Amachine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. the change in length is given by the function `l(t) = t^2 - sqrt(t)`, and the change in width is given by `w(t) = t^2 - 2t^(1/2)`. which function gives the change in area of the metal strips? a. `a(t) = t^4 + 2t` b. `a(t) = t^4 + 2t + 3t^(5/2)` c. `a(t) = t^4 - 3t^(5/2) + 2t` d. `a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)`

The change of area A(t) = t^4 - 3t^(5/2) + 2t ⇒ answer C

Step-by-step explanation:

* Lets study the problem

- The metal strip is in a shape of rectangle

- The change in length l(t) = t² - √t

- The change is the width w(t) = t² - 2t^1/2

* We must find function gives the change of area

∵ The area of the rectangle = length × width

∴ The change of rate of area A(t) = l(t) × w(t)

- We can write the √t in exponential form t^1/2

∴ l(t) = t² - t^1/2

∵ w(t) = t² - 2t^1/2

∵ A = l × w

∴ A(t) = l(t) × w(t)

∴ ⇒use the foil method

∴

- If we multiply two same numbers have exponents, then we add

 the power of them

∴

∴

* Now lets add the like terms

∴

* The change of area A(t) = t^4 - 3t^(5/2) + 2t

ok so the answer to your question is simple as long as you look at the different dimensions that contain the exemplary letters that combined in the right order give you words that eventually within the 5th dimension will conform and give you the correct answer to your question. hope i , stop looking at this easily, look at it with a spectral view.

step-by-step explanation:

told you

b

step-by-step explanation: