Category: Mathematics

A particle moves along a straight line with its position at time ( t ) given by the equation ( s(t) = 3t3 – 12t2 + 9t + 5 ), where( s(t) ) is the position in meters and
( t ) is the time in seconds.
(a)Determine the velocity of the particle at any time ( t ). (5 marks)
(b) Find the acceleration of the particle at any time ( t ). (5 marks)
(c)At what time(s) is the particle at rest? (5 marks)
(d) Determine the total distance traveled by the particle during the first 4 seconds. (5 marks)

use excel worksheet to complete the homework questions. I have included the figures 9.3 and 9.4 as well as 9.17 and 9.18

**15. P2:**
a) Show that the solutions of the equation (x^2 – 6x – 43 = 0) can be written in the form (x = p pm frac{qsqrt{13}}{13}), where (p) and (q) are positive integers.
(4 points)
b) Based on the above or any other method, solve the inequality (x^2 – 6x – 43 le 0).
(2 points)
**16. P1:**
A function (f) is defined by (f(x) = 3(x-1)^2 – 18), (x in mathbb{R}).
a) Write (f(x)) in the form (ax^2 + bx + c), where (a), (b), and (c) are constants.
(2 points)
b) Find the coordinates of the vertex of the graph of (f).
(1 point)
c) Find the equation of the axis of symmetry of the graph of (f).
(1 point)
d) Indicate the range of (f).
(2 points)
e) The graph of (f) is translated by the vector (begin{pmatrix} 2 \ -1 end{pmatrix}) to form a new curve that represents a new function (g(x)).
Find (g(x)) in the form (px^2 + qx + r), where (p), (q), and (r) are constants.
(3 points)
**17. P1:**
a) Solve the equation (8x^2 + 6x – 5 = 0) by factorization.
(2 points)
b) Determine the range of values of (k) for which the equation (8x^2 + 6x – 5 = k) has no real solutions.
(3 points)
**18. P1:**
Consider the function (f(x) = -x^2 – 10x + 27), (x in mathbb{R}).
a) Show that the function (f) can be expressed in the form (f(x) = a(x-h)^2 + k), where (a), (h), and (k) are constants.
(3 points)
b) Based on the above, write the coordinates of the vertex of the graph of (y = f(x)).
(1 point)
c) Based on the above, write the equation of the axis of symmetry of the graph of (y = f(x)).
(1 point)
**19. P1:**
The quadratic curve (y = x^2 + bx + c) cuts the x-axis at ( (10, 0) ) and has the equation of the line of symmetry (x = frac{5}{2}).
a) Find the values of (b) and (c).
(4 points)
b) Based on the above, or any other method, find the other two coordinates where the curve intersects the y-axis.
(2 points)
**20. P1:**
Consider the function (f(x) = 2x^2 – 4x – 8), (x in mathbb{R}).
a) Show that the function (f) can be expressed in the form (f(x) = a(x-h)^2 + k), where (a), (h), and (k) are constants.
(3 points)
b) The function (f(x)) can be obtained through a sequence of transformations of (g(x) = x^2). Describe each transformation in order.
(3 points)
**21. P1:**
Consider the equation (f(x) = 2kx^2 + 6x + k), (x in mathbb{R}).
a) For the case where the equation (f(x) = 0) has two equal real roots, find the possible values of (k).
(4 points)
b) For the case where the equation of the axis of symmetry of the curve (y = f(x)) is (x + 1 = 0), find the value of (k).
(2 points)
c) Solve the equation (f(x) = 0) when (k = 2).
(3 points)
**22. P1:**
A curve (y = f(x)) passes through the points with coordinates (A(-12, 10)), (B(0, -16)), (C(2, 9)), and (D(14, -10)).
a) Write the coordinates of each point after the curve has been transformed by (f(x) rightarrow f(2x)).
(4 points)
b) Write the coordinates of each point after the curve has been transformed by (f(x) rightarrow f(-x) + 3).
The homework is in Spanish I’m going to download the picture for you but this is the translation.

solve three questions and give explanation in each question. Afterthat,I want you to give me a script for each question as paragraph regarding what we did from first to end.

Scenario You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report: Are housing prices in your regional market lower than the national market average? Is the square footage for homes in your region different than the average square footage for homes in the national market? For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market? You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below. Directions Introduction Region: Start by picking one region from the following list of regions: West South Central, West North Central, East South Central, East North Central, Mid Atlantic Purpose: What is the purpose of your analysis? Sample: Define your sample. Take a random sample of 500 house sales for your region. Describe what is included in your sample (i.e., states, region, years or months). Questions and type of test: For your selected sample, define two hypothesis questions (see the Scenario above) and the appropriate type of test for each. Address the following for each hypothesis: Describe the population parameter for the variable you are analyzing. Describe your hypothesis in your own words. Identify the hypothesis test you will use (1-Tail or 2-Tail). Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem. 1-Tail Test Hypothesis: Define your hypothesis. Define the population parameter. Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter. Specify your significance level. Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test. Provide at least one histogram of your sample data. In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel: =QUARTILE([data range], [quartile number]) Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric. Check the conditions. Determine if the normal condition has been met. Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods. Hypothesis test calculations: Complete hypothesis test calculations. Calculate the hypothesis statistics. Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean. Calculate the probability (p value). Note: This calculation is done with the T.DIST function in Excel: =T.DIST([test statistic], [degree of freedom], True) The degree of freedom is calculated by subtracting 1 from your sample size. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis. Relate the p value and significance level. Make the correct decision (reject or fail to reject). Provide a conclusion in the context of your hypothesis. 2-Tail Test Hypotheses: Define your hypothesis. Define the population parameter. Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter. State your significance level. Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test. Provide at least one histogram of your sample data. In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel: =QUARTILE([data range], [quartile number]) Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note: For shape, think about the distribution: skewed or symmetric. Check the assumptions. Determine if the normal condition has been met. Determine if there are any other conditions that should be checked on and whether they have been met. Note: Think about the central limit theorem and sampling methods. Hypothesis test calculations: Complete hypothesis test calculations. Calculate the hypothesis statistics. Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.] Determine the probability (p value). Note: This calculation is done with the TDIST.2T function in Excel: =T.DIST.2T([test statistic], [degree of freedom]) The degree of freedom is calculated by subtracting 1 from your sample size. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis. Compare the p value and significance level. Make the correct decision (reject or fail to reject). Provide a conclusion in the context of your hypothesis. Comparison of the test results: Revisit Question 3 from the Scenario section: For your region, what is the range of values for the 95% confidence interval of square footage for homes? Calculate and report the 95% confidence interval. Show or describe your method of calculation. Final Conclusions Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language. Discuss: Discuss whether you were surprised by the findings. Why or why not?

The SECOND change is to save up or get a loan to renovate the backyard. Outline the changes that would need to be made in their budget. You are expected to demonstrate your understanding of Trigonometry (trig ratios, sine law, cosine law, etc) and Geometry (area of 2D composite shapes with the measurements, surface area and volume of a composite 3D figure consisting of a cylinder, triangular prism and a rectangular prism) to build or design their new renovated backyard. The THIRD change will be to ensure that the family has a retirement plan that will work. Research and prepare a retirement savings plan and suggest savings to ensure the plan will be met or exceeded. Include the types of savings (RRSP, Tax Free Savings Accounts, ….).

The SECOND change is to save up or get a loan to renovate the backyard. Outline the changes that would need to be made in their budget. You are expected to demonstrate your understanding of Trigonometry (trig ratios, sine law, cosine law, etc) and Geometry (area of 2D composite shapes with the measurements, surface area and volume of a composite 3D figure consisting of a cylinder, triangular prism and a rectangular prism) to build or design their new renovated backyard.
The THIRD change will be to ensure that the family has a retirement plan that will work. Research and prepare a retirement savings plan and suggest savings to ensure the plan will be met or exceeded. Include the types of savings (RRSP, Tax Free Savings Accounts, ….).

can you finish my desmos graphing project pls. I need around 150 more lines added, following this list: 5 linear functions (slope intercept form) ＝ mx+b 5 quadratic functions (vertex form) y ＝ a (x-p)2+4 3 Linear-Linear System. 3 linear inequality with shading y ˃mx+b: 3 quadratic inequality with shading y 2 a(x-p)2+q Additional suggestions: Linear- Quadratic System. Quadratic-Quadratic system. Linear absolute value functions Piecewise function Quadratic absolute value function Reciprocal functions (identify the equations for the vertical-asymptotes) Circles or ellipses functions. also shade the lips! Here is the link to the graph: https://www.desmos.com/calculator/omvnbiusdx

can you finish my desmos graphing project pls. I need around 150 more lines added, following this list: 5 linear functions (slope intercept form) ＝ mx+b 5 quadratic functions (vertex form) y ＝ a (x-p)2+4 3 Linear-Linear System. 3 linear inequality with shading y ˃mx+b: 3 quadratic inequality with shading y 2 a(x-p)2+q Additional suggestions: Linear- Quadratic System. Quadratic-Quadratic system. Linear absolute value functions Piecewise function Quadratic absolute value function Reciprocal functions (identify the equations for the vertical-asymptotes) Circles or ellipses functions. also make sure to include shading on the lips! Here is the link to the graph: https://www.desmos.com/calculator/omvnbiusdx

Hello, thank you for taking this task! Please read the instructions, create an excel, and use Solver to solve the problem and by possibility, if you can take a video of going thru it (no voiceover needed).
If this can be done by today (Sunday, 6/16/2024), I would GREATLY appreciate it. But if not, it’s totally okay!
Thank you very much!