Question

If y=sinax,where a>0,and (d^(2)y)/(dx^(2))=-16y,what the constant value of a

Answer 1

To find the constant value of a, we differentiate y=sin(ax) twice and equate it to the given second derivative -16y. We deduce that a²=16, hence a=4.

Step-by-step explanation:

The student's question asks for the constant value of a if y=sin(ax), where a>0, and the second derivative of y with respect to x, denoted by (d²y)/(dx²), equals -16y. To find the value of a, we need to differentiate y=sin(ax) twice.

The first derivative of y with respect to x is dy/dx = a*cos(ax). The second derivative is (d²y)/(dx²) = -a²*sin(ax).

Given that (d²y)/(dx²) = -16y, we can equate -a²*sin(ax) to -16*sin(ax). This implies that a² = 16. Therefore, a = 4, considering a>0.