Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Step-by-step explanation:
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
Answer:
(12/5)m^3
Step-by-step explanation:
It's easier for most of us to write out a fraction / ratio without the " / " symbol:
48m^7
------------
20 m^4
Separate the coefficients from the powers of m:
48 m^7
----- * -------- Now let's reduce each fraction separately:
20 m^4
48/20 = 12/5, and
(m^7) / (m^4) = m^(7-4) = m^3
... so that our final answer is (12/5)m^3.
125 cubes since the little cubes are all 1 volume you can just say the normal volume.
1. (x , y) → (kx , ky) = Dilation ; similar image
2. (x , y) → (y , -x) = Rotation 90 counterclockwise ; congruent
3. (x , y) → (-x , y) = Reflection over y-axis ; congruent
4. (x , y) → (-x , -y) = Rotation 180 ; congruent
5. (x , y) → (x, -y) = Reflection over x-axis ; congruent
6. (x , y) → (-y , x) = Rotation 90 clockwise ; congruent
7. (x , y) → (x + a , y + b) = Translation ; congruent
Hope this helps :)
