A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is increasing by 4 in/sec and the long leg is
shrinking at 9 in/sec. What is the rate of change of the hypotenuse?

Given:

A right triangle has legs of 18 inches and 24 inches.

The short leg is increasing by 4 in/sec and the long leg is  shrinking at 9 in/sec.

To find:

The rate of change of the hypotenuse.

Solution:

Let x be the shorter leg (Base), y be the larger leg (Perpendicular) and z be the hypotenuse.

We have,

According to the Pythagoras theorem,

          ...(i)

Taking square root on both sides.

Side cannot be negative. So,

Differentiating (i) with respect to time t, we get

Divide both sides by 60.

Here, negative sign means hypotenuse is decreasing.

Therefore, the hypotenuse is shrinking at 4.8 in/sec.

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

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: