Question

starting from city a, a car drives 250 miles east to city b, then 300 miles north to city c, and finally 700 miles west to city d. what is the distance between city a and city d? show your work for credit.
quiz instructions

1. answer all questions.
2. for credit, show your work where necessary.
3. all answers to be done on canvas.
4. do not download the respondus lockdown browser (rlb) when taking the exam.
5. refer all technical problems with rlb to msu dit team @ the main library.
6. if facing technical challenges with your technology - laptop, ipad & wi - fi, plan to take the exam at main library.
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8. for extra credit, a handwritten \cheat\ sheet, pdf format, can be submitted to a canvas message to the instructor immediately after the exam.

question 13

Explanation:

Step1: Analyze the movements

We consider the east - west and north - south displacements separately. East - west: drives 250 miles east and 700 miles west. North - south: drives 300 miles north.

Step2: Calculate the net east - west displacement

The east - west displacement $d_{ew}=250 - 700=- 450$ miles (negative means west - ward). The north - south displacement $d_{ns}=300$ miles.

Step3: Use the Pythagorean theorem

The distance $d$ between the starting point (city A) and the ending point (city D) is given by $d=\sqrt{d_{ew}^{2}+d_{ns}^{2}}$. Substitute $d_{ew}=-450$ and $d_{ns}=300$ into the formula: $d = \sqrt{(-450)^{2}+300^{2}}=\sqrt{202500 + 90000}=\sqrt{292500}=5\sqrt{11700}=150\sqrt{13}\approx540.83$ miles.

Answer:

$150\sqrt{13}\approx540.83$ miles