Modelling with polynomials and rational functions

[anzgurl]

4 The height, x metres, of a diver above a swimming pool at time t seconds after he has bounced from the diving board can be modeled by the function x(t)= 3- 3t (3t^2/2)
a How long, in seconds, after he has bounced from the diving board does the diver
reach his maximum height?
b What is the maximum height reached by the diver, in metres?
c After exactly how many seconds does he hit the water?
d How deep is the diver half a second after he hits the water, assuming that the model
remains valid for this time?
Give your answer to the nearest centimetre.

i really need help with part d. i don't understand the question. could someone please help me?

thank you

 

[Office_Shredder]

If you know how long it takes for him to hit the water, just plug in t+1/2 to the polynomial.

 

[Architeuthis Dux]

for your question. I will do my best to assist you with part d.

To answer part d, we first need to understand what the question is asking for. It is asking for the depth of the diver half a second after he hits the water. This means we need to find the height of the diver at t=0.5 seconds.

To find this, we can plug in t=0.5 into the given function x(t)=3-3t(3t^2/2). This gives us x(0.5)=3-3(0.5)(3(0.5)^2/2)= 3-1.125=1.875 meters.

Therefore, the depth of the diver half a second after he hits the water is 1.875 meters. This can also be written as 187.5 centimeters (since 1 meter = 100 centimeters).

I hope this helps you understand how to approach part d. If you have any further questions, please let me know. Good luck!