First, you must change all of this into improper fractions, like shown below.
Now you must change the sign.
Then we must reciprocalize 2/3.
Now we multiply, to get 2 4/10.
Since a(n)=-3(a(n-1)) the common ratio is -3, and a(1)=-3 so
a(n)=-3(-3^(n-1)) so the first four terms are:
-3, 9, -27, 81
Slope = -1
and it goes through (1, -7)
Define
g = 9.8 32.2 ft/s², the acceleration due to gravity.
Refer to the diagram shown below.
The initial height at 123 feet above ground is the reference position. Therefore the ground is at a height of - 123 ft, measured upward.
Because the initial upward velocity is - 11 ft/s, the height at time t seconds is
h(t) = -11t - (1/2)gt²
or
h(t) = -11t - 16.1t²
When the ball hits the ground, h = -123.
Therefore
-11t - 16.1t² = -123
11t + 16.1t² = 123
16.1t² + 11t - 123 = 0
t² + 0.6832t - 7.64 = 0
Solve with the quadratic formula.
t = (1/2) [-0.6832 +/- √(0.4668 + 30.56) ] = 2.4435 or -3.1267 s
Reject the negative answer.
The ball strikes the ground after 2.44 seconds.
Answer: 2.44 s
- Subtraction can be thought of as the inverse operation of addition, OR as addition itself, if you look at it as adding a negative number.
- The number line allows us to interpret subtraction (or addition of a negative) geometrically; we can view it as a movement to the left on the number line with a distance equal to the number being subtracted.
- Lastly, the value of any expression a - b (where a and b are real numbers) is determined by the relative sizes of the numbers. If a > b, then a - b > 0 (a positive result). If b > a, then a - b < 0 (a negative result.
