surface area in m^2/radius in meters is meters
radians is arc, no units
so
meters per radian
can you guys help me with these questions
Which of the following could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor?
square millimeters per millimeter
millimeters per centimeter
meters per second
gallons per hour
meters per radian
Which points on the curve of x2 − xy − y2 = 5 have vertical tangent lines?
(1, −2)
(2, −1) and (−2,1)
(0, squre root of 5)
There are no vertical tangents to this curve.
None of the above
2 answers
I assume you mean
x^2 - x y - y^2 = 5
2 x dx - x dy -y dx - 2 y dy = 0
(2y-x)dy = (2x-y)dx
dy/dx = (2x-y)/(2y-x)
slope is undefined (vertical) when
2y-x = 0
or
x = 2y
so
x^2 - x y - y^2 = 5
4y^2 -2y^2-y^2 = 5
y = +/-sqrt 5
then x = +/- 2 sqrt 5
x^2 - x y - y^2 = 5
2 x dx - x dy -y dx - 2 y dy = 0
(2y-x)dy = (2x-y)dx
dy/dx = (2x-y)/(2y-x)
slope is undefined (vertical) when
2y-x = 0
or
x = 2y
so
x^2 - x y - y^2 = 5
4y^2 -2y^2-y^2 = 5
y = +/-sqrt 5
then x = +/- 2 sqrt 5
1 answer