Question

an airplane flies from city a in a straight line to city b, which is 110 kilometers north and 165 kilometers west of city a. how far does the plane fly (in kilometers)? (round your answer to the nearest kilometer.) km

1. -/1 points

a store had sales of $488.7 billion in 2016 and $539.6 billion in 2018. use the midpoint formula to estimate the sales (in billions of dollars) in 2017. assume that the sales followed a linear pattern. s = billion

Explanation:

Step1: Identify right - triangle for first problem

The north - south and west - east displacements form a right - triangle. The distance $d$ between city A and city B is the hypotenuse. Using the Pythagorean theorem $d=\sqrt{a^{2}+b^{2}}$, where $a = 110$ km and $b = 165$ km.
\[d=\sqrt{110^{2}+165^{2}}=\sqrt{12100 + 27225}=\sqrt{39325}\]

Step2: Calculate the value of $d$

\[d=\sqrt{39325}\approx198.31\approx198\] km

Step3: Apply mid - point formula for second problem

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=\frac{y_1 + y_2}{2}$. Here, $x_1 = 2016,y_1=488.7,x_2 = 2018,y_2 = 539.6$. Since we are interested in the value of $y$ (sales) for $x = 2017$, we use $S=\frac{488.7+539.6}{2}$
\[S=\frac{488.7 + 539.6}{2}=\frac{1028.3}{2}=514.15\] billion

Answer:

198 km
514.15 billion