Question

name
constant of proportionality:
equation: c =
problem 4
a map of colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. are these two ways of reporting the scale the same? explain your reasoning.
problem 5
here is a polygon on a grid.
a. draw a scaled copy of the polygon using a scale factor of 3. label the copy a.
b. draw a scaled copy of the polygon with a scale factor 1/2. label it b.
grade 7 unit 2 lesson 4: practice problems
tennessee standards edition cc by - nc 4.0. download for free at openup.org.

Explanation:

Problem 1 (finding constant of proportionality and equation for the table)

Step1: Recall the formula for constant of proportionality

The relationship for two proportional quantities $C$ and $d$ is $C = kd$, where $k$ is the constant of proportionality. We can find $k$ by dividing $C$ by $d$ for any pair of values in the table.
For $d = 2$ and $C=6.28$, $k=\frac{C}{d}=\frac{6.28}{2}=3.14$.
We can check with other pairs:
For $d = 3$, $C = 9.42$, and $\frac{C}{d}=\frac{9.42}{3}=3.14$.
For $d = 5$, $C = 15.7$, and $\frac{C}{d}=\frac{15.7}{5}=3.14$.
For $d = 10$, $C = 31.4$, and $\frac{C}{d}=\frac{31.4}{10}=3.14$.

Step2: Write the equation

Since the constant of proportionality $k = 3.14$, the equation relating $C$ and $d$ is $C=3.14d$.

Step1: Convert 1 inch to 20 miles to a ratio

We know that 1 mile = 5280 feet and 1 foot = 12 inches. So, 1 mile $=5280\times12 = 63360$ inches.
Then 20 miles $=20\times63360=1267200$ inches.
The ratio for the scale "1 inch to 20 miles" is $1:1267200$.
The other scale is given as $1:1267200$.

Answer:

Constant of proportionality: $3.14$
Equation: $C = 3.14d$

Problem 4 (comparing map - scales)