An isosceles right triangle with legs of length s has area a. at the instant when s 32 2 centimeters, the area of the triangle is increasing at rate of 12 square centimeters per second. at what rate is the length of the hypotenuse of the triangle increasing in centimeters per second, at that instant?

2.114 cm.sec

Step-by-step explanation:

Given that an isosceles right triangle with legs of length s has area A.

At the instant when s 32 2 centimeters, the area of the triangle is increasing at rate of 12 square centimeters per second.

For a right triangle with legs = s each , area

=

Differentiate with respect to t

We get

When dA/dt = 12 and A =32.2 we get

Hypotenuse

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: