1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nikolay [14]
3 years ago
5

The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan−1(t2), where t is measured in days

. What is the instantaneous rate of change of the mass of the colony, in grams per day, at the moment the colony reaches a mass of 6 grams?
Physics
1 answer:
ololo11 [35]3 years ago
4 0

Answer:

<em>P'(1.015)=4.93 grams</em>

Explanation:

<u>Instantaneous Rate Of Change </u>

If one variable y is a function of another variable x, the rate of change can be measured by changing x by a small amount (dx) and computing the change in y (dy). The rate of change is

\displaystyle \frac{dy}{dx}

When dx tends to zero, we call it the instantaneous rate of change and is easily computed as the first derivative of y

Note: We'll be using the standart notation atan for the inverse tangent

We are given the relation between the mass of a colony of bacteria in grams P(t) and the time t in days

P(t)=2+5atan(t^2)

Let's find its first derivative, recalling that

[atan(u)]'=\displaystyle \frac{u'}{1+u^2}

P'(t)=\displaystyle 5\frac{(t^2)'}{1+(t^2)^2}

P'(t)=\displaystyle 5\frac{2t}{1+t^4}

P'(t)=\displaystyle \frac{10t}{1+t^4}

We need to know the value of t, so we use the provided condition P=6 gr

P(t)=2+5atan(t^2)=6

\displaystyle atan(t^2)=\frac{4}{5}

\displaystyle (t^2)=tan\left ( \frac{4}{5} \right )

\displaystyle t=\sqrt{tan\left ( \frac{4}{5} \right )}

\displaystyle t=1,015\ days

We use this value in the derivative:

P'(1.015)=\displaystyle \frac{10(1.015)}{1+(1.015)^4}

P'(1.015)=4.93\ grams

You might be interested in
What is the kinetic energy of a car of 1500 kg moving 25 m/s?
Ivan
Is this a multi choice?
4 0
3 years ago
I need help with answer 51.
Troyanec [42]

Answer:

2

Explanation:

5 0
2 years ago
Two sacks contain the same number of identical apples and are separated by a distance r. The two sacks exert a gravitational for
stepan [7]

Answer:

Explanation:

im sleppy

3 0
3 years ago
Which of the following would most likely cause a decrease in the quality supplied
soldier1979 [14.2K]

AWhich of the following would most likely cause a decrease in the quantity supplied? A decrease in price.

4 0
2 years ago
A dog is walking at 2m/s and then begins to run at a speed of 6m/s. What is his acceleration if his total travel time is 2 secon
fiasKO [112]
The formula for velocity vf = vi + at

First list your given information

2m/s Is your initial velocity (vi)
6m/s is you final velocity (vf)
2 seconds is your time (t)

Since you want the a for acceleration get a by itself

a = (vf-vi)/t

So a= (6-2)/2

a= 4/2

a=2

Now units

the units for acceleration are m/sx^{2}

2m/sx^{2}
7 0
3 years ago
Other questions:
  • A sample of 4.50 g of methane occupies 12.7 dm3 at 310 K. (a) Calculate the work done when the gas expands isothermally against
    10·1 answer
  • Which description accurately describes the tide represented by the image below?
    14·2 answers
  • The magnetic field at 8 cm distance from a long straight wire, carrying is 0.2x10^-5 T. How much is the electric current in the
    15·1 answer
  • 1) A substance has a half life of 20 years. what percentage would be left after 40 years?
    6·1 answer
  • To develop muscle tone, a woman lifts a 2.50 kg weight held in her hand. She uses her biceps muscle to flex the lower arm throug
    13·1 answer
  • You are camping in the breathtaking mountains if Colorado. You spy an unopened diet soda can floating motionless below the surfa
    7·1 answer
  • Niagara Falls is a set of very large waterfalls located on the border between New York and Ontario, Canada. Over 200,000 cubic f
    11·2 answers
  • 1. Where is the water in the pot going?
    12·1 answer
  • 3. What current is drawn by a 90 W light bulb on a 110 V household circuit?<br> Please answer!!!
    11·1 answer
  • 7. A 2.0 kg block, starting from rest, is pushed by a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!