Find the equation of the line tangent to the graph of y = sin^-1 (x/5) at x = 5/2. Show your work.

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

Simplify:

We can factor out the denominator within the square root:

Simplify:

So, we can find the slope of the tangent line at x = 5/2. By substitution:

Evaluate:

We will also need the point at x = 5/2. Using our original equation, we acquire that:

So, the point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

Distribute:

Isolate. Hence, our equation is:

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5

answer: 30

step-by-step explanation: its 30 because im a basketball player and stephen curry hits most of his shots so if you put 30 you might make the shot goodluck