Math, asked by nikhilrajesh18, 5 months ago

Suppose that z= x3y2, where both x and y are changing with time. At a certain instant when x= 1 and y=2, x is decreasing at the rate of 2 units/s, and y is increasing at the rate of 3 units/s. How fast is z changing at this instant?
Is z increasing or decreasing?​

Answers

Answered by Flaunt
24

\huge\bold{\gray{\sf{Answer:}}}

\bold{Explanation:}

z =  {x}^{3}  {y}^{2}

we differentiate 'z' with respect to the time.Here,we differentiate it by multiplication method:

 =  >  \frac{dz}{dt}  =  {3x}^{2}  \frac{dx}{dt}  {y}^{2}  +  {x}^{3} 2y \frac{dy}{dt}

Given that when x =1 ,x is decreasing at the rate of 2units /s

It implies that:

=> \left.\dfrac{dx}{dt}\right  |_{x = 1 }=  - 2\:units/s

when y =2,y is increasing at the rate of 3units/s

=> \left. \dfrac{dy}{dt}\right  |_{y = 2 }= 3\:units/s

Z change at this instant:-

=> \left. \dfrac{dz}{dt} \right |_{x = 1,y = 2 }=( 3 {x}^{2}  \frac{dx}{dt}  |x = 1) {y}^{2}  +  {x}^{3} (2y \frac{dy}{dt}  |y = 2)

=> \left. \dfrac{dz}{dt} \right |_{(x = 1)(y=2)}= 3 {(1)}^{2} ( - 2) {(2)}^{2}  +  {(1)}^{3}(4)(3)

 =  - 12units/s

\thereforez is decreasing


amitkumar44481: Great :-)
Answered by gowrarajinchara
2

Answer:

answer is

-12units/s

z is decreasing

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