Solving Other Problems (2.8.3)

Question 1

• When working with problems with decimals, many people will multiply through by 10, 100, or whatever power of 10 required to “clear” the decimals from the problem. As long as you multiply both sides of the equation, this procedure is valid and protects the balance of the equation. Clearing the decimals helps you think about the numbers involved since most of us prefer to work with whole numbers.

Answer 1

• When working with problems with decimals, many people will multiply through by 10, 100, or whatever power of 10 required to “clear” the decimals from the problem. As long as you multiply both sides of the equation, this procedure is valid and protects the balance of the equation. Clearing the decimals helps you think about the numbers involved since most of us prefer to work with whole numbers.

Question 2

In landing an aircraft the pilot must balance two things, the
distance available for the landing and the speed needed to
land safely without stalling.
The formula for this problem is set in s, the plane’s speed,
and L, the length of the runway.
The problem tells us the runway is 800 feet long, so we know
that L = 800.
Before you start working, you may want to multiply through
by 10 to clear the decimals.
Once you have cleared the decimals, move everything to one
side of the equation. Then you find the values you need for
the quadratic formula:
a = 1, b = –30, c = –7780.
Substitute those values into the formula and solve.
Discard the negative solution since the speed of the airplane
cannot be negative.
You are left with one valid answer.
Approximate its value in decimals to find the speed, in
feet/second that the plane must use.

Answer 2

In landing an aircraft the pilot must balance two things, the
distance available for the landing and the speed needed to
land safely without stalling.
The formula for this problem is set in s, the plane’s speed,
and L, the length of the runway.
The problem tells us the runway is 800 feet long, so we know
that L = 800.
Before you start working, you may want to multiply through
by 10 to clear the decimals.
Once you have cleared the decimals, move everything to one
side of the equation. Then you find the values you need for
the quadratic formula:
a = 1, b = –30, c = –7780.
Substitute those values into the formula and solve.
Discard the negative solution since the speed of the airplane
cannot be negative.
You are left with one valid answer.
Approximate its value in decimals to find the speed, in
feet/second that the plane must use.