Question

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engineers measure angles in gradients, which are smaller than degrees. the table shows the conversion of some angle measures in degrees to angles in gradients. what is the slope of the line representing the conversion of degrees to gradients? express your answer as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can consider the degrees as $x$ - values and gradients as $y$ - values. Let's take two points from the table, say $(0,0)$ and $(90,100)$.

Step2: Calculate the slope

Substitute $x_1 = 0,y_1 = 0,x_2=90,y_2 = 100$ into the slope formula. $m=\frac{100 - 0}{90 - 0}=\frac{100}{90}\approx1.11$.

Answer:

$1.11$