-4k²(k+6)(k-1). The expression can be factored by factor completely to the expression -4k²(k+6)(k-1).
To factor the polynomial by factor completely, we must to use the pattern as follows:
1. Greatest Common Factor
factored into
2. Factor the trinomial
Answer:
5
Step-by-step explanation:
Let's take the numerator first
3 1/2 - 9 3/4
Convert to improper fraction
7/2 - 39/4
Find the LCM
= -25/4
Now let's take the denominator
-2.5
Convert to fraction
-5/2
Combine the two parts of the fraction
-25/4 / (-5/2)
This becomes;
-25/2 * -2/5
= +5
This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:
Where:
So:
Finally, the equation is:
The rocket will reach the maximum height at the vertex of the parabola described by the equation . Therefore, our goal is to find
at this point. In math, a parabola is described by the quadratic function:
So the x-coordinate of the vertex can be calculated as:
From our equation:
So:
So the rocket will take its maximum value after 1.99 seconds.
<h2>c. What is the maximum height the rocket will reach?</h2>
From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by . Thus, we can find this as follows:
So the maximum height the rocket will reach is 66.68ft
<h2>d. How long is the rocket in the air?</h2>
The rocket is in the air until it hits the ground. This can be found setting , so:
We can't have negative value of time, so the only correct option is and rounding to the nearest hundredth we have definitively: