Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
The rate at which the height is changing is ( 5 / x ) m / hr
We know that,
Area of an equilateral triangle A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4
h = [tex]\sqrt{3}[/tex] x / 2
Where,
x = Side
h = Height
Given that,
dA / dt = 5 [tex]m^{2}[/tex] / hr
h = [tex]\sqrt{3}[/tex] x / 2
Differentiate both sides with respect to t
dh / dt = ( [tex]\sqrt{3}[/tex] / 2 ) ( dx / dt )
dx / dt = ( 2 / [tex]\sqrt{3}[/tex] ) ( dh / dt )
A = [tex]\sqrt{3}[/tex] [tex]x^{2}[/tex] / 4
Differentiate both sides with respect to t
dA / dt = ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( dx / dt )
5 = ( [tex]\sqrt{3}[/tex] / 4 ) ( 2x ) ( 2 / [tex]\sqrt{3}[/tex] ) ( dh / dt )
dh / dt = ( 5 / x ) m / hr
Rate of change of height is defined as the rate at which height of an object changes with respect to time. It is represented as dh / dt
Therefore, the rate at which the height is changing is ( 5 / x ) m / hr
To know more about Rate of change of height
https://brainly.com/question/13283964
#SPJ4
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
