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2 years ago

25 Points:PLEASE HELP ASAP

Mathematics

1 answer:

alekssr [168]2 years ago

8 0

Answer:

I am sorry, what is your question? What do you <em>have </em>a question on?

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A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P dollars per year in a fund f

Andrews [41]

Answer:

$A = \frac{P}{r}\left( e^{rt} -1 \right)$

Step-by-step explanation:

This is <em>a separable differential equation</em>. Rearranging terms in the equation gives

$\frac{dA}{rA+P} = dt$

Integration on both sides gives

$\int \frac{dA}{rA+P} = \int dt$

where $c$ is a constant of integration.

The steps for solving the integral on the right hand side are presented below.

$\int \frac{dA}{rA+P} = \begin{vmatrix} rA+P = m \implies rdA = dm\end{vmatrix} \\\\\phantom{\int \frac{dA}{rA+P} } = \int \frac{1}{m} \frac{1}{r} \, dm \\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \int \frac{1}{m} \, dm\\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |m| + c \\\\&\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |rA+P| +c$

Therefore,

$\frac{1}{r} \ln |rA+P| = t+c$

Multiply both sides by $r.$

$\ln |rA+P| = rt+c_1, \quad c_1 := rc$

By taking exponents, we obtain

$e^{\ln |rA+P|} = e^{rt+c_1} \implies |rA+P| = e^{rt} \cdot e^{c_1} rA+P = Ce^{rt}, \quad C:= \pm e^{c_1}$

Isolate $A$ .

$rA+P = Ce^{rt} \implies rA = Ce^{rt} - P \implies A = \frac{C}{r}e^{rt} - \frac{P}{r}$

Since $A = 0$ when $t=0$ , we obtain an initial condition $A(0) = 0$ .

We can use it to find the numeric value of the constant $c$ .

Substituting $0$ for $A$ and $t$ in the equation gives

$0 = \frac{C}{r}e^{0} - \frac{P}{r} \implies \frac{P}{r} = \frac{C}{r} \implies C=P$

Therefore, the solution of the given differential equation is

$A = \frac{P}{r}e^{rt} - \frac{P}{r} = \frac{P}{r}\left( e^{rt} -1 \right)$

4 0

2 years ago

a baseball team played 147 regular season games. The ratio of the games they won to the number of games they lost was 2/5. How m

postnew [5]

Answer:

~59 games won, ~88 games lost

Step-by-step explanation:

I divided 147 by 5 to do a base unit. Then I multiplied by 2 for the amount won, then I multiplied by 3 for the amount lost. Hope this helps!

7 0

2 years ago

What is close to 3/4? is it 13/26, 11/32, 1/2, or 3/8

jonny [76]

Answer:

1/2 is the closest at .5

Step-by-step explanation:

13/26 is 1/2

3/8 is . 375

11/32 is .344

3 0

2 years ago

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The cost of 6 pounds of almonds is $23.28. What is the constant of proportionality that relates y, the cost in dollars, to x, th

solniwko [45]

Step-by-step explanation:

y = 23.28/6 x

y = 3.88 x

so, the constant of proportionality is 3.88

5 0

2 years ago

Harrizon [31]

Answer:

Step-by-step explanation:

The lowest common denominator for 1/2 and 1/4 is also the lowest common multiple of 2 and 4. Since 4 is a multiple of 2, 4 itself is the lowest common multiple.

1/4 would remain, and 1/2 would be written as 2/4.

8 0

2 years ago

Read 2 more answers