Calculus word problem Please Help?
2016-06-26 9:25 pm
Each side of a square is increasing at a rate of 2 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm2?
回答 (3)
2016-06-26 9:39 pm
✔ 最佳答案
x cm : the length of the side of the squareA cm³ : the area of the square
When A = 16 :
16 = x²
x = 4 or x = -4 (rejected)
A = x²
dA/dt = 2x (dx/dt)
When dx/dt = 2 and x = 4 :
dA/dt = 2 * 4 * 2
dA/dt = 16
The rate of the increase of the area = 16 cm²/s
2016-06-26 9:38 pm
Let side of the square be denoted as x and area as A.
dx/dt = 2,
A = 16,
A = x^2, x = A^(0.5),
dA/dt = d (x^2)/dt = 2x*dx/dt = 2*[A^(0.5)] *dx/dt = 2 * 4 * 2 = 16cm^2
dx/dt = 2,
A = 16,
A = x^2, x = A^(0.5),
dA/dt = d (x^2)/dt = 2x*dx/dt = 2*[A^(0.5)] *dx/dt = 2 * 4 * 2 = 16cm^2
2016-06-26 9:34 pm
A = s² --- {When the area of the square is 16 cm², the side length is 4 cm}
dA/dt = 2s • ds/dt
dA/dt = 2(4) • (2)
dA/dt = 16 cm²
dA/dt = 2s • ds/dt
dA/dt = 2(4) • (2)
dA/dt = 16 cm²
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