(29) a runner is running 10 miles per hour.
a. what conversion factors should be used to convert 10 mi/hr to ft/s?

The conversions factors needed are 1 mile= 5280 feet and 1 hour = 3600 seconds, speed in ft/s = 14.67 ft/s  

Solution:

Given, A runner is running 10 miles per hour.  

We have to find what conversion factors should be used to convert 10 mi/hr to ft/s?

Now, speed of runner = 10 miles per hour.

But we need the units to be in ft / s.

Then, conversion factors are miles to feet and hours to seconds.

Now, miles to feet ⇒ 1 mile = 5280 feet.

Now, hours to seconds ⇒ 1 hour = 3600 seconds

Hence, the conversions needed are 1 mile = 5280 feet and 1 hour = 3600 seconds, speed in ft/s = 14.67 ft/s

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

step-by-step explanation:

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