Lesson 6 Towers and Cylinders Solidify Understanding

Ready

What does it mean to have a $50$ / $50$ chance?

Probability is the measure of how likely an event will occur. Probabilities are written as fractions or decimals from $0$ to $1$ , or as percentages from $0 %$ to $100 %$ .

Write not possible, unlikely, as likely as not, likely, or certain to describe each event. The following scale might help you think about your answers.

1.

A quarter lands heads up.

2.

The sun will come up tomorrow.

3.

You will roll an even number on a standard $6$ -sided die.

4.

The month of February will have $30$ days.

5.

Carlos guesses the correct number between $1$ and $1,000$ .

6.

The football team has won $8$ of its last $9$ games. The team will win the next game.

7.

Your mother is $4^{'} 10^{″}$ and your dad is $5^{'} 4^{″}$ . You will be $6^{'}$ tall.

8.

You get a citation for driving your car $55 mph$ in a school zone.

Set

You have $144$ masonry tiles that you plan to lay out in your backyard to create a rectangular patio, but you haven’t decided on the dimensions of the patio. The tiles are $1 foot$ square. You begin by laying each tile out in a really long line so you can make sure each one is clean and not damaged.

This makes a rectangle that measures $1 ft$ by $144 ft$ . You know you don’t want a patio with these dimensions, but you decide to methodically explore the dimensions you may want by next creating a rectangle that measures $2 ft$ by $72 ft$ . You continue on making rectangles until you’ve tried all of the possibilities. Since it’s hard to keep all of the dimensions in your head, you decide to make a table that organizes all of the widths, lengths, and the fixed area you want.

9.

Complete the table to show the dimensions of the rectangles until they repeat. Then sketch a graph from the ordered pairs and draw a smooth curve through the points.

Width $(x) ft$	$1$	$2$	$3$	$4$	--	$6$	--	$8$	$9$	--	--	$12$
Length $(y) ft$	$144$	$72$
Area $(x y) {ft}^{2}$	$144$	$144$	$144$	$144$	$144$	$144$	$144$	$144$	$144$	$144$	$144$	$144$

Width

$(x) ft$

$1$

$2$

$3$

$4$

$6$

$8$

$9$

$12$

Length

$(y) ft$

$144$

$72$

Area

$(x y) {ft}^{2}$

$144$

10.

What happens to the length as the width increases? Why? Would the graph change if the width became the dependent variable and the length became the independent variable? Explain.

11.

This type of relation is called an inverse variation. Explain why it is called that.

12.

For each ordered pair in the table, what does $(width) (length)$ equal?

Solve the equation you just wrote for length.

13.

What is the value of $k$ , the constant of variation, in this story?

14.

When you solve for $y$ in the general formula for inverse variation, what is the location of $k$ in the equation?

Go

Solve the following equations. Show each step in your solution process. Check your solution(s).

15.

$10 = 2 \sqrt{x}$

16.

$\sqrt{6 x} = 6$

17.

$\sqrt{- 3 x} = 2$

18.

$\sqrt{x^{2} + 3 x} = 2$

19.

$\sqrt{x^{2} - 2 x + 1} = 2$

20.

$\sqrt{x^{2} - 3 x - 3} = 5$