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2 years ago

28 POINTS SHOW WORK

Mathematics

1 answer:

lesantik [10]2 years ago

7 0

Answer:

at ten minutes it will be at 60.7 and at 12 minutes itll be at 57.7

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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)

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

From Ash To Sam This is yours

NARA [144]

Answer:

I'll bring Sam here

Step-by-step explanation:

#Nova

4 0

2 years ago

Which of the following describes the relationship between the area of a rectangle and its width, as width varies and length stay

sergejj [24]

I think the correct answer from the choices listed above is option C. The relationship between the area of a rectangle and its width, as width varies and length stays the same, would be that as width decreases, area decreases. Hope this answers the question. Have a nice day.

3 0

3 years ago

liubo4ka [24]

Answer:

3/5

Step-by-step explanation:

We are to find the similarity ratio of a cube with volume $729 m^3$ to a cube with volume $3375 m^3$ .

We know the formula for the ratio of two cubes:

$\frac{V_1}{V_2} =k^3$

where $k$ is the similarity ratio of the two cubes.

Substituting the given values in the formula to find $k$ :

$k^3 = \frac {729} {3375}$

$k^3 = \frac {27} {125}$

$k^3 = (\frac {27} {125})^3$

$k=\frac{3}{5}$

Therefore, the similarity ratio of the two cubes is 3/5.

8 0

3 years ago

Read 2 more answers

What is the equation of line with a slope m=-1/4 that passes through (2,0)

Reika [66]

If you use the equation y-y1=m(x-x1) it would give you y-0=-1/4(x-2) which you would then have to simplify into slope intercept from rather than point slope form.
you do this by using the distributive property on the -1/4(x-2) which would give you y=-1/4x+1/2

4 0

3 years ago