5 and 1/4 can be cut from the ribbon
Divide 3 1/2 and 2/3
Δx (delta x) is about a secant line, a line between two points representing the rate of change between those two points. That's a "differential" (between the two points).
dx is about a tangent line to one point, representing an instantaneous rate of change. That makes it a "derivative."
Answer:
-4/5
Step-by-step explanation:
To find the slope of the tangent to the equation at any point we must differentiate the equation.
x^3y+y^2-x^2=5
3x^2y+x^3y'+2yy'-2x=0
Gather terms with y' on one side and terms without on opposing side.
x^3y'+2yy'=2x-3x^2y
Factor left side
y'(x^3+2y)=2x-3x^2y
Divide both sides by (x^3+2y)
y'=(2x-3x^2y)/(x^3+2y)
y' is the slope any tangent to the given equation at point (x,y).
Plug in (2,1):
y'=(2(2)-3(2)^2(1))/((2)^3+2(1))
Simplify:
y'=(4-12)/(8+2)
y'=-8/10
y'=-4/5
Answer: C. 113.1 cubic centimeters
Step-by-step explanation:
Volume of a sphere=
(3.14)(r)^3
Since we know r then just plug in to get 4/3(3.14)(3)^3= 113.1
So the answer is C