Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
So we have the expression:
And we wish to factor it.
First, let's make a substitution. Let's let u be equal to x². Therefore, our expression is now:
This is a technique called quadratic u-substitution. Now, we can factor in this form.
We can use the numbers -3 and -2. So:
For the first two terms, factor out a u.
For the last two terms, factor out a -3. So:
Grouping:
Now, substitute back the x² for u:
And this is the simplest form.
And we're done!
Answer:
45
Step-by-step explanation:
Answer:
10.47 s
Step-by-step explanation:
We must solve the quadratic equations for t.
1. On the moon
h = -0.8t² + 10t +2
The standard form of a quadratic equation is
y = ax² + bx + c = 0
By comparing like terms, we see that
a = -0.8; b = 10; c = 2
We can now use the quadratic formula:
(a) Evaluate the discriminant D
D = b² - 4ac = 10² - 4 × (-0.8) × 2 = 100 + 6.4 = 106.4
(b) Solve for x
2. On the Earth
(a) Evaluate the discriminant
D = b² - 4ac = 10² - 4 × (-4.9) × 2 = 100 + 39.2 = 139.2
(b) Solve for x
3. Difference in time of flight
Time on Moon - time on Earth = 12.70 s - 2.22 s = 10.47 s
The ball will stay in flight 10.47 s longer on the moon than on Earth.
The graphs below show the times of flight on the Moon and on Earth