The feeder in the Example had 16 fl oz of food in it to start. How much food does it<br> have now?

The rate of change of the mass, A, of salt at time t is proportional to the square of the mass of salt present at time t. Initia

Brums [2.3K]

Answer:

(a) -dA/dt = kA², A₀ = 10

(b) A =10/(1+ kt)

(c) t > 60 h

Step-by-step explanation:

(a) Find the IVP

A differential equation with an initial condition y₀ = f(x₀) is called an initial value problem.

The rate of decrease of A is proportional to A², and A₀ = 10, so the IVP is

-dA/dt = kA², A₀ = 10

(b) Solve the IVP

$\begin{array}{rcl}-\dfrac{\text{d}A}{\text{d}t} & = & kA^{2}\\\\\dfrac{\text{d}A}{A^{2}} & =&-k\text{d}t\\\\-\dfrac{1}{A} & = & -kt + C\\\\\dfrac{1}{A} & = & kt + C\\\\\end{array}$

Apply the initial condition: A₀ = 10 (when t = 0)

$\dfrac{1}{10} = C\\\\\dfrac{1}{A} = kt + \dfrac{1}{10}\\\\\dfrac{10}{A} = 10kt + 1\\\\\mathbf{A} = \mathbf{\dfrac{10}{1+ kt}}$

(c) Find the time when A(t) < 1

(i) Find the value of k (A₁₀ = 4)

$\begin{array}{rcl}A& =&\dfrac{10}{1+ kt}\\\\4 & =& \dfrac{10}{1 + 10k}\\\\4 + 40 k & = & 10\\\\40k & = & 6\\k & = & 0.15\\\end{array}\\\\\mathbf{A} =\mathbf{ \dfrac{10}{0.15t + 1}}$

(ii) Find t when A < 1

$\begin{array}{rcl}A(t) & < & 1\\\dfrac{10}{0.15t + 1} & < & 1\\\\10 & < & 0.15t + 1\\9 & < & 0.15t\\t & > & 60\\\\\end{array}\\\mathbf{A < 1} \textbf{ when }\mathbf{ t >60}$

The figure below shows the graph of A vs t.

6 0

3 years ago

PLEASE HELP ME 40 PTS!!!!!!

SSSSS [86.1K]

Answer:

The sequence converges to infinity.

Step-by-step explanation:

$a_n = \frac{n^3 - n}{n^2 + 5n}\\\\ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{n^3 - n}{n^2 + 5n}$

$= \lim_{n \to \infty} \frac{n(n^2 - 1)}{n(n + 5)} \\\\= \lim_{n \to \infty} \frac{(n^2 - 1)}{(n + 5)}\\\\= \lim_{n \to \infty} \frac{n(n - \frac{1}{n})}{n(1 + \frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n - \frac{1}{n})}{(1 + \frac{5}{n})}$

$denominator = \lim_{n \to \infty} 1 + \frac{5}{n} = 1 + \lim_{n \to \infty} \frac{5}{n} = 1+0 = 1$

$numerator = \lim_{n \to \infty} n - \frac{1}{n} = \infty$

Therefore,

$\lim_{n \to \infty} a_n = \frac{ \infty}{1} = \infty$

8 0

3 years ago

Please help! Will mark brainliest

Gennadij [26K]

It’s the third one.

144. 6 x 6 = 36

36 x 8 = 288

288 divided by 2 ( divide by half the dotted line)

answer : 144

7 0

3 years ago

A sign in front of a roller coaster says "You must be 40 inches tall to ride."

Naya [18.7K]

Answer:

54/40 = 1.35 or 135%

Step-by-step explanation:

7 0

3 years ago

Jack earns 100$ on the first day, 60$ on the second day, 150$ on the third day, 80$ on the fourth day and 90$ on the fifth day.

madam [21]

To solve this you would add up all the money then divide it by the number of days the guy worked

100+60+150+80+90= 480

480÷5= 96

Jacks average earnings was 96 dollars per day

6 0

4 years ago

Read 2 more answers

The feeder in the Example had 16 fl oz of food in it to start. How much food does it have now?