Evaluate the function at the specified value and simplify when possible.

Which property is illustrated by the following statement? 3x(-5)=(-5)3x

Marina86 [1]

That would be the commutative property

3 0

3 years ago

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

Determine the type and number of solutions of 6x^2-7x-4=0

Delicious77 [7]

I think it is C-two real solution

3 0

2 years ago

I need help with this question can someone please help me?

zlopas [31]

Answer: y= -1/1x - 1

Okay, to find the equation you must find the y-intercept and the slope.

To find the y-intercept, you must find (0,y). This is the point on the y-axis where x is 0. So, where along the y-axis is there a point? There is a point at (0,-1). Therefore, your y-intercept is -1.

To find the slope, you must do rise/run. Go to a point on the line, such as (0,-1). You must go up (or down) until you get lined up with next point on the line. You go up one time. Then, you must go right (or left) to get to the exact point. In this case, the point would be (-1,0). You go left one time.

If you go down or left when doing rise/run, the number would be negative. Since you went left, that number would be negative.

So, our slope would be 1/-1, which can also be written as -1/1.

Now, write the equation. There is always an x next to the slope. y= -1/1x

Then, put the y-intercept next to it. If it is positive, use a +. If it is negative, use a -. It is negative.

Therefore, the answer is y= -1/1x -1.

5 0

2 years ago

What does x = help please

Allisa [31]

Answer:

x= 90/4*2x

Step-by-step explanation:

4 0

2 years ago

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Evaluate the function at the specified value and simplify when possible.​

Evaluate the function at the specified value and simplify when possible.