Two boats sail away from a buoy making a 90 degree angle. the first boat is 165 meters away and is traveling at 25 m/s. the second boat has been traveling at 35 m/s for pi minutes. what is the rate of change in distance between the two boats?

Step-by-step explanation:

lets say in the shown triangle x=165

so speed

and  

Also since distance = speed* time

time = pi minutes = pi/60 seconds

y =

y =

Now using the pythagorean :

derivate the equation so  we get :

m/s

So Rate of change = 25.387 m/s

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: