Select All equivalent expressions to 4( x + 2)

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 a separable differential equation. 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

Chrissie thinks of a number. 30% of her number is 270. What is the number she is thinking of? Please help.

MrRissso [65]

Answer:

81

Step-by-step explanation:

hope it helps

3 0

1 year ago

2. A carpenter wants to cut a wood board that is feet long

belka [17]

Answer:

2 whole pieces

5/24 feet left

Step-by-step explanation:

divide 5/6 by 5/16 = 2 2/3 pieces

so there are 2 whole pieces and 2/3 small piece.

The 2/3 small short equals to 5/16 x 2/3 = 5/24 ft

8 0

2 years ago

Which inequality is true when G = 3/5 ?

GREYUIT [131]

Answer:

D. 15G > 9

Step-by-step explanation:

Given: G = 3/5

Here we have to check each options and find which is true.

Let's start from A.

G - 1 > 2/5

G > 2/5 + 1

G > 7/5 is not true.

B. -10G > 6

Dividing both sides by -10 , we get

G < -6/10

G < -3/5 Is not true.

C. 1 2/5 + G > 3

Now convert 1 2/5 to improper fraction.

1 2/5 = 7/5

7/5 + G > 3

G > 3 - 7/5

G > (15 - 7)/5

G > 8/5 is not rule.

D. 15G > 9

Dividing both sides by 15, we get

G > 9/15

Now we have to simplify 9/15

G > 3/5 which is true.

Answer: D. 15G > 9

Thank you.

4 0

3 years ago

Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by takin

m_a_m_a [10]

Answer:

1-

P(X=1) = 1/36

P(X=2) = 3/36 = 1/12

P(X=3) = 5/36

P(X=4) = 7/36

P(X=5) = 9/36 = ¼

P(X=6) = 11/36

2-

7/36

Step-by-step explanation:

1-

Attached, you will find a table with the possible values of X.

(See table attached)

As we can see, there are 36 entries so,

P(X=1) = 1/36

P(X=2) = 3/36 = 1/12

P(X=3) = 5/36

P(X=4) = 7/36

P(X=5) = 9/36 = ¼

P(X=6) = 11/36

2-

It can be noticed that the only possible value of X which is divisible by 4 is 4 and there are 7 entries in the table, so

P(X divisible by 4) = P(X=4) = 7/36

3 0

3 years ago