# Check out the latest Post Secondary Math questions Parametric equations, polar coordinates, and vector-v ### to what property does (-6 + 3 ) + 1 = -6 + (3 + 1) belong to

Multivariable functions ### Write formulas for the indicated partial derivatives for the multivariable function. $$\displaystyle{f{{\left({x},{y}\right)}}}={7}{x}^{{2}}+{9}{x}{y}+{4}{y}^{{3}}$$ a)$$\displaystyle\frac{{\partial{f}}}{{\partial{x}}}$$ b)(delf)/(dely)ZSK c)$$\displaystyle\frac{{\partial{f}}}{{\partial{x}}}{\mid}_{{{y}={9}}}$$

Modeling data distributions ### a) To calculate: The least squares regression line for the data points using the table given below. \begin{array}{|c|c|} \hline Fertilizer & x & 100 & 150 & 200 & 250 \\ \hline Yield & y & 35 & 44 & 50 & 56 \\ \hline \end{array} b)To calculate: The approximate yield when 175 pounds of fertizers were used per acre of land.

Random variables ### A population of values has a normal distribution with $$\displaystyle\mu={133.5}$$ and $$\displaystyle\sigma={5.2}$$. You intend to draw a random sample of size $$\displaystyle{n}={230}$$. Find the probability that a single randomly selected value is between 133.6 and 134.1. $$\displaystyle{P}{\left({133.6}{<}{X}{<}{134.1}\right)}=$$? Write your answers as numbers accurate to 4 decimal places.

Laplace transform ### Determine $$L^{-1}\left[\frac{(s-4)e^{-3s}}{s^2-4s+5}\right]$$

Laplace transform ### Obtain the Laplace Transform of $$L\left\{e^{-2x}+4e^{-3x}\right\}$$ ### The simplified form of the expression$$\displaystyle{\sqrt[{{3}}]{{a}}}{\sqrt[{{6}}]{{a}}}\ \text{in radicalnotation is}\ \sqrt{a}.$$

Transformation properties ### For large value of n, and moderate values of the probabiliy of success p (roughly, $$0.05\ \Leftarrow\ p\ \Leftarrow\ 0.95$$), the binomial distribution can be approximated as a normal distribution with expectation mu = np and standard deviation $$\sigma = \sqrt{np(1\ -\ p)}$$. Explain this approximation making use the Central Limit Theorem.

Parametric equations, polar coordinates, and vector-valued functions ### Write a short paragraph explaining this statement. Use the following example and your answers Does the particle travel clockwise or anticlockwise around the circle? Find parametric equations if the particles moves in the opposite direction around the circle. The position of a particle is given by the parametric equations $$x = sin t, y = cos t$$ where 1 represents time. We know that the shape of the path of the particle is a circle.

Vectors and spaces ### Let $$\displaystyle{A}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{a}&{b}\backslash{c}&{d}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}$$ and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

Differential equations ### How to integrate $$\displaystyle{{\cos}^{{2}}{\left({2}{x}\right)}}$$?

Two-way tables ### Baseball star David Ortiz-nicknamed "Big Papi"-is known for his ability to deliver hits in high-pressure situations. Here is a two-way table of his hits, walks, and outs in all of his regular-season and post-season plate appearances from 1997 through 2014. Choose a plate appearance at random. Are the events "Hit" and "Post-season" independent? Justify your answer.

Green's, Stokes', and the divergence theorem ### Use Green's Theorem to evaluate the line integral $$\displaystyle\int_{{C}}{\left({y}+{e}^{{x}}\right)}{\left.{d}{x}\right.}+{\left({6}{x}+{\cos{{y}}}\right)}{\left.{d}{y}\right.}$$ where C is triangle with vertices (0,0),(0,2)and(2,2) oriented counterclockwise. a)6 b)10 c)14 d)4 e)8 f)12

Upper Level Math ### In one Tech region the number of students in Math 136 is 20% more than the number of students in Math 123. If there are 480 students in Maths 136, how many students are in Math 123?

Confidence intervals ### Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The differences (After - Before) in the reasoning scores have mean 3.618 and standard deviation 3.055.

Transformation properties ### Complete the tasks to determine: a)To graf: The function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}.$$ b)The domain of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}$$ in the interval notation. c)The range of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}$$ in the interval notation. d)The equation of the asymptote of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}.$$

Vectors and spaces ### Let the vector space $$P^{2}$$ have the inner product $$\langle p,q\rangle=\int_{-1}^{1} p(x)q(x)dx.$$ Find the following for $$p = 1\ and\ q = x^{2}.$$ $$(a) ⟨p,q⟩ (b) ∥p∥ (c) ∥q∥ (d) d(p,q)$$

Comparing two groups ### The mean + 1 sd of In [calcium intake (mg)] among 25 females, 12 to 14 years of age, below the poverty level is $$6.56 + 0.64.$$ Similarly, the mean + 1 sd of In [calcium intake (mg)] among 40 females, 12 to 14 years of age, above the poverty level is $$6.80 + 0.76.$$ 8.2 Test for a significant difference between the variances of the two groups. 8.3 What is the appropriate procedure to test for a signifi- cant difference in means between the two groups? 8.4 Implement the procedure in Problem 8.3 using the critical-value method. 8.5 What is the p-value corresponding to your answer to Problem 8.4? 8.6 Compute a $$95\%$$ Cl for the difference in means between the two groups.

Analyzing categorical data  