Answer:
Step-by-step explanation:
In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:

Moving the 9 to the other side since the derivative of a constant is 0 gives us

By implicit differentation, the derivative of that function is

To find the derivative, we have to solve for dy/dx:

Factor out the dy/dx to get:

Now divide to get your slope formula (first derivative):

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:
y-y₁ = m(x-x₁)
Filling in we get:
y - 0 = 5/3(x - 5) so the equation of the tangent line is:

Good luck in your calculus class!
P a p a party party p q p w party
Answer:
D
Step-by-step explanation:
Negative numbers are less than zero.
Answer:
60.2 m
Step-by-step explanation:
Let x represent the width of the river. The distance from the point across from the tree to the second point is 15 m. The angle from this point to the tree across the river is 76°.
This makes the side opposite the angle x, the width of the river. It also means the 15 m side is adjacent to this angle.
The ratio opposite/adjacent is the ratio for tangent; this gives us the equation
x/15 = tan(76)
Multiply both sides by 15:
15(x/15) = 15(tan(76))
x = 15(tan(76)) ≈ 60.2