
summer school TT
i need help with some problems
i will add more to this post
for each direct variation, find the constant of variation. then find the value of y when x = 5
y=2 when x=7
AVIATION
a speed of 60 mi/h is equal to a speed of 88 ft/s find the speed in mph of an aircraft travaling 1000ft/s

1. I'm going to assume that y varies directly to x.
If y varies directly to x, then
$\displaystyle y = k \cdot x$
K is the constant of variation. Find constant of variation using the numbers given in the question, then replace in the equation above. Then find y when x = 5.
2.
Given:
$\displaystyle v = \frac{60\ mi}{1 h} = \frac{88\ ft}{1\ s}$
Using this given relation, you can find out how many feet are there in 1 mile:
$\displaystyle \frac{60\ mi}{3600\ s} = \frac{88\ ft}{1\ s}$
$\displaystyle 60\ mi = \frac{88\ ft \cdot 3600\ \not{s}}{1\ \not{s}}$
$\displaystyle 1\ mi = \frac{88\ ft \cdot 3600}{60} = 5280\ ft$
$\displaystyle \frac{1000\ ft}{1\ s} = \frac{ ?\ mi}{ ?\ h}$
Now, let's divide this into two parts.
a. Find how many miles are there in 1000 ft.
b. Find how how many hours in a second.
b. Substitute.
a.
$\displaystyle ? mi = \frac{1000}{5280}$
b. There are 3600 seconds in an hour. So how many hours are there in one second?
$\displaystyle \frac{1}{3600}$
Can you continue?


$\displaystyle \frac{1000\ ft}{1\ s} = \frac{\frac{1000}{5280}\ mi}{\frac{1}{3600}\ s}$
I'll leave the computations for you. :)
