A square image of an object on a video game has an initial side length of 25 pixels. To make the object appear closer, the side length of the square is increased by 10 pixels per second. This length change is represented by the function s(t) = 25 + 10t, where t is time in seconds. If the area of the square is A(s) = sa, find the formula for the area as a function of time, and then determine A(s(3)). A(t) equals +2+ t + 625 The area of the square image after 3 seconds is square pixels.

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librabby108 librabby108 · Answer 1 · 2020-08-24T20:32:33+02:00

Answer: A(t) = 100t^2 + 500t + 625

3,025 square pixels

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ap8997154 ap8997154 · Answer 2 · 2022-06-09T12:56:15+02:00

A function assigns the values. The area of the square image after 3 seconds is 3,025 sq. pixels.

A function assigns the value of each element of one set to the other specific element of another set.

A.) The area of the video game will be,

A(s) = [s(t)]²

A(s) = (25+10t)²

A(s) = 625 + 100t² + 500t

A(s) = 100t² + 500t +625

B.) The value of A(s(3)) will be,

A(s(t)) = 100(25+10t)² + 500(25+10t) + 625

A(s(t)) = 10,000t² + 50,000t + 62,500 + 12,500 + 5,000t + 625

A(s(t)) = 10,000t² + 55,000t + 75,625

A(s(3)) = 10,000(3)² + 55,000(3) + 75,625

A(s(3)) = 270,000 + 165,000 + 75,625

A(s(3)) = 510,625

The area of the square image after 3 seconds is,

A(s) = 100t² + 500t +625

A(3) = 100(3)² + 500(3) +625

A(3) = 900 + 1500 +625

A(3) = 3,025

Hence, The area of the square image after 3 seconds is 3,025 sq. pixels.

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