Answer to Question #252561 in Calculus for Nick

Question #252561

An equilateral triangle made of metallic sheet is expanding because it is being heated. Its area A is given by


A =(√3x^2)/4



square centimeters, where x is the length of one side in centimeters. Find the instantaneous rate of change in A with respect to x at the instant when x = 10 centimeters.


1
Expert's answer
2021-10-19T17:05:03-0400
"A_x=\\dfrac{\\sqrt{3}}{4}(2x)=\\dfrac{\\sqrt{3}x}{2}"

"x=10\\ cm"


"A_x=\\dfrac{\\sqrt{3}(10)}{2}=5\\sqrt{3}(cm^2\/cm)"

The instantaneous rate of change in A with respect to x at the instant when x = 10 centimeters is

"5\\sqrt{3}\\ cm^2\/cm"


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