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Chapter 1: Problem 35
How many inches are in 30.7484 miles?
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Two flies sit exactly opposite each other on the surface of a spherical balloon. If the balloon's volume doubles, by what factor does the distance between the flies change?
A position vector has components \(x=34.6 \mathrm{~m}\) and \(y=-53.5 \mathrm{~m} .\) Find the vector's length and angle with the \(x\) -axis.
If \(\vec{A}\) and \(\vec{B}\) are vectors and \(\vec{B}=-\vec{A},\) which of the following is true? a) The magnitude of \(\vec{B}\) is equal to the negative of the magnitude of \(\vec{A}\). b) \(\vec{A}\) and \(\vec{B}\) are perpendicular. c) The direction angle of \(\vec{B}\) is equal to the direction angle of \(\vec{A}\) plus \(180^{\circ}\) d) \(\vec{A}+\vec{B}=2 \vec{A}\).
The force \(F\) a spring exerts on you is directly proportional to the distance \(x\) you stretch it beyond its resting length. Suppose that when you stretch a spring \(8.00 \mathrm{~cm},\) it exerts a 200. N force on you. How much force will it exert on you if you stretch it \(40.0 \mathrm{~cm} ?\)
A friend walks away from you a distance of \(550 \mathrm{~m}\), and then turns (as if on a dime) an unknown angle, and walks an additional \(178 \mathrm{~m}\) in the new direction. You use a laser range-finder to find out that his final distance from you is \(432 \mathrm{~m} .\) What is the angle between his initial departure direction and the direction to his final location? Through what angle did he turn? (There are two possibilities.)
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