diff --git a/calculus/source/03-AD/03.ptx b/calculus/source/03-AD/03.ptx index 3c524520..35e0d46b 100644 --- a/calculus/source/03-AD/03.ptx +++ b/calculus/source/03-AD/03.ptx @@ -279,40 +279,41 @@ recall that when y is a function of x, which in turn is a function + +

Recall that in a right triangle with sides a,b, and hypotenuse c we have the relationship +

+ a^2 + b^2 = c^2. +

You might know this as the Pythagorean theorem, even though this relationship was known by the Babylonians already a thousand years before his time! +

+ + + -

Recall that in a right triangle with sides a,b and hypotenuse c we have the relationship

- a^2 + b^2 = c^2, -

also known in the western world as the Pythagorean theorem (even though this result was well know well before his time by other civilizations).

- - - - +

Consider the relationship between the lengths of the sides of a right triangle given by . +

+ +

Notice that by differentiating the equation above with respect to t we get a relationship between a,b,c, \frac{da}{dt}, \frac{db}{dt}, \frac{dc}{dt}. Find this related rates equation.

- -

A rectangle has one side of 8 cm. How fast is the diagonal of the rectangle changing at the instant when the other side is 6 cm and increasing at a rate of 3 cm per minute?

- - -

A 10 m ladder leans against a vertical wall and the bottom of the ladder slides away at a rate of 0.5 m/sec. - When is the top of the ladder sliding the fastest down the wall? +

A 10 m ladder leans against a vertical wall whilst the bottom of the ladder is sliding away at a rate of 0.5 m/sec. + At which time is the top of the ladder sliding down the wall the fastest?

  1. When the bottom of the ladder is 4 meters from the wall.

  2. When the bottom of the ladder is 8 meters from the wall.

  3. The top of the ladder is sliding down at a constant rate.

-