A vector is first rotated by displaystyle{90}^{circ} along x-axis and then scaled up by 5 times is equal to displaystyle{left({15},-{10},{20}right)}. What was the original vector

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asked 2020-11-01

Given f(x)=6x+5, describe how the graph of g compares with the graph of f. g(x)=6(0.2x)+5
Select the correct choice below, and fill in the answer box to complete your choice.
A. The graph of g(x) is translated _ unit(s) to the left compared to the graph of f(x).
B. The graph of g(x) is translated _ unit(s) down compared to graph of f(x).
C. g(x) has a scale factor of _ compared to f(x). Because it scales the vertical direction, the graph is stretched vertically.
D. g(x) has a scale factor of _ compared to f(x). Because it scales the vertical direction, the graph is compressed vertically.
E. g(x) has a scale factor of _ compared to f(x). Because it scales the horizontal direction, the graph is stretched horizontally.
F. g(x) has a scale factor of _ compared to f(x). Because it scales the horizontal direction, the graph is compressed horizontally.
G. The graph of g(x) is translated _ unit(s) to the right compared to the graph of f(x).
H. The graph of g(x) is translated _ unit(s) up compared to graph of f(x).

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asked 2021-03-11

An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by
\(\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.\)
\(\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)
(A) Complete the table below.
\(\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)
(Round to one decimal place as needed.)
\(A. 20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.
\(B. 20602060xf(x)\)
Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.
Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.
\(C. 20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.
\(D.20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.
(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29
\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) and for 35
\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)
The mileage for the tire pressure \(\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) is
The mileage for the tire pressure \(\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}\) in. is
(Round to two decimal places as needed.)
(D) Write a brief description of the relationship between tire pressure and mileage.
A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.
B. As tire pressure increases, mileage decreases.
C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.
D. As tire pressure increases, mileage increases.

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asked 2020-12-27

Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a vertical, hollow, metal cylinder with a thin wire, insulated from the cylinder, running along its axis. A large potential difference is established between the wire and the outer cylinder, with the wire at lower potential. This sets up a strong radial electric field directed inward. The field produces a region of ionized air near the wire. Smoke enters the precipitation at the bottom, ash and dust in it pick up electrons, and the charged pollutants are accelerated toward the outer cylinder wall by the electric field. Suppose the radius of the central wire is 90.0 u(m,the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kG is established between the wire and the cylinder. Also assume that the wire and cylinder are both very long in comparison to the cylinder radius.
(a) What is the magnitude of the electric field midway between the wire and the cylinder wall? (V/m)
(b) What magnitude of charge must a 30.0 u(gas particle have if the electric field computed in part (a) is to exert a force ten times the weight of the particle? (c)

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asked 2020-11-09

Two scatterplots are shown below.
Scatterplot 1
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 60) up and right to approximately (95, 85).
The points are somewhat scattered.
Scatterplot 2
A scatterplot has 10 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 55) steeply up and right to approximately (70, 90), and then steeply down and right to approximately (85, 60).
The points are somewhat scattered.
Explain why it makes sense to use the least-squares line to summarize the relationship between x and y for one of these data sets but not the other.
Scatterplot 1 seems to show a relationship between x and y, while Scatterplot 2 shows a relationship between the two variables. So it makes sense to use the least squares line to summarize the relationship between x and y for the data set in , but not for the data set in .

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asked 2020-11-30

Find the dimensions of the reduction.
To place a picture in his class newsletter, Joaquin must reduce the picture by a scale factor of 0.3 . Find the dimensions of the reduced picture if the origin is 15 centimeters wide and 10 centimeters high.

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asked 2020-11-12

Finance bonds/dividends/loans exercises, need help or formulas
Some of the exercises, calculating the Ri is clear, but then i got stuck:
A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?
A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?
At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.
What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€
You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.

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asked 2020-10-21

Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or \(\displaystyle{90}^{{\circ}}\). u = (-1, -1, 8, 0), v = (5,6,1,4)

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asked 2020-11-07

Prove that \(\displaystyle{T}{\left({x},{y}\right)}={\left({3}{x}+{y},{2}{y},{x}-{y}\right)}\) defines a linear transformation \(\displaystyle{T}:\mathbb{R}^{2}\to\mathbb{R}^{3}\). Give the full and correct answer.

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asked 2020-10-23

The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P \((A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).\)
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.

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asked 2021-02-19

(a) The new coordinates geometrically if X represents the point \((0,\ \sqrt{2})\) m and this
point is rotated about the origin \(45^{\circ}\) clockwise and then translated 2 units to the right and 3 units upward.
(b) The value of \(Y = ABX,\) and explain the result.
(c) If ABX equal to BAX. Interpret the resul.
(d) A matrix that translate Y back to X

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Answer 1

Let us consider the vector (x, y, z).
The vector is first rotated by \(\displaystyle{90}^{\circ}\) along x - axis and then scaled up by 5 times.
Ratation: In homogeneous coordinates, the matrix for a rotetion about the origin through a given angle \(\displaystyle\theta\ {i}{s}\ {B}={\left[\begin{matrix} \cos{\theta}&- \sin{\theta}&{0}\\ \sin{\theta}& \cos{\theta}&{0}\\{0}&{0}&{1}\end{matrix}\right]}\)
The vector (x, y, z) is rotated by \(\displaystyle{90}^{\circ}\) along x-axis then the vector becomes
\(\displaystyle{\left[\begin{matrix}{ \cos{{90}}^{\circ}-}{ \sin{{90}}^{\circ}{0}}\\{ \sin{{90}}^{\circ} \cos{{90}}^{\circ}}\\{0}{0}{1}\end{matrix}\right]}{\left[\begin{matrix}{x}\\{y}\\{z}\end{matrix}\right]}\)
\(\displaystyle={\left[\begin{matrix}{0}-{1}{0}\\{1}{0}{0}\\{0}{0}{1}\end{matrix}\right]}{\left[\begin{matrix}{x}\\{y}\\{z}\end{matrix}\right]}\)
\(\displaystyle={\left[\begin{matrix}-{y}\\{x}\\{z}\end{matrix}\right]}\)
Now, the vector is scaled up by 5 times.
Scaling: In homogeneous coordinates, a scaling about the origin with scale factors c in the x-direction and c in the y-direction is computed by multiplying the vector by the matrix
\(\displaystyle{A}={\left[\begin{matrix}{c}{0}{0}\\{0}{c}{0}\\{0}{0}{1}\end{matrix}\right]}\)
Thus, the vector becomes
\(\displaystyle{\left[\begin{matrix}{5}{0}{0}\\{0}{5}{0}\\{0}{0}{1}\end{matrix}\right]}{\left[\begin{matrix}{x}\\{y}\\{z}\end{matrix}\right]}\)
\(\displaystyle={\left[\begin{matrix}-{5}{y}\\{5}{x}\\{z}\end{matrix}\right]}\)
Now, given that the reduced vector is \(\displaystyle{\left({15},-{10},{20}\right)}\). Therefore, we have
\(\displaystyle{\left[\begin{matrix}-{5}{y}\\{5}{x}\\{z}\end{matrix}\right]}={\left[\begin{matrix}{15}\\-{10}\\{20}\end{matrix}\right]}\)
By the equality of two matrices we have
\(\displaystyle{\left\lbrace\begin{matrix}-{5}{y}={15}\\{5}{x}=-{10}\\{z}={20}\end{matrix}\right.}={\left\lbrace\begin{matrix}{y}=-{3}\\{x}=-{2}\\{z}={20}\end{matrix}\right.}\)
Thus, the original vector is (-2, -3, 20)

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A vector is first rotated by displaystyle{90}^{circ} along x-axis and then scaled up by 5 times is equal to displaystyle{left({15},-{10},{20}right)}. What was the original vector

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