The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function y=−16t^2+30t+2 , which of the following correctly identifies the y-intercept and best explains its meaning?(1 point) Responses The y-intercept is at (0,0) . The shirts are launched from the ground. The y -intercept is at left parenthesis 0 comma 0 right parenthesis . The shirts are launched from the ground. The y-intercept is at (0,2) . The shirts are launched at an initial height of 2 feet. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirts are launched at an initial height of 2 feet. The y-intercept is at (0,2) . The shirt will reach the ground after 2 seconds from being launched. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirt will reach the ground after 2 seconds from being launched. The y-intercept is at (2,0) . The shirts are launched at an initial height of 2 feet.

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1 answer

The correct response is:

The y-intercept is at (0,2). The shirts are launched at an initial height of 2 feet.

Explanation: In the function $ y = -16t^2 + 30t + 2 $, the y-intercept occurs when $ t = 0 $. Plugging $ t = 0 $ into the equation gives:

\[ y = -16(0)^2 + 30(0) + 2 = 2 \]

Thus, the y-intercept is (0, 2), which means that when the T-shirts are launched (at time $ t = 0 $), they are at an initial height of 2 feet off the ground.

answered by GPT-4o mini

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Question

The cheerleaders at a football game launch T-shirts into the crowd from the back of a golf cart that is 2 feet off the ground. The T-shirts have an upward velocity of 30 feet per second. Using the function y=−16t^2+30t+2 , which of the following correctly identifies the y-intercept and best explains its meaning?(1 point) Responses The y-intercept is at (0,0) . The shirts are launched from the ground. The y -intercept is at left parenthesis 0 comma 0 right parenthesis . The shirts are launched from the ground. The y-intercept is at (0,2) . The shirts are launched at an initial height of 2 feet. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirts are launched at an initial height of 2 feet. The y-intercept is at (0,2) . The shirt will reach the ground after 2 seconds from being launched. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirt will reach the ground after 2 seconds from being launched. The y-intercept is at (2,0) . The shirts are launched at an initial height of 2 feet.

1 answer

The correct response is:

The y-intercept is at (0,2). The shirts are launched at an initial height of 2 feet.

Explanation: In the function $ y = -16t^2 + 30t + 2 $, the y-intercept occurs when $ t = 0 $. Plugging $ t = 0 $ into the equation gives:

\[ y = -16(0)^2 + 30(0) + 2 = 2 \]

Thus, the y-intercept is (0, 2), which means that when the T-shirts are launched (at time $ t = 0 $), they are at an initial height of 2 feet off the ground.

GPT-4o mini · Answer

The correct response is: **The y-intercept is at (0,2). The shirts are launched at an initial height of 2 feet.** **Explanation:** In the function $ y = -16t^2 + 30t + 2 $, the y-intercept occurs when $ t = 0 $. Plugging $ t = 0 $ into the equation gives: $$ y = -16(0)^2 + 30(0) + 2 = 2 $$ Thus, the y-intercept is (0, 2), which means that when the T-shirts are launched (at time $ t = 0 $), they are at an initial height of 2 feet off the ground.