H = 151t - 16t²
The height of the ball when it return to the ground will be 0
0 = 151t - 16t²
The zero product property is that when two numbers are being multiplied and the product is 0, one of them must be equal to 0. Therefore, we can factorize this equation:
16t² - 151t = 0
t(16t - 151t) = 0
By the zero product property:
t = 0 or 16t - 151 = 0
So t = 0 or t = 9.44 seconds
The first solution is before he releases the ball and the second is when the ball comes back to the ground. Thus, the ball's air time is 9.44 seconds.
QUESTION:- EVALUATE THE EXPRESSION
EXPRESSION:-
![{( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2}](https://tex.z-dn.net/?f=%7B%28%20%5Csqrt%5B6%5D%7B27%20%7Ba%7D%5E%7B3%7D%20%20%7Bb%7D%5E%7B4%7D%20%7D%20%29%7D%5E%7B2%7D%20)
<h3>ANSWER-></h3>
![{( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2} \\ {( {27 {a}^{3} {b}^{4} } )}^{ \frac{2}{6} } \\ {({27 {a}^{3} {b}^{4} } )}^{ \frac{ \cancel{2}}{ \cancel6 {}^{ \: 3} } } \\ {(27)}^{ \frac{1}{3} } {a}^{ \frac{3}{3} } {b}^{ \frac{4}{3} } \\{(3)}^{ \frac{ \cancel3}{ \cancel3} } {a}^{ \frac{ \cancel3}{ \cancel3} } {b}^{\frac{3 + 1}{3} } \\3a {b}^{ \frac{ \cancel3}{ \cancel3} } {b}^{ \frac{1}{3} }](https://tex.z-dn.net/?f=%7B%28%20%5Csqrt%5B6%5D%7B27%20%7Ba%7D%5E%7B3%7D%20%20%7Bb%7D%5E%7B4%7D%20%7D%20%29%7D%5E%7B2%7D%20%20%5C%5C%20%7B%28%20%7B27%20%7Ba%7D%5E%7B3%7D%20%20%7Bb%7D%5E%7B4%7D%20%7D%20%29%7D%5E%7B%20%5Cfrac%7B2%7D%7B6%7D%20%7D%20%20%5C%5C%20%7B%28%7B27%20%7Ba%7D%5E%7B3%7D%20%20%7Bb%7D%5E%7B4%7D%20%7D%20%29%7D%5E%7B%20%5Cfrac%7B%20%5Ccancel%7B2%7D%7D%7B%20%5Ccancel6%20%7B%7D%5E%7B%20%5C%3A%20%203%7D%20%7D%20%7D%20%5C%5C%20%7B%2827%29%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%7Ba%7D%5E%7B%20%5Cfrac%7B3%7D%7B3%7D%20%7D%20%20%7Bb%7D%5E%7B%20%5Cfrac%7B4%7D%7B3%7D%20%7D%20%5C%5C%7B%283%29%7D%5E%7B%20%5Cfrac%7B%20%5Ccancel3%7D%7B%20%5Ccancel3%7D%20%7D%20%20%7Ba%7D%5E%7B%20%5Cfrac%7B%20%5Ccancel3%7D%7B%20%5Ccancel3%7D%20%7D%20%20%7Bb%7D%5E%7B%5Cfrac%7B3%20%2B%201%7D%7B3%7D%20%7D%20%5C%5C3a%20%7Bb%7D%5E%7B%20%5Cfrac%7B%20%5Ccancel3%7D%7B%20%5Ccancel3%7D%20%7D%20%20%7Bb%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20)
![\\ ANSWER->3ab \sqrt[3]{b} \: \: \: \: \: or \: \: 3a {b}^{ \frac{4}{3} }](https://tex.z-dn.net/?f=%20%5C%5C%20ANSWER-%3E3ab%20%5Csqrt%5B3%5D%7Bb%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%5C%3A%203a%20%7Bb%7D%5E%7B%20%5Cfrac%7B4%7D%7B3%7D%20%7D%20)
21/30 simplifies to 2.1/3 so it's a little bit bigger
