A helicopter gets into difficulty at time t= 0. Its altitude (in meters) is given by p(t)=31³-1²-4t+200 from time t=0 until t = 50 seconds when the pilot feels that everything is back to normal. A) At what speed is the helicopter falling when the frightened pilot first gets into difficulty? B) What is the (vertical component of the) acceleration of the helicopter at time t = 10, still frightening the pilot? C) At what time is the vertical velocity zero? D) What is the minimum height reached by the helicopter during those difficult times? Hint: What would then be the vertical speed at such a moment?
A helicopter gets into difficulty at time t= 0. Its altitude (in meters) is given by p(t)=31³-1²-4t+200 from time t=0 until t = 50 seconds when the pilot feels that everything is back to normal. A) At what speed is the helicopter falling when the frightened pilot first gets into difficulty? B) What is the (vertical component of the) acceleration of the helicopter at time t = 10, still frightening the pilot? C) At what time is the vertical velocity zero? D) What is the minimum height reached by the helicopter during those difficult times? Hint: What would then be the vertical speed at such a moment?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Can tou please answer question 3.34
![1 of 1
Question 3.31)
A) Compute f'(x), ƒ"(x) and ƒ"(x) for f(x)=sin²(x).
B) Let g(x)=√√9+4x². Evaluate g(2), g'(2), g"(2).
C) By observing a pattern that occurs with the first few derivatives of h(x), find
h(25) (2) for h(x) = sin(√2x).
Do not compute all 25 derivatives! Compute a handful and figure out the 25th from there.
Question 3.32)
A population of chipmunks moves into a new region at time t = 0.
After t years, the population is given by: P(t)=1
() = 100[1+1+1²].
A) How long does it take for this population to double its initial size?
B) What is the rate of growth of the population when P = 200?
Question 3.33)
A certain sports car is being tested for its performance. Putting the engine at maximum capacity starting
from rest, its position as a function of time turns out as:
x(t) = 8t √t.
(x in meters, t in seconds.)
A) How much time does it take for the car to reach 100 km/hr ? (27.78 m/s)
B) At what speed does the car go though the 100m line?
Question 3.34)
A helicopter gets into difficulty at time t = 0. altitude (in meters) is given by
p(t)=300³-²-4t+200
from time t = 0 until t = 50 seconds when the pilot feels that everything is back to normal.
A) At what speed is the helicopter falling when the frightened pilot first gets into difficulty?
B) What is the (vertical component of the) acceleration of the helicopter at time t = 10, still frightening
the pilot?
C) At what time is the vertical velocity zero?
D) What is the minimum height reached by the helicopter during those difficult times?
Hint: What would then be the vertical speed at such a moment?
Question 3.35)
An expert in the housing market tells you that the price of midsize houses in a certain neighborhood of
Montreal is expected to increase for the next few years according to the formula
V=400+10t+4t² -0.41³ (Vin thousands of dollars, t in years).
where t= 0 corresponds to the present date.
A) What is the present value of houses, and at what rate is it presently increasing?
B) What is the expected value of houses in 1 year?
How do you compare this value with both your answers in A) ?
C) What is the average rate at which the price of houses is expected to increase during the period of the
five years to come from now?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2af5a58a-26e3-4baa-9073-1b18b1512b13%2F642e88ad-2e66-4c38-ba5c-b2f5ce37c7d0%2Fy5g1ivq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 of 1
Question 3.31)
A) Compute f'(x), ƒ"(x) and ƒ"(x) for f(x)=sin²(x).
B) Let g(x)=√√9+4x². Evaluate g(2), g'(2), g"(2).
C) By observing a pattern that occurs with the first few derivatives of h(x), find
h(25) (2) for h(x) = sin(√2x).
Do not compute all 25 derivatives! Compute a handful and figure out the 25th from there.
Question 3.32)
A population of chipmunks moves into a new region at time t = 0.
After t years, the population is given by: P(t)=1
() = 100[1+1+1²].
A) How long does it take for this population to double its initial size?
B) What is the rate of growth of the population when P = 200?
Question 3.33)
A certain sports car is being tested for its performance. Putting the engine at maximum capacity starting
from rest, its position as a function of time turns out as:
x(t) = 8t √t.
(x in meters, t in seconds.)
A) How much time does it take for the car to reach 100 km/hr ? (27.78 m/s)
B) At what speed does the car go though the 100m line?
Question 3.34)
A helicopter gets into difficulty at time t = 0. altitude (in meters) is given by
p(t)=300³-²-4t+200
from time t = 0 until t = 50 seconds when the pilot feels that everything is back to normal.
A) At what speed is the helicopter falling when the frightened pilot first gets into difficulty?
B) What is the (vertical component of the) acceleration of the helicopter at time t = 10, still frightening
the pilot?
C) At what time is the vertical velocity zero?
D) What is the minimum height reached by the helicopter during those difficult times?
Hint: What would then be the vertical speed at such a moment?
Question 3.35)
An expert in the housing market tells you that the price of midsize houses in a certain neighborhood of
Montreal is expected to increase for the next few years according to the formula
V=400+10t+4t² -0.41³ (Vin thousands of dollars, t in years).
where t= 0 corresponds to the present date.
A) What is the present value of houses, and at what rate is it presently increasing?
B) What is the expected value of houses in 1 year?
How do you compare this value with both your answers in A) ?
C) What is the average rate at which the price of houses is expected to increase during the period of the
five years to come from now?
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