Answer :
To determine the height of the toy rocket 3 seconds after it is launched, we'll use the given quadratic function that describes its height over time:
[tex]\[ f(x) = -4.9x^2 + 16x \][/tex]
where \( x \) is the time in seconds after the rocket is launched.
Let's find the height of the rocket at \( x = 3 \) seconds.
First, plug \( x = 3 \) into the function:
[tex]\[ f(3) = -4.9(3)^2 + 16(3) \][/tex]
Next, calculate the square of 3:
[tex]\[ 3^2 = 9 \][/tex]
Now, multiply by -4.9:
[tex]\[ -4.9 \times 9 = -44.1 \][/tex]
Next, multiply 16 by 3:
[tex]\[ 16 \times 3 = 48 \][/tex]
Now, add the two results together:
[tex]\[ -44.1 + 48 = 3.9 \][/tex]
From this step-by-step calculation, we can see that the height of the rocket 3 seconds after it is launched is
[tex]\[ \boxed{3.9} \][/tex]
Thus, the correct answer is:
(d) 3.9
[tex]\[ f(x) = -4.9x^2 + 16x \][/tex]
where \( x \) is the time in seconds after the rocket is launched.
Let's find the height of the rocket at \( x = 3 \) seconds.
First, plug \( x = 3 \) into the function:
[tex]\[ f(3) = -4.9(3)^2 + 16(3) \][/tex]
Next, calculate the square of 3:
[tex]\[ 3^2 = 9 \][/tex]
Now, multiply by -4.9:
[tex]\[ -4.9 \times 9 = -44.1 \][/tex]
Next, multiply 16 by 3:
[tex]\[ 16 \times 3 = 48 \][/tex]
Now, add the two results together:
[tex]\[ -44.1 + 48 = 3.9 \][/tex]
From this step-by-step calculation, we can see that the height of the rocket 3 seconds after it is launched is
[tex]\[ \boxed{3.9} \][/tex]
Thus, the correct answer is:
(d) 3.9
