Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.
Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.
This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.
To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.
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suppose the probability of finding a prize in your cereal box is 0.990.99. what are the odds of finding a prize? express your answer in the form a:ba:b.
If you assume that there is a 0.990.99 percent chance that you will find a prize in the cereal box, the odds are 99:1.
In mathematics, what does fundamental probability mean?A probability is a measure of how likely or likely it is that a certain event will occur. Probabilities can be represented as percentages between 0% and 100% as well as proportions between 0 and 1.
Probability's significanceHow likely an event is to occur is determined by the concept of probability. For instance, meteorologists can predict the possibility of rain by looking at weather patterns. In epidemiology, probability theory is used to understand the relationship between exposures as well as the risk of health effects.
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The semicircular disk having a mass of 10 kg is rotating at ω = 4 r a d / s \omega = 4 rad/s ω=4rad/s at the instant θ = 60 ° \theta = 60° θ=60°.
The f< [tex]f_{max}[/tex] the semicircular disk does not slip at the given instant.
The semicircular disk having a mass of 10 kg.
ω = 4 rad/s, θ = 60 °
First we have to draw the free body diagram,
Calculate the distance AG.
[tex]$$\begin{aligned}A G & =\sqrt{O G^2+O A^2-2 \times O G \times O A \times \cos \theta} \\& =\sqrt{\left(\frac{4 \times 0.4}{3 \pi}\right)^2+0.4^2-2 \times \frac{4 \times 0.4}{3 \pi} \times 0.4 \times \cos 60^{\circ}} \\\end{aligned}$$[/tex]
=0.3477 m.
Calculate the angle ∝.
[tex]$$\begin{aligned}& \frac{\sin \alpha}{O G}=\frac{\sin 60^{\circ}}{0.3477} \\& \alpha=25.01^{\circ}\end{aligned}$$[/tex]
Calculate the normal acceleration at A.
[tex]$$\begin{aligned}a_{A, y} & =\omega^2\left(r_{A O}\right) \\& =4^2 \times 0.4 \\& =6.4 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]
Calculate the acceleration at G.
[tex]& \mathbf{a}_G=\mathbf{a}_A+\boldsymbol{\alpha} \times r_{G / A}-\omega^2\left(\mathbf{r}_{G / A}\right) \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}a_{A, x} \mathbf{i}+a_{A,} \mathbf{j}+\alpha \mathbf{k} \times A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j}) \\-\omega^2[A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j})]\end{array}\right\} \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}0+6.4 \mathbf{j}+\alpha \mathbf{k} \times 0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j}) \\-4^2[0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j})]\end{array}\right\} \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=(0.3151 \alpha-2.352) \mathbf{i}+(0.147 \alpha-1.3584) \mathbf{j}\end{aligned}$$[/tex]
Equate i coefficient:
[tex]-a_{G, x}=0.3151 \alpha-2.352[/tex][tex]-a_{G, x}=0.3151 \alpha-2.352[/tex]
Equate j coefficient:
[tex]$$-a_{G, y}=0.147 \alpha-1.3584$$[/tex]
The free body diagram and the kinematic diagram of the semicircular disk is as follows:
Calculate the mass moment of inertia of the semicircular disk about point O.
[tex]$$\begin{aligned}I_0 & =\frac{1}{2}\left(\frac{1}{2} m r^2\right) \\& =\frac{1}{2}\left(\frac{1}{2} \times 10 \times 0.4^2\right) \\& =0.4 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$[/tex]
Calculate the mass moment of inertia of the semicircular disk about point G.
[tex]$$\begin{aligned}I_G & =I_0-m(O G)^2 \\& =0.4-10\left(\frac{4 \times 0.4}{3 \pi}\right)^2 \\& =0.1118 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$\\[/tex]
Consider moment equilibrium condition about point A.
[tex]$$\begin{aligned}& \sum M_A=I_G \alpha+\sum m a_G d \\& m g(A G \sin \beta)=I_G \alpha+m a_{G, x}(A G \cos \beta)+m a_{G, y}(A G \sin \beta) \\& 10 \times 9.81\left(0.3477 \times \sin 25.01^{\circ}\right)=\left\{\begin{array}{l}0.1118 \alpha+10 a_{G, x}\left(0.3477 \cos 25.01^{\circ}\right) \\+10 a_{G, y}\left(0.3477 \sin 25.01^{\circ}\right)\end{array}\right\} \\& 0.118 \alpha+3.151 a_{G, x}+1.47 a_{G, y}=14.42\end{aligned}$$[/tex]
Solve the equations (1), (2), and (3), the values obtained are as follows:
[tex]$$\begin{aligned}& \alpha=18.04 \mathrm{rad} / \mathrm{s}^2 \\& a_{G, x}=3.333 \mathrm{~m} / \mathrm{s}^2 \\& a_{G, y}=1.294 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]
Consider the force equilibrium along the horizontal direction:
[tex]$$\begin{aligned}& \sum F_x=m a_{G, x} \\& f=m a_{G, x} \\& f=10 \times 3.33\end{aligned}$$[/tex]
f=33.33 N.
Consider the force equilibrium along the vertical direction:
[tex]$$\begin{aligned}& \sum F_y=m a_{G, y} \\& m g-N=m a_{G, y} \\& (10 \times 9.81)-N=10 \times 1.294 \\& N=85.16 \mathrm{~N}\end{aligned}$$[/tex]
Calculate the maximum frictional force at point A.
[tex]$$\begin{aligned}f_{\max } & =\mu_s N \\& =0.5 \times 85.16 \\f_{\max } & =42.58 \mathrm{~N}\end{aligned}$$[/tex]
Since, f< [tex]f_{max}[/tex]the semicircular disk does not slip at the given instant.
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Challenge A large university accepts 40% of the students who apply. Of the students the university accepts, 50% actually
enroll. If 30,000 students apply, how many actually enroll?
students would actually enroll.
Help me please
Answer: 6000 students
Step-by-step explanation:
First, we find the 40% that the university accept
40% = 0.4
Take 30000 times 0.4 = 12000 students got accept
Now we find the 50%
50% = 0.5
Take 12000 times 0.5 = 6000 students
6000 students would actually enroll
2. It take one Super Giant Pizza to feed 3 people. If you invite 36 people, how many pizza will you need?
Answer:
12
Step-by-step explanation:
1 -----> 3
?------>36
By make Cross
36*1/3 =12
Antonio's dad bought gas for their family's ATV two weeks in a row. Last week, he bought 12 gallons for $35.40. This week, he bought 9 gallons for $25.83. How much more did Antonio's dad pay per gallon last week?
$
per gallon
Answer: $0.08
Step-by-step explanation:
First, let's find last week's price
Take 35.40 divided by 12 = $2.95 per gallon
Next, find this week's price
Take 25.83 divided by 9 = $2.87 per gallon
Then take 2.95 - 2.87 = $0.08
The um of two number i 92. Their difference i 20. Find the number. Let x and y repreent the 2 number. Let x=the lager value and urge maller value
The sum of two number is 92. Their difference i 20Let x and y represent the 2 number. Let x=the lager value and smaller valuex = 92 + 20 = 11,y = 92 - 20 = 72
Let x = the larger value and y = the smaller value.
We know that the sum of x and y is 92, so
x + y = 92
We also know that the difference between x and y is 20, so
x - y = 20
Add the two equations to get
2x = 112
Divide by 2 to get
x = 112
Substitute x = 112 into the first equation to get
112 + y = 92
Subtract 112 from both sides to get
y = 72
Therefore, the two numbers are x = 112 and y = 72.
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A preschool has 100 feet of fencing to enclose 3 sides of a rectangular playground. The fourth side is formed by a wall of the school. The function A(x) = 100x − 2x2 represents the possible area of the playground with side length x feet. Which range is appropriate for this situation?
Answer:
This answer assumes that the function is A(x) = 100x − 2x^2. The function as written is A(x) = 100x - (4 or 4x)
The domain is 0 - 50 feet.
Step-by-step explanation:
The area function is a polynomial with a vertex (hghest area possible) at (25,1250). This is telling us that for a side length of 25 feet, the area is at a maximum of 1250 ft^2. This is actually not totally correct. We only need 3 sides of fencing since the school wall will make up the fourth. The given equation does not seem to allow for this caveat, since it uses 100 feet for all four sides.
Given the equation, the domain for the function A(x) is positive for all values between 0 and 50 feet. The domain is 0 - 50 feet.
Describe the transformation of f(x)=x^5 represented by g(x) = (x − 2)³—1
The graph of g is a translation 2 (blank) units and 1 unit (blank)
of the graph of f
Identify the graph of g.
The transformation from the parent function is a translation by 2 units right and 1 unit up
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x³
g(x) = (x − 2)³ - 1
First, we have the transformation to be:
From f(x) = x³ to f'(x) = (x − 2)³
This means the function is translated right by 2 units
Next, we have:
From f'(x) = (x − 2)³ to g(x) = (x − 2)³- 1
This means the function is translated up by 1 unit
Hence, the transformation is 2 units right and 1 unit up
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Please help me with this
a) The equation is y = 4/x².
b) The value of x is 2/9 when y = 25.
What is relationship?
The relation in mathematics is the connection between two or more sets of values. Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.
Given table is
x 1 2 3 4
y 4 1 4/9 1/4.
Given that y is inversely proportional to the square of x.
y∝ 1/x²
y = k/x² where k is proportional constant.
Putting x = 1 and y = 4 in equation y = k/x²:
4 = k/1²
k = 4
Putting x = 2 and y = 1 in equation y = k/x²:
1 = k/2²
k = 4
Putting k = 4 in y = k/x²:
y = 4/x²
Putting y = 25 in y = 4/x²
25 = 4/x²
25x² = 4
Divide both sides by 25:
x² = 4/25
Take square root on both sides:
x = 2/5
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What is the actual length of the wings of thethe airplane from tip to tip?
Answer:
68cm
Step-by-step explanation:
Because the scale factor is 2, which means the drawing is 2 times smaller than the actual airplane, multiply 34, the length of the wings tip to tip in the drawing by 2.
34 x 2 = 68
Answer: 68 meters
(Hope I'm correct, but read the explanation to make sure)
Step-by-step explanation:
Let's start with what we know. We know that the scale factor is 2, so in our model, from tip to tip, it is 34 cm. However, since the scale factor is 2:
34 * 2 = 68 meters
someone help me i hate log functions
Answer:
Step-by-step explanation:
[tex]log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4[/tex]
[tex]log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1[/tex]
[tex]log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0[/tex]
A construction company is building a roof on a house. The horizontal distance from the edge of the
roof to the peak is 25 feet. The vertical distance from the edge of the roof to the peak is 6.25 feet. What is the slope of
the roof? Write in the simplest form.
The slope of the roof is 0.25
What is a slope ?
A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).
To find slope
= 6.25 / 25
= 0.25
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A tree, which i approximately 80% of it full height, i preently 60 feet tall. How tall will the tree be when it i fully grown?
The tree will be 75 feet tall when it will be fully grown.
The total tree height is the distance between the tree's base and its highest point on the ground. A yardstick provides a quick and relatively accurate way to gauge the height of a tree.
If the tree is currently 60 feet tall and is approximately 80% of its full height, we can assume that the tree will be 100% of its full height when it is fully grown. To determine the full height of the tree, we can use the proportion:
60 feet / 80% = X feet / 100%
We can then cross-multiply to solve for X:
X = (60 feet * 100%) / 80%
= 75 feet
So, when the tree is fully grown, it will be approximately 75 feet tall.
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HELP ME PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!
In the first circle, the measure of angle ABC is 24°
In the second circle, the measure of angle ABC is 20°
Circle Geometry: Calculating the measure of anglesFrom the question, we are to determine the measure of angle ABC
In the first diagram,
The measure of the arc is 48°
From one of the circle theorems, we have that
The angle subtended by an arc in a circle is twice the angle subtended at the circumference.
Then, we can write that
2 × ∠ ABC = 48°
∠ ABC = 48°/2
∠ ABC = 24°
Question 5
Using the same theorem,
The angle subtended by an arc at the center of the circle is twice the angle subtended at the circle
∠ ABC = 1/2 × 40°
∠ ABC = 20°
Hence, the measure of the angle is 20°
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HELP WILL MARK BRAINLIEST
The measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, center of dilation is P and scale factor is 1/3.
In the given triangle ABC, AB=12.4 units, AC=6.7 units and BC=12.7 units
Now, A'B'=12.4/3
A'B'= 4.1 units
A'C'=6.7/3
A'C'= 2.2 units
B'C'=12.7/3
B'C'= 4.2 units
Therefore, the measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
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What value of x is in the solution set of the inequality 9(2x 1) < 9x – 18? –4 –3 –2 –1
The value of x in the solution set of the inequality is -4.
What are inequalities?Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.
How to solve inequalities?We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).
9(2x+1) < 9x - 18
2x+1 < x - 2
2x < x - 3
x < -3
This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.
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Answer:
-4
Step-by-step explanation:
taking test
5b. State the domain and range for each graph below. Then state whether or not it is a function.
The area of a rectangle i 42 quare millimeter. The length i 7 millimeter. What i the perimeter of the rectangle?
millimeter
The area of a rectangle is 42 quare millimeter. The length is 7 millimeter. 28 millimeters is the perimeter of the rectangle.
Perimeter = 2 × (Length + Width)
Perimeter = 2 × (7 + 6)
Perimeter = 28 millimeters
To calculate the perimeter of a rectangle, we need to multiply the length and the width of the rectangle, and then multiply that value by 2. In this case, the length is 7 millimeters, and the area is 42 square millimeters. To calculate the width, we can divide the area by the length, which is 42 divided by 7, which is equal to 6. So the width is 6 millimeters. Now we can calculate the perimeter using the formula: Perimeter = 2 × (Length + Width). Plugging in the values, we get: Perimeter = 2 × (7 + 6) = 28 millimeters.
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Determine the intercepts of the line. Do not round your answers.4x−1=3y+5. x intercept: (?,?), y intercept: (?,?)
Answer:
x intercept= (1.5,0)
y intercept= (0,-2)d
Step-by-step explanation:
Rearrange the equation to be in the form y=mx+c:
4x-1=3y+5
y=(4x-6)/3
y=4/3(x)-2
y intercept= c from equation above =-2
y intercept=-2
x intercept => when y=0
sub 0=y
0=4/3(x)-2
2=4/3(x)
x=1.5
Conider the following function. (If an anwer doe not exit, enter DNE. ) f(x) = e^−x2
The function has no vertical asymptotes and the horizontal asymptotes of the function is y=0.
In the given question,
Consider the following function.
f(x) = e^{−x^2}
We have to find the vertical asymptote(s), x = Find the horizontal asymptote(s) or y = .
As we know that, a vertical asymptote is a line that runs vertically and guides the graph of the function but does not actually exist on it. Due to its position at an x-value that is outside of function's domain, it is difficult for the curve to ever pass it.
The function f(x) = e^{−x^2} has no undefined points. So the function has no vertical asymptotes.
The limit of the function at x→±∞ is calculated as follows:
[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = [tex]\lim_{x\rightarrow \pm\infty }[/tex]e^{−x^2}
[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = 0
So the horizontal asymptotes of the function is y=0.
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The right question is:
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = e^{−x^2}. Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)
y =
The following is an example of what type of sequence? 3, 11, 19, 27, 35… a. geometric c. ratio b. arithmetic d. difference Please select the best answer from the choices provided A B C D
Answer:
b) arithmetic
Step-by-step explanation:
Knowledge Needed
c and d are not valid sequence types.
Geometric Sequences are when the values of terms are found by multiplying the previous term's value by the same number.
Example:
1, 2, 4, 8, 16
x2
2, 6, 18, 54, 162
x3
20, 10, 5, 2.5, 1.25
x0.5
Arithmetic Sequences are when the values of terms are found by adding the previous term's value by the same number.
Example:
5, 6, 7, 8
+1
7, 19, 31, 43
+12
9, 6, 3, 0
-3
Question
Examine the sequence. From viewing the first 2 terms, we know that it can either be a geometric sequence that multiplies by 11/3 every time the term increases or an arithmetic sequence that adds 8 every time the term increases.
Looking at the 2nd and 3rd term, we know it is an arithmetic sequence because 19 is not equal to 11 times 11/3.
1 2/5m-3/5(2/3m+1) please help me
Answer:
m - 3/5 or m - 0.6-----------------------------------------
Simplify the expression:
1 2/5m - 3/5(2/3m + 1) = Convert mixed number to fraction 7/5m - 3/5(2/3)m - 3/5 = Distribute 7/5m - 2/5m - 3/5 = Simplify(7 - 2)/5m - 3/5 = Collect terms with m5/5m - 3/5 = Simplifym - 3/5 AnswerPlease help me respond this question
Answer: Median is 12, mode is 5, mean is 13.71
Step-by-step explanation:
Answer:
The median is 18
The mode is 5
The mean is 13
Step-by-step explanation:
Amy, Becky and Chloe went shopping.
Becky spent only 15% of what Chloe spent.
However, Amy spent 60% more than Chloe.
Together they spent £55.
How much did Amy spend?
Let's say Chloe spent X
Then Amy spent 60% more so Amy spent
X+60% of X =X + 0.6X =1.6X
Becky spent 15% of what Chloe spent so amount spent by Becky =15% of X = .15X
Now, in total, they spent 0.15X+ X + 1.6X =2.75X which is given as £55
So , X=55/2.75 = 20
Amount spent by Amy = 1.6X = 1.6 *20 =£32
A company began construction of a new manufacturing plant. The plant was completed on october 31, 2024. Expenditures on the project were as follows ($ in millions): on july 1, 2023, the company obtained a $76 million construction loan with a 9% interest rate. The loan was outstanding through the end of october, 2024. The company's only other interest-bearing debt was a long-term note for $100 million with an interest rate of 11%. This note was outstanding during all of 2023 and 2024. The company's fiscal year-end is december 31
The interest amount that will be capitalized is $4.04 million.
What is the interest amount that will be capitalized?The entire cost to purchase a good or service is referred to as an expense. A $30 million piece of equipment with a six-year useful life, for instance, is considered a capital expenditure. An expense is something that calls for the transfer of funds, or fortune in general, from one person or group to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students.
The following can be deduced from the information:
Average Expenditure for 2023
= 78 million* 6/6 month + 46 million ** 3/6 month
= 101 million
Amount of interest that should capitalized in 2023 using a specific interest method
= Average expenditure for 2023 * interest rate *6/12 month
= $101 million * 8% * 6/12
= $4.04 million
The interest amount is $4.04 million.
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Find the value of z such that 0.12 of the area lies to the right of z. Round your answer to two decimal places.
Answer:
Step-by-step explanation:
To find the value of z such that 0.12 of the area lies to the right of z, we need to know the distribution of the data and the total area under the curve. If the data follows a normal distribution, the area under the curve is always 1, and 0.12 of the area corresponds to a z-value of approximately 0.84.
We can use a standard normal table or a calculator to find the exact value of z. For example, using a standard normal table, we can find that the z-value corresponding to an area of 0.12 to the right of z is 0.8416.
Therefore, the value of z such that 0.12 of the area lies to the right of z is approximately 0.84.
Michael’s skateboard was 1 toy out of 50 that Santa had on his sleigh. What percentage is this?
Answer: 18
Step-by-step explanation:
there you go <3
Select all the expression that are equivalent to 8^-6 x 8^-5
Answer:
f(x)=3x+4 and g(x)=2x3
find.
a:fg(x)
b:gf(x)
3 DECENT & QUICK MATH QS! PRATICALLY FREE 35 POINTS! HURRY PLS!!
The real and imaginary parts of the three complex numbers are:
Real part: - 7, Imaginary part: 0Real part: 5, Imaginary part: 2√6Real part: 37, Imaginary part: 0How to determine the real and imaginary component of a complex number.
In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:
Case 1: - 7
The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.
Case 2: 5 - √(- 24)
First, we rewrite the entire expression in standard form:
5 - √(- 24)
5 - √[(- 1) · 24]
5 - √(- 1) · √24
5 - i √24
5 - i 2√6
The real part is 5 and the imaginary part is 2√6.
Case 3: (6 - i) · (6 + i)
We expand and simplify the resulting expression:
(6 - i) · (6 + i)
6 · (6 - i) + i · (6 - i)
36 - i 6 + i 6 - i²
(36 - i²)
36 + 1
37
37 + i 0
The real part is 37 and the imaginary part is 0.
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Answer:
The real and imaginary parts of the three complex numbers are:Real part: - 7, Imaginary part: 0Real part: 5, Imaginary part: 2√6Real part: 37, Imaginary part: 0How to determine the real and imaginary component of a complex number.In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:Case 1: - 7The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.Case 2: 5 - √(- 24)First, we rewrite the entire expression in standard form:5 - √(- 24)5 - √[(- 1) · 24]5 - √(- 1) · √245 - i √245 - i 2√6The real part is 5 and the imaginary part is 2√6.Case 3: (6 - i) · (6 + i)We expand and simplify the resulting expression:(6 - i) · (6 + i)6 · (6 - i) + i · (6 - i)36 - i 6 + i 6 - i²(36 - i²) 36 + 137 37 + i 0The real part is 37 and the imaginary part is 0.
Step-by-step explanation: hope this helps0^0
Several friends bought flowers to make table centerpieces. Write the ratios of purple flowers to white flowers for each friend.
The ratio of purple flower to white flowers is 1:1 for each friend.
What do we mean by centerpiece?A system of arrangement where objects are set at the center position.
In another words the piece that kept in the center position.
As example, for the purpose of decorating a table with flowers, we need to keep the flowers in such a way that all the flowers occupy the center position.
Which ratio that we need to maintain while decorating a table as a centerpiece?If we want to display a table as centerpieces with white and purple flowers, we must keep the two flowers in the same ratio to look the display more attractive.
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