The following topics related to irrational numbers are appropriate for either individual or group research projects. A report should be given to the class on the researched topic. The Golden Rectangle in Art and Architecture

Consider the following problem.

One number is 3 less than 6 times a second number. Their sum is 46. Find the numbers.

If x represents the second number, which equation is correct for solving this problem?

A. $46-(x+3)=6x$

B. $(3-6x)+x=46$

C. $46-(3-6x)=x$

D. $(6x-3)+x=46$

Find the critical value(s) and rejection region(s) for the type of z-test with level of significance

$$\alpha$$

. Include a graph with your answer. Right-tailed test,

$$\alpha = 0.025$$

A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

Rodrlgo and Juan are constructing a model of the mirror grid In the solar wind concentrator used during the Genesis space mission to collect charged solar particles. They know that a cross section of the mirror grid can be modeled by the equation $y=\frac{x^{2}}{80}$, with dimensions in centimeters.

Juan writes an equation for a parabola with vertex (0, 0) and directrix x = -4. Which equation could he have written?

$$\begin{array}{ll}{A\quad x=\frac{y^{2}}{16}} & {\text { C } \quad y=\frac{x^{2}}{16}} \\ {B\quad x=\frac{y^{2}}{4}} & {\text { D }\quad y=\frac{x^{2}}{4}}\end{array}$$

Thomas Jefferson wrote the Declaration of Independence in 1776. He died exactly 50 years later. In what year did he die?

Solve each system of equations by means of Cramer's Rule. You may use technology to compute the determinants involved.

$$\left\{ \begin{aligned} 2 x + y + z & = 7 \\ 3 x - y - z & = - 2 \\ x + 2 y - 3 z & = - 4 \end{aligned} \right.$$

Let $\mathbf{v}_{1}=(3,2,2,2), \mathbf{v}_{2}=(2,1,2,1), \mathbf{v}_{3}=(4,3 ,2,3), \mathbf{v}_{4}=(1,2,3,4)$ and let $S=\{v_1,v_2,v_3, v_4 \}$ be a set of vectors in $\mathbf{R}^{4}$. Find a subset of $S$ that forms a basis for the subspace of $\mathbf{R}^{4}$ spanned by $S .$

Why do many less developed countries need to rely on foreign investment rather than internal financing?

If you consume a diet of 2,500 calories per day, what percentage of your Daily Value for fiber would one serving provide? A. 8 percent B. 10 percent C. 12 percent D. 15 percent

Graph the linear equation.

$$y=-3$$

Briefly explain the importance of each of the following. sweatshop

What keeps the particles in a colloidal dispersion from coalescing?

What are some processes that shape landforms?