A) The equation in factored form is (4t + 1)(t - 2) = 0
B) The solutions of the equation are t = -1/4 and t = 2
C) It will take 2 seconds for the rocket to hit the ground
Step-by-step explanation:
* Lets study the information in the problem
- A child launches a toy rocket from the top of a slide
- The equation of the motion is -16² + 28t + 8 = 0, where t is the time
of rocket to hit the ground
* Now lets solve the problem
- At first simplify the equation
∵ -16t² + 28t + 8 = 0
∵ Al the terms have a factor 4
- Divide all terms by 4
∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1
∴ 4t² - 7t - 2 = 0
- Lets factorize
∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket
∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket
∵ 4t + -2 = -8t ⇒ product of the extremes
∵ 1t × 1 = 1t ⇒ product of means
∵ -8t + 1t = -7t ⇒ middle term
∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)
∴ (4t + 1)(t - 2) = 0
A) The equation in factored form is (4t + 1)(t - 2) = 0
- Lets use the zero product property to solve the equation
∵ (4t + 1)(t - 2) = 0
- Equate each factor by 0
∵ 4t + 1 = 0 ⇒ subtract 1 from both sides
∴ 4t = -1 ⇒ divide both sides by 4
∴ t = -1/4
OR
∵ t - 2 = 0 ⇒ add 2 for both sides
∴ t = 2
B) The solutions of the equation are t = -1/4 and t = 2
C) We can not accept the answer t = -1/4 because there is no negative
value for the time
∴ The answer is t = 2 only
* It will take 2 seconds for the rocket to hit the ground
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