. (4 + 3i) - (6 +2i)
this above equation becomes :
4 + 3i - 6 - 2i
add like terms together
4 - 6 +3i - 2i = -2 - i
3. (4 + 5i) - (3 - 4i)
this above equation becomes :
4 + 5i - 3 + 4i
add like terms together
4 - 3 + 5i + 4i = 1 + 9i
4. (5 + 4i) - (9 + i)
this above equation becomes :
5 + 4i -9 -i
add like terms together
5 -9 + 4i - i = -4 + 3i
In order to solve for complex numbers remember that a bracket in mathematics means that a multiplication operation should be carried out. Also, pay cognisance to the rules guiding the multiplication of negative and positive numbers
Here is a similar question and answer on how to solve for complex numbers : https://brainly.com/question/1459664?referrer=searchResults
How to change unit from feet to cm
to change unit from feet to cm just divide the length value by 30.48......
find the value of trigonometric ratio
Answer:
8/17
Step-by-step explanation:
cosC = adjacent/hypotenuse = BC/AC = 8/17
Am I right? Please help me out
Answer:
[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]
Step-by-step explanation:
Given
[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]
Required
Determine [tex]\cos(\theta)[/tex]
We have:
[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]
Split
[tex]\tan(\theta) = -\frac{\sqrt{19}}{\sqrt{17}}[/tex]
tan is calculated as:
[tex]\tan(theta) = \frac{opposite}{adjacent}[/tex]
So:
[tex]Opposite = -\sqrt{19[/tex]
[tex]Adjacent = \sqrt{17[/tex]
And:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex] --- Pythagoras theorem
[tex]Hypotenuse^2 = (-\sqrt{19})^2 + (\sqrt{17})^2[/tex]
[tex]Hypotenuse^2 = 19 + 17[/tex]
[tex]Hypotenuse^2 = 36[/tex]
Take square roots
[tex]Hypotenuse = 6[/tex]
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(\theta) = \frac{\sqrt{17}}{6}[/tex]
Since it is in the second quadrant, then:
[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]
You have collected data about the average response time of participants in your study. You are delighted to find that the variable is normally distributed. More than half your respondents take longer than 16 seconds to respond and one third take less than 12 seconds to respond. What is the median response time of your participants
Answer:
15
Step-by-step explanation:
It's 15 because it would be the median (middle) between 16 and 12 if there was more variability in 16 seconds.
What is the slope-intercept equation of the line below?
Answer:
y=-5/4x+3
Step-by-step explanation:
y=mx+c
m = (y1-y2)/(x1-x2) =(-2-3)/(4-0) =-5/4
sub the values y=3, x=0 to find c,
3 =-5/4(0) + c
c = 3
what is the value of f'(6) if the formula is f(x)=-8x-3
Explanation:
Applying the derivative to f gets us
f(x) = -8x - 3
f ' (x) = -8
The fact that f(x) being linear directly means that the derivative is simply the slope value. No matter what we replace x with, the result is always -8.
Answer:
f'(6) = -8
Step-by-step explanation:
f(x)=-8x-3
First find the derivative of the function
f'(x) = -8
This is a constant so when x=6 it will be -8
f'(6) = -8
Give the domain and range of G={(6.0),(-9,-3),(1,-3)}
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Answer:
domain: {-9, 1, 6}range: {-3, 0}Step-by-step explanation:
The domain is the list of the first numbers of the ordered pairs. If there are any duplicates, the relation is not a function. Here, the first numbers are {6, -9, 1}. Most folks find it convenient to list them in numerical order:
{-9, 1, 6} . . . . domain of G
__
The range is the list of second numbers of the ordered pairs. Only the distinct values are reported. Here, the second numbers are {0, -3, -3}.
{-3, 0} . . . . range of G
What is the sum of the coefficients in the expression of 4x^4 - x^3 - 2x^2 + 3 - 4
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Answer:
0
Step-by-step explanation:
The coefficients are the numerical values that are not exponents. Their sum is ...
4 -1 -2 +3 -4 = 0
Can somebody help me
Answer:
The x interceprs are (-3,0) and (2,0)
Step-by-step explanation:
The reason is that when you plug in a -3 in the left parentheses it would become 0, and any number times 0 would be zero, making the equation equal to zero. The same would be true for the terms in the right parentheses, plugging in a two would make it equal to zero. This would make the entire equation equal to zero, finding you the x intercepts.
A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
Three children have some marbles.
Shireen has m marbles.
Nazaneen has three times as many marbles as Shireen.
Karly has 4 more marbles than Shireen.
(a) Write down an expression, in terms of m, for
(i) the number of marbles Nazaneen has,
Here we want to create algebraic expressions for different quantities.
i) Nazaneen has 3*m marbles.
ii) Karly has m + 4 marbles.
a) The given data is:
Shireen has m marbles.
Nazaneen has three times as many marbles as Shireen.
Knowing that Shireen has m marbles, we can conclude that Nazaneen has:
3*m marbles.
Karly has 4 more marbles than Shireen, then Karly has m + 4 marbles.
Then the equations for the number of marbles that each one has are:
Shireen = m
i) Nazaneen has 3*m marbles.
ii) Karly has m + 4 marbles.
If you want to learn more, you can read:
https://brainly.com/question/24327241
Find the missing ? Step by step need it
Answer:
30 degrees
Step-by-step explanation:
Use the Tan formula.
The distribution of sample means uses
to measure how much distance
is expected on average between a sample mean and the population mean.
re
o the standard error of M
none of these
the standard deviation of the sample
the standard deviation of the population
< Previous
Next
Answer:
A: the standard error of the mean
Step-by-step explanation:
The most frequently used measure to determine how much difference there is between population mean and sample mean is by calculating the standard deviation of the sampling distribution of the mean. This standard deviation is also referred to as the sew Station.
There is 60% chance of making $12,000, 10% chance of breaking even and 30% chance of losing $6,200. What is the expected value of the purchase?
Answer:
$5,340
Step-by-step explanation:
Given :
Making a probability distribution :
X : ___12000 ____0 _____-6200
P(X) __ 0.6 _____ 0.1 _____ 0.3
Tge expected value of the purchase si equal to the expected value or average, E(X) :
E(X) = ΣX*p(X)
E(X) = (12000 * 0.6) + (0 * 0.1) + (-6200 * 0.3)
E(X) = 7200 + 0 - 1860
E(X) = $5,340
HELP PLEASE!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t
Question:
Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.
The logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
-------------
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.-------------
The original function is:
[tex]y = f(x) = e^{0.4x}[/tex]
To find the inverse function, first, we exchange y and x, so:
[tex]e^{0.4y} = x[/tex]
Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]y = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
A similar question is given at https://brainly.com/question/24290183
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2).
A. (–2, 0)
B. (0, –2)
C. (5, –7)
D. (5, –2)
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Answer:
B. (0, –2)
Step-by-step explanation:
Put the (x, y) values into the given formula.
(x, y) ⇒ (x +5, y -2)
B(-5, 0) ⇒ B'(-5+5, 0-2) = B'(0, -2)
Kenneth needs $5,000 for university in 5 years. His parents plan to invest some money in an account paying interest at a rate of 7.2% per annum, compounded monthly. How much should they invest now to have $5,000 in 5 years.
Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
<
Prev
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]
The following operation is given:
[tex]R_1 \rightarrow -6R_2 + R_1[/tex]
In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.
Updating the first line:
[tex]R_{1,1} = -6*1 + 6 = 0[/tex]
[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]
[tex]R_{1,3} = -6*0 + 5 = 5[/tex]
Thus, the filled matrix will be given by:
[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]
For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657
square root of v-5=6
[tex] \sqrt{x - 5 = 6}[/tex]
Answer:
I think you mean this :
[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]
Or,
Square root of x-5=6 is :
[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]
Given FE=23.5, find BD.
Answer:
11.75
Step-by-step explanation:
The required triangle is attached below :
The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;
HENCE, The Length of the midsegment BD = 1/2FE
Hence, BD =. 1/2 * 23.5
BD = 23.5 / 2 = 11.75
Cahrlotte is 19/5 YEARS YONGER THAN RACHEL. 2 YEARS LATER, RACHEL WILL BE THRICE AS OLD AS CHARLOTTE. FIND THEIR AGES SFTER 3 YEARS. (ESTAMATE THE AGE TO THE NEAREST WHOLE NUMBER).
Answer:
Step-by-step explanation:
Charlotte starts at 19 years old.
Rachel starts at 24 years old.
Then two years later, Rachel is 26 and Charlotte is 21. This is not 3 times Charlotte's age.
Do you have all the right info?
A study is conducted to examine the correlation between Training Time and the Error Rate of employees. If the correlation coefficient of Training Time and Error Rate is -0.76, what is your conclusion?
(The answer is NOT B) HELP Please!!
A Moderate positive correlation
B Strong negative correlation
C No conclusion possible
D No correlation is shown
E Strong positive correlation
Answer:
No conclusion possible
Suppose the discrete random variable X has the probability distribution below:
X 0 1 2 3 4
P(X) 0.11 0.52 0.19 0.12 0.06
1pt a right parenthesis space F i n d space P left parenthesis X less than 3 right parenthesis
2pt b right parenthesis space F i n d space P left parenthesis X greater or equal than 1 right parenthesis
2pt c right parenthesis space F i n d space mu subscript X
2pt, 1pt d right parenthesis space F i n d space sigma subscript X squared space a n d space sigma subscript X
(a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.11 + 0.52 + 0.19 = 0.82
(b) P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.52 + 0.19 + 0.12 + 0.06 = 0.89
(c) µ = 0×0.11 + 1×0.52 + 2×0.19 + 3×0.12 + 4×0.06 = 1.5
(d) σ² = (0²×0.11 + 1²×0.52 + 2²×0.19 + 3²×0.12 + 4²×0.06) - µ² = 1.07
σ = √(σ²) ≈ 1.03
Wayne has a rectangular painting. The width of the painting is
5/6
of a foot, and the length is
3/4
of a foot. What is the area of the painting?
Answer:
5/8 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 5/6 * 3/4
A = 3/6 * 5/4
A = 1/2 * 5/4
A = 5/8 ft^2
(b) Two isosceles triangles PQR and PQS are drawn on opposite sides.
of a common base PQ. If PQR = 66° and PSQ = 109°, calculate
the value of RQS.
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Answer:
101.5°
Step-by-step explanation:
Angle PQS will be the complement of half of angle PSQ, so is ...
∠PQS = 90° -109/2° = 35.5°
Angle RQS is the sum of angles RQP and PQS:
∠RQS = 66° +35.5° = 101.5°
Help please if you know, thanks
Answer:
xsqrt(2)
Step-by-step explanation:
sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt(22x^6) / sqrt(11x^4)
sqrt(22x^6/11x^4)
sqrt(2x^2)
We know sqrt(ab) = sqrt(a) sqrt(b)
sqrt(x^2) sqrt(2)
xsqrt(2)
Nine Increased by the product of a number and 4 is greater than or equal to -15
Use the variable y for the unknown number
Answer:
9+4y ≥ -15
y ≥ -6
Step-by-step explanation:
Nine Increased by the product of a number
9+4y
is greater than or equal to -15
9+4y ≥ -15
Subtract 9 from each side
9-9+4y ≥ -15-9
4y ≥ -24
Divide by 4
4y/4 ≥ -24/4
y ≥ -6
What ordered pairs are the solutions of the system of equations shown in the graph below?
The solutions are where the two lines cross over each other.
(0,3) and (4,-5)
Fisk Corporation is trying to improve its inventory control system and has installed an online computer at its retail stores. Fisk anticipates sales of 84,500 units per year, an ordering cost of $12 per order, and carrying costs of $1.20 per unit.
Required:
a.What is the economic ordering quantity?
b. How many orders will be placed during the year?
c. What will the average inventory be?
d. What is the total cost of ordering and carrying inventory?
Answer: A) Economic ordering quantity ==$1,300
B)Orders placed during the year= 65 orders
C)average inventory= 650units
D)total cost of ordering and carrying inventory= $1,560
Step-by-step explanation:
A) Economic ordering quantity =[tex]\sqrt{2 x Annual demand x ordering cost /carrying cost}[/tex]
=[tex]\sqrt{2 x 84,500 x 12} /1.20[/tex]
=[tex]\sqrt{1,690,000}[/tex]
=$1,300
B)Orders placed during the year= Annual demand ÷ economic order quantity
= $84,500 ÷ 1,300 units
= 65 orders
C)average inventory= Economic order quantity ÷ 2
= 1,300 units ÷ 2
=650units
D)total cost of ordering and carrying inventory
Ordering cost = Number of orders × ordering cost per order
= 65 orders × $12
= $780
Carrying cost = average inventory × carrying cost per unit
= 650 units × $1.20
= $780
The total would be = $780 + $780 = $1,560
