Question
A bird flew down from a tree to grab a worm on the ground. The equation y=36.79x2−59.66x+24.19
represents the path of the bird, where x is time in seconds and y is the height above the ground in feet. Using the model, find the initial height of the bird in the tree. Round to the nearest tenth.(1 point)
Responses
24.1 feet
24.1 feet
36.8 feet
36.8 feet
0.8 feet
0.8 feet
24.2 feet
represents the path of the bird, where x is time in seconds and y is the height above the ground in feet. Using the model, find the initial height of the bird in the tree. Round to the nearest tenth.(1 point)
Responses
24.1 feet
24.1 feet
36.8 feet
36.8 feet
0.8 feet
0.8 feet
24.2 feet
Answers
GPT-4o mini
To find the initial height of the bird in the tree using the equation \( y = 36.79x^2 - 59.66x + 24.19 \), we need to determine the height at time \( x = 0 \), since the initial height corresponds to the point when the bird has just started its flight.
We substitute \( x = 0 \) into the equation:
\[
y = 36.79(0)^2 - 59.66(0) + 24.19
\]
Simplifying this:
\[
y = 0 - 0 + 24.19
\]
\[
y = 24.19
\]
Rounding 24.19 to the nearest tenth gives us 24.2.
Therefore, the initial height of the bird in the tree is **24.2 feet**.
We substitute \( x = 0 \) into the equation:
\[
y = 36.79(0)^2 - 59.66(0) + 24.19
\]
Simplifying this:
\[
y = 0 - 0 + 24.19
\]
\[
y = 24.19
\]
Rounding 24.19 to the nearest tenth gives us 24.2.
Therefore, the initial height of the bird in the tree is **24.2 feet**.