Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of Ax^2 + By^2 = C can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.

Question
Conic sections
asked 2021-02-13
Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of \(Ax^2 + By^2 = C\) can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.

Answers (1)

2021-02-14
Consider the equation, \(Ax^2 + By^2 = C\) When A and B both appear are on the same side and have coefficients with opposite sign, the equation is that of a hyperbola. So the equation of hyperbola is \(Ax^2 + By^2 = C\) When A and B both appear are on the same side and have coefficients with same sign, the equation is that of an ellipse. So the equation of ellipse is \(Ax^2 + By^2 = C\). When A and B terms both appear are on the same side and are equal, the equation is that of a circle. So the equation of circle is \(Ax^2 + By^2 = C\) Hence the statement “I noticed that depending on the values for A and B assuming that they are not both zero, the graph of \(Ax^2 + By^2 = C\) can represent any of the conic sections other than a parabola.” Make sense. Conclusion: The equation of parabola must have either \(x^2 or y^2\) term.
0

Relevant Questions

asked 2020-10-21
Determine whether the statement, 'I noticed that depending on the values for A and C, assuming that they are not both zero, the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represent any of the conic sections', makes sense or does not make sense, and explain your reasoning.
asked 2021-01-27
Determine whether statement, 'I’ve noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication'. makes sense or does not make sense, and explain your reasoning.
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.
asked 2020-10-23
Determine whether the statement "I’ve noticed that for sine, cosine, and tangent, the trig function for the sum of two angles is not equal to that trig function of the first angle plus that trig function of the second angle", makes sense or does not make sense, and explain your reasoning.
asked 2020-11-06
Determine whether the statement makes sense or does not make sense, and explain your reasoning : By modeling attitudes of college freshmen from 1969 through 2013, I can make precise predictions about the attitudes of the freshman class of 2040.
asked 2021-02-24
I’m solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables.Determine whether the statement makes sense or does not make sense, and explain your reasoning
asked 2021-03-12
When using the half-angle formulas for trigonometric functions of \(alpha/2\), I determine the sign based on the quadrant in which \(alpha\) lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
asked 2020-12-16
When using the half-angle formulas for trigonometric functions of \(\displaystyle\frac{\alpha}{{2}}\), I determine the sign based on the quadrant in which \(\displaystyle\alpha\) lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
asked 2021-02-11
Several models have been proposed to explain the diversification of life during geological periods. According to Benton (1997), The diversification of marine families in the past 600 million years (Myr) appears to have followed two or three logistic curves, with equilibrium levels that lasted for up to 200 Myr. In contrast, continental organisms clearly show an exponential pattern of diversification, and although it is not clear whether the empirical diversification patterns are real or are artifacts of a poor fossil record, the latter explanation seems unlikely. In this problem, we will investigate three models fordiversification. They are analogous to models for populationgrowth, however, the quantities involved have a differentinterpretation. We denote by N(t) the diversification function,which counts the number of taxa as a function of time, and by rthe intrinsic rate of diversification.
(a) (Exponential Model) This model is described by \(\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{e}}}{N}\ {\left({8.86}\right)}.\) Solve (8.86) with the initial condition N(0) at time 0, and show that \(\displaystyle{r}_{{{e}}}\) can be estimated from \(\displaystyle{r}_{{{e}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ {\left({8.87}\right)}\)
(b) (Logistic Growth) This model is described by \(\displaystyle{\frac{{{d}{N}}}{{{\left.{d}{t}\right.}}}}={r}_{{{l}}}{N}\ {\left({1}\ -\ {\frac{{{N}}}{{{K}}}}\right)}\ {\left({8.88}\right)}\) where K is the equilibrium value. Solve (8.88) with the initial condition N(0) at time 0, and show that \(\displaystyle{r}_{{{l}}}\) can be estimated from \(\displaystyle{r}_{{{l}}}={\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{K}\ -\ {N}{\left({0}\right)}}}{{{N}{\left({0}\right)}}}}\right]}\ +\ {\frac{{{1}}}{{{t}}}}\ {\ln{\ }}{\left[{\frac{{{N}{\left({t}\right)}}}{{{K}\ -\ {N}{\left({t}\right)}}}}\right]}\ {\left({8.89}\right)}\) for \(\displaystyle{N}{\left({t}\right)}\ {<}\ {K}.\)
(c) Assume that \(\displaystyle{N}{\left({0}\right)}={1}\) and \(\displaystyle{N}{\left({10}\right)}={1000}.\) Estimate \(\displaystyle{r}_{{{e}}}\) and \(\displaystyle{r}_{{{l}}}\) for both \(\displaystyle{K}={1001}\) and \(\displaystyle{K}={10000}.\)
(d) Use your answer in (c) to explain the following quote from Stanley (1979): There must be a general tendency for calculated values of \(\displaystyle{\left[{r}\right]}\) to represent underestimates of exponential rates,because some radiation will have followed distinctly sigmoid paths during the interval evaluated.
(e) Explain why the exponential model is a good approximation to the logistic model when \(\displaystyle\frac{{N}}{{K}}\) is small compared with 1.
asked 2020-12-24
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although \(20x^{3}\) appears in both \(20x^{3} + 8x^{2} and 20x^{3} + 10x\), I’ll need to factor \(20x^{3}\) in different ways to obtain each polynomial’s factorization?
...