From an elevation of 3.5 m below the surface of the water, a northern bottlenose whale dives at a rate of -1.8 m/s. write a rule that gives the whale's depth d as a function of time in minutes. what is the whale's depth after 4 in?

Step-by-step explanation:

We want to find the depth d in function of time,  for a constant speed, this will take the form  

,

we know that at time t = 0 the whale its at 3,5 m below the surface, so we can write:

Now, the whale dives at a rate of -1.8 m/s, so the depth increases by 1.8 m/s this must be our b, but before putting it in our equation, we need to convert this to m/min, luckily, we know that one minute has 60 seconds, so :

,

dividing for 1 min of each side, we can get our conversion factor:

.

Then, we can multiply the whale dives rate for this conversion factor, we are allowed to do that cause the conversion factors equals 1:

We can put this in our equation for depht:

To find what is the depth after 4 min, we just take t = 4 min

,

,

,

So the whale's depth after 4 min will be 435.5 m.

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.

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: