All categories

3 years ago

Solve the equation for r C=(r+k)m

Mathematics

1 answer:

alexira [117]3 years ago

7 0

Answer:

r = c -km÷m

Step-by-step explanation:

C=( r+k) m (multiple the m with the letters in the brackets)

rm + km= c (cross the km over the equal sign and it will be a negative)

rm= c- km (then divide everything by my)

rm÷m = c - km÷ m

r = c- km÷ m

You might be interested in

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

3 years ago

Factor out the greatest common factor ?

Natasha_Volkova [10]

Answer:

wait im srry i didnt get the question wht grade u in?

8 0

2 years ago

Read 2 more answers

Here is a list of number 51 38 48 36 39 40 39 47 WHAT is the median

Nikitich [7]

Answer:

Step-by-step explanation:

Median is the Middle number in the sequence.

Hope this Helps!!

:D

5 0

2 years ago

Read 2 more answers

PLEASE HELP :)

Gnom [1K]

Answer:

Math can help us do many things that are important in our everyday lives. ... As a parent, you could talk to your teen about how you use math in your daily life. You ... Share with your child the examples of everyday math applications, which are listed ... Your teen will learn skills in algebra class that will help them with money.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please help me with this question. Please!

erica [24]

150=i^2
150^.5=12.2474
11^2=121
12^2=144
13^2=169
between 12 and 13, D

8 0

3 years ago