Question

d. 99754000 m² into km²

1. convert the rates below into the designated rates.

a. 110 km/h into km/sec (1 h = 60 min; 1 min = 60 sec)
c. 150 rpm into revolutions per second (1 min = 60 sec)

Explanation:

Step1: Recall conversion factor for length - squared

We know that $1\ km = 1000\ m$, so $1\ km^{2}=(1000)^{2}\ m^{2}= 1000000\ m^{2}$.

Step2: Perform the conversion for $99754000\ m^{2}$ to $km^{2}$

Divide the number of square - meters by the number of square - meters in a square - kilometer. Let $x$ be the area in $km^{2}$, then $x=\frac{99754000}{1000000}$.
$x = 99.754\ km^{2}$

Step3: Recall conversion factor for time in speed conversion (for part a)

Since $1\ h=60\ min$ and $1\ min = 60\ s$, then $1\ h=60\times60\ s = 3600\ s$.

Step4: Convert $110\ km/h$ to $km/s$

To convert $110\ km/h$ to $km/s$, divide the speed in $km/h$ by the number of seconds in an hour. Let $v$ be the speed in $km/s$, then $v=\frac{110}{3600}=\frac{11}{360}\approx0.0306\ km/s$.

Step5: Recall conversion factor for time in revolution - rate conversion (for part c)

We know that $1\ min = 60\ s$.

Step6: Convert $150\ rpm$ to revolutions per second

To convert $150\ rpm$ (revolutions per minute) to revolutions per second, divide the number of revolutions per minute by the number of seconds in a minute. Let $r$ be the number of revolutions per second, then $r=\frac{150}{60}=2.5$ revolutions per second.

Answer:

d. $99.754\ km^{2}$
a. $\frac{11}{360}\ km/s\approx0.0306\ km/s$
c. $2.5$ revolutions per second